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					Unit 1, Activity 1, Rational Number Line Cards - Student 1




                                      Grade 8
                                     Mathematics




Blackline Masters, Mathematics, Grade 8                      Page 1
Louisiana Comprehensive Curriculum, Revised 2008
Unit 1, Activity 1, Rational Number Line Cards - Student 1


Cut these cards apart. Each group of students should have one set of cards.




         1                       1                       3                      1
                                                                             
         2                       4                       4                      8

       3                         7                        1                    2
     
       8                         8                        3                    3

        5                         5                       1                     2
                                                                              
        6                         8                       5                     5

         3                      4                         1                     12
                                                                             
         5                      5                        10                     12

Blackline Masters, Mathematics, Grade 8                                         Page 1
Louisiana Comprehensive Curriculum, Revised 2008
Unit 1, Activity 1, Rational Number Line Cards - Student 2

Cut these cards apart. Each group of students should have one set of card.




   -0.50                     0.25                     0.75                   -0.125



  0.375 -0.875  0.333 0.66 6


  0.833 -0.625                                        0.20                   -0.40



    0.60                    -0.80                     0.10                   -1.00


Blackline Masters, Mathematics, Grade 8                                         Page 2
Louisiana Comprehensive Curriculum, Revised 2008
Unit 1, Activity 1, Rational Number

                                        Compare and Order


Name __________________________________ Date _________ Hour ____________

Place the following numbers in the most appropriate location along the number line.

                           3                            5      7    1  12            2
     0.1 , 0.05 , -0.5 ,     ,   -1 ,   1,   -3 ,   -     , 2,   , - ,    , 75% , -2
                           4                            3      8    2  12            6




                                                         0


Write 3 different inequalities using the numbers from the number line above using symbols <,
>, =, ≤, ≥. (example: -1 < 1)

1.


2.


3.

Write 2 repeating inequalities using the numbers from the number line above using the symbols.
<, >, =, ≤, ≥. (example: -1 ≤ 1 ≤ 2)

1.


2.




Blackline Masters, Mathematics, Grade 8                                               Page 3
Louisiana Comprehensive Curriculum, Revised 2008
Unit 1, Activity 1, Compare and Order Word Grid



                                     Compare and Order


Name __________________________________ Date _________ Hour ____________

Use the two numbers in column one and add, subtract, multiply or divide them according to the
heading. Determine whether or not the answer would result in a true statement.




                      sum > 1         difference < 1     product < sum          product <
                                                                                 quotient
    Example         2 ½ + -3 = - ½    2 ½ - (-3) = 5 ½   (5/2)(-3) = -15/2   5/2 ÷ - 3/1 = -5/6
                                                              =-7½
    2 ½ , -3             NO                 NO                 YES                  NO
       1 3
     1 ,
       2 4
      2, 1
          ,
      3 4
           1
      2,
           2
     5 7
        ,
     6 8

      1, 1




Blackline Masters, Mathematics, Grade 8                                                  Page 4
Louisiana Comprehensive Curriculum, Revised 2008
Unit 1, Activity 1, Compare and Order Word Grid with Answers

                                     Compare and Order


Use the two numbers in column one and add, subtract, multiply or divide them according to the
heading. Determine whether or not the answer would result in a true statement.




                      sum > 1         difference < 1     product < sum          product <
                                                                                 quotient
    Example         2 ½ + -3 = - ½    2 ½ - (-3) = 5 ½   (5/2)(-3) = -15/2   5/2 ÷ - 3/1 = -5/6
                                                              =-7½
    2 ½ , -3          NO                 NO                    YES               NO
       1 3         1½+¾=2¼             1½-¾=¾             1 ½ ( ¾ ) = 9/8      1½÷¾=2
     1 ,
       2 4                YES              YES                YES                 YES
      2, 1                11/12            5/12             24/12 = 2            2<2 2/3
          ,
      3 4                 NO               YES                 NO                  YES
           1              2½               1½                   1                  1<4
      2,
           2              YES               NO                YES                 YES
     5 7              1    17/24           -1/24         420/576 = 35/48      35/48 < 20/21
        ,
     6 8                  YES              YES                NO                   YES
                           2                0                 1<2                  1=1
      1, 1
                          YES              YES                 YES                  NO




Blackline Masters, Mathematics, Grade 8                                                  Page 5
Louisiana Comprehensive Curriculum, Revised 2008
    Unit 1, Activity 2, Grouping Dilemma


                                           Grouping Dilemma

    Name ____________________________________ Date _______ Hour ___________

    Circle or loop groups of tiles that will help determine the total number of tiles without counting
    each and every tile. Beneath each tile pattern, write a mathematical expression that represents
    the „looping‟ used to determine the number of tiles.




Expression to represent grouping          Expression to represent grouping        Expression to represent grouping
                              = 15                                      = 15                                     = 15




  Expression to represent grouping         Expression to represent grouping         Expression to represent grouping
                                = 15                                     = 15                                     = 15




 Expression to represent grouping        Expression to represent grouping           Expression to represent grouping
                              = 15                                      = 15                                     = 15




    Blackline Masters, Mathematics, Grade 8                                                   Page 6
    Louisiana Comprehensive Curriculum, Revised 2008
        Unit 1, Activity 2, Grouping Dilemma with answers

        Circle or loop groups of tiles that will help determine the total number of tiles without counting
        each and every tile. Beneath each tile pattern, write a mathematical expression that represents the
        „looping‟ used to determine the number of tiles.




Expression to represent grouping          Expression to represent grouping         Expression to represent grouping
        3 x 3 + 2 x 3= 15                         (3 x 4) + 3= 15                          (4 x 4)-1          = 15




 Expression to represent grouping           Expression to represent grouping         Expression to represent grouping
         4+4+4+3            = 15                    (2 x 3) + (2 x 3) + 3= 15                (2 x 4 – 1) + 2 x 4= 15




Expression to represent grouping          Expression to represent grouping         Expression to represent grouping
        (4 x 3) + 3= 15                           (6 x 2) + 4 -1= 15               (2 x 2) + (2 x 2) + (2 x 2) + 2 x 2 -1)= 15




        Blackline Masters, Mathematics, Grade 8                                                    Page 7
        Louisiana Comprehensive Curriculum, Revised 2008
Unit 1, Activity 5, Missing

                                           Missing

Name ____________________________________ Date _______ Hour ___________

      1. Samantha is 75 feet from the shore at 10 a.m. Every hour she moves forward 15 feet,
         and the current pulls her backward 6 feet. At this rate, what time will Samantha reach
         the shore? Explain your solution.

      2. There are six boys in a race. Carl is ahead of Bill who is two places behind Frank.
         Allen is two places ahead of Dwight, who is two places ahead of Evan, who is last.
         Which of the boys is closest to the finish line? Explain your solution.
                                                                                   11
      3. A group of students have gathered around the center
         circle of the basketball court. The students are evenly
         spaced around the circle. Student #11 is directly across
         from student #27. How many students have gathered
         around the circle? Explain your solution.                    3                           19



      How are the problems below different from the problems
      above?

      4. The world record high dive is 176 feet 10 inches. What is                 27

         the difference between Jack‟s highest dive and the world
         record?

      5. Mary wants to find the amount of carpet needed to carpet her bedroom. She measures
         the length of the room. How much carpet does she need to carpet the bedroom?

      6. Greg Louganis holds 17 U. S. national diving records. How many of these did he earn
         before the 1988 Olympics?




Blackline Masters, Mathematics, Grade 8                                              Page 8
Louisiana Comprehensive Curriculum, Revised 2008
Unit 1, Activity 5, Missing with Answers


       1. Samantha is 75 feet from the shore at 10 a.m. Every hour she moves forward 15 feet,
           and the current pulls her backward 6 feet. At this rate, what time will Samantha reach
           the shore? Explain your solution.
               Solution: 6:12 p.m.- since she gains about 9 feet every hour 75  9 = 8 hours plus
               three feet left. Set a proportion 15ft/3ft = 9 ft/x to find the part of an hour the 3
               feet would take. I came up with 1/5 of an hour and that is 12 minutes.
       2. There are six boys in a race. Carl is ahead of Bill who is two places behind Frank.
           Allen is two places ahead of Dwight, who is two places ahead of Evan. Evan is last.
           Which of the boys is closest to the finish line? Explain your solution.
               Solution: Carl is closest to the finish line. Carl is first, Allen second (two places
               ahead of Dwight), Frank is third(two places ahead of Bill), Dwight is fourth, Bill
               is fifth (two people behind Frank), and Evan last (two
                                                                                           11
               places behind Dwight.
       3. A group of students have gathered around the center
           circle of the basketball court. The students are evenly
           spaced around the circle. Student #11 is directly across
           from student #27. How many students have gathered                  3                        19

           around the circle? Explain your solution.
               Solution: 32 students. Sketch a model to get an idea
               as to positioning. There are 15 students between #11
               and #27 and the median from 12 to 26 is 19. The
               opposite side had to increase from 27 but also                              27

               decrease from 11 to 1. Listing these numbers and then
               finding the median gives me the opposite person. Listing the numbers also gives
               the number of people in the circle.)
Have the students examine problems like the ones below and discuss how these are different
from the earlier problems (They are missing information.).
        The world record high dive is 176 feet 10 inches. What is the difference between
           Jack‟s highest dive and the world record? We need to know the height of Jack’s dive.
        Mary wants to find the amount of carpet needed to carpet her bedroom. She measures
           the length of the room. How much carpet does she need to carpet the bedroom? She
           needs the width of the room.
        Greg Louganis holds 17 U. S. national diving records. How many of these did he earn
           before the 1988 Olympics? We need to know when he earned these 17 records.




Blackline Masters, Mathematics, Grade 8                                                  Page 9
Louisiana Comprehensive Curriculum, Revised 2008
Unit 1, Activity 6, Practice reading circle graphs


                               London, Paris, Rome or . . . ?

Name ____________________________________ Date _______ Hour ___________



      The pie graph below shows the total number of 200 vacationers who went to London,
      Rome, Paris, Madrid or other European countries. Study the graph and answer the
      questions.


                                                1. What number of vacationers chose London?
                                                Show your work.

       Paris          Rome
       25%            25%



   Madrid                                       2. What number of vacationers did not choose
   11%                                          Madrid?
                        London                  Show your work.
                        28%
        Other
        11%




      3. The vacationers who chose either London, Paris, or Rome would be closest to what
          fraction?

               1                    1                     3                           9
         a.                    b.                    c.                         d.
               2                    3                     4                          10



         4. A vacationer in Paris decided to buy an Eiffel Tower souvenir for $12.00. The store
            was having a 10% off sale. What is the total cost of the statue before tax? Show
            your work.




Blackline Masters, Mathematics, Grade 8                                              Page 10
Louisiana Comprehensive Curriculum, Revised 2008
Unit 1, Activity 7, Bull’s Eye Chart

                                      Bull’s Eye Chart

Name ____________________________________ Date _______ Hour ___________
1. Write an estimated answer for each of the problems in estimate column without a calculator.
2. Get with a partner and using your calculator, record the exact answers in the exact column
   for each of the problems.
3. Use your calculator to divide your estimate by the exact answer, and record the quotient in
   the estimate/exact column. Round your answers to the nearest hundredth.
4. To determine the number of points scored for each estimate, use the number line on the
   bottom of the Bull‟s Eye Target to find the point that most closely matches your quotient.
   Record your points on your chart

                                 Estimated       Exact answer Estimated ÷          Points
                                 answer                       Exact answer         scored
           4.872 x 3.127

            25.2 x 20.02

             0.62 x 0.57

            19.8 ÷ 1.52

            0.91 ÷ 12.13

           54.45 ÷ 14.79
                                                                  Total game 1
                                 Estimated      Exact answer Estimated ÷           Points
                                 answer                      Exact answer          scored
               2  1 
                8 
               5  4 
              9  5 
              3  
              10  7 
            1  3 
            9  6 
            5  4 
              9    2
                
             10    5
             8     3
                
            25     8
              3      1
          11  6
              5      2
                                                                  Total game 2



Blackline Masters, Mathematics, Grade 8                                            Page 11
Louisiana Comprehensive Curriculum, Revised 2008
Unit 1, Activity 7, Bull’s Eye Chart with Answers

                                      Bull’s Eye Chart
Possible answers are shown as an example for the first problem.
                             Estimated       Exact answer Estimated ÷       Points
                             answer                          Exact answer   scored
                               5 x 3 = 15      15.234744          .98         10
     4.872 x 3.127
                                               504.504
     25.2 x 20.02
                                                .3534
      0.62 x 0.57
                                            13.02631579
     19.8 ÷ 1.52
                                              .07502061
     0.91 ÷ 12.13
                                             3.681541582
    54.45 ÷ 14.79


                                                  Total game 1


                             Estimated      Exact answer Estimated ÷        Points
                             answer                      Exact answer       scored
      2       1                  60                3
         x8                         3          3             .91              5
      5       4                  20               10
          9 5                                     11
        3 x                                     2
         10 7                                     14
        1      3                                    1
      9 x6                                     62
        5      4                                   10
         9 2                                       1
                                                2
        10 5                                       4
         7 3                                        5
                                                 1
        12 8                                        9
         3    1                                   51
       11  6                                   1
         5    2                                   65
                                                                Total game 2




Blackline Masters, Mathematics, Grade 8                                         Page 12
Louisiana Comprehensive Curriculum, Revised 2008
 Unit 1, Activity 7, Bull’s Eye Target



                                 Bull’s Eye Target




                                         1 point




                                         2 points



                                          5 points




                                          10 points



0.8       0.85       0.9        0.95                  1.05   1.1   1.15       1.2
                                            1.0




 Blackline Masters, Mathematics, Grade 8                            Page 13
 Louisiana Comprehensive Curriculum, Revised 2008
Unit 1, Activity 9, How Much. . . About?


                                 How Much . . . About?


Name ____________________________________ Date _______ Hour ___________

SAMPLE SALE AD FOR STORE




                                                   Cap: Original Price: $18.75
                                                   now 25% off


    Sweater: Original Price: $22.95
    now 15% off




                                               Shoes: Now selling for
                                               $25.95 after a 30% discount



Jester‟s hat: now sells for $15.00
After receiving 1 off the original
                   4
price




Blackline Masters, Mathematics, Grade 8                                  Page 14
Louisiana Comprehensive Curriculum, Revised 2008
Unit 1, Activity 9, How Much. . . About? with answers



                                     How Much . . . About?

      Answer Key
      Sweater
      Estimate: 15% x $20 = $3
                $20 - $3 = $17

      Actual: 15% x $22.95 = $3.44
              $22.95 - $3.44 = $19.51

      With Tax: $19.51 x 7.5% = $1.46
                $19.51 + %1.46 = $20.97
      Cap
      Estimate: 25% x $20 = $5
                $20 - $5 = $15

      Actual: 25% x $18.75 = $4.69
              $18.75 - $4.69 = $14.06

      With Tax: 7.5% x $14.06 = $1.05
                  $14.06 + $1.05 = $15.11
      Jester’s Hat
      Estimate: ¾ x ___ = $15
                 ¾ ÷ ¾ x ___ = $15 ÷ ¾
                 ___ = $20
      * Since the new price reflects a ¼ discount, that means you are actually paying ¾
        of the original price.
      Actual: ¾ x ___ = $15
                 ¾ ÷ ¾ x ___ = $15 ÷ ¾
                 ___ = $20
       Check: ¼ x $20 = $5
               $20 – 5 = $15

      With Tax: 7.5% x $15 = $1.13
                $15 + $1.13 = $16.13
      Shoes
      Estimate: 70% x ___ = $30
                70% ÷ 70% x ___ = $30 ÷ 70%
                ___ = $40

      Actual: 70% x ___ = $25.95
               70% ÷ 70% x ___ = $25.95 ÷ 70%
                ___ = $37.07
      * Since the new price reflects a 30% discount, that means you are actually paying
        70% of the original price.
      With Tax: 7.5% x $25.95 = $1.95
                  $25.95 + $1.95 = $27.90



Blackline Masters, Mathematics, Grade 8                                                   Page 15
Louisiana Comprehensive Curriculum, Revised 2008
Unit 1, Activity 10, Order Cut Apart Cards

                                                   Cards for activity. Cut these apart




        1                    1                       7                           3
                           
        2                    2                      12

      3                    1.5                         1                         2
    
      4                                                3                         3

       1                 -.25                        7                    0.30
                                                  
       4                                             8
        5                     1                      1                           5
                                                   3
        8                     4                      6                           6
Blackline Masters, Mathematics, Grade 8                                            Page 16
Louisiana Comprehensive Curriculum, Revised 2008
 Unit 1, Activity 10, Order Recording Sheet


                                     Order Recording Sheet

 Name ____________________________________ Date _______ Hour ___________

 Use the following to record your equations. Be sure to use three different functions. Explain
 your strategy to your partner.




                                                                                    =

First term                                                                                Solution
(card 1)                                                                                  (card 2)



                                                                                    =

First term                                                                                Solution
(card 1)                                                                                  (card 2)
                                                                                    =

First term                                                                                Solution
(card 1)                                                                                  (card 2)


                                                                                    =

First term                                                                                Solution
(card 1)                                                                                  (card 2)

                                                                                    =

First term                                                                                Solution
(card 1)                                                                                  (card 2)


                                                                                    =

First term                                                                                Solution
(card 1)                                                                                  (card 2)




 Blackline Masters, Mathematics, Grade 8                                                Page 17
 Louisiana Comprehensive Curriculum, Revised 2008
Unit 1, Activity 12, My Dream House

                                      My Dream House

Budgeting your Income
      You work for a major company in ____(your city)_________ and your salary is $45,000
      a year. You get paid the first of every month. Your pay is equally distributed each month.
      Your employer must take 30% out of your check each month for taxes.

       You need to buy a home, a car and one big item.
       Your house payment cannot be over 25% of your take home pay.
       The down payment for your home must be 5%.
       Home interest rate is 6.5%.

       SALARY
       Yearly salary $45,000
       Monthly salary ______________________ (before taxes)
       Taxes taken out ____________________ (each month)
       Take home pay ___________________ (each month)

       HOME
       Cost of home ________________________________
       Down payment (5%) ______________________
       Cost of home after down payment ___________________________

       Interest (6.5%) for (# of)_____________years
       Total Interest_________________
       Cost of home with interest ________________________________________
       Monthly note ______________________
       Is your house payment over 25% of your take home salary? If it is, you may need to
       refigure your house note for a longer period of time or buy a cheaper house.
       *IF you need to refigure, leave the other one alone, and refigure here.

       REFIGURING YOUR HOME, if needed
       Cost of home_________________________
       Down payment (5%) ______________________
       Cost of home with down payment_______________________

       Interest (6.5%) for (# of)_____________years
       Total Interest _______________
       Monthly note_____________________

       What are some of the other expenses that you may encounter in a month?




Blackline Masters, Mathematics, Grade 8                                             Page 18
Louisiana Comprehensive Curriculum, Revised 2008
Unit 1, Activity 12, My Dream House

      Suppose you have some unexpected expenses, do you have enough monthly income to
      take care of these unexpected expenses? If not, you might need to refigure your expenses.




      Looking back at the house you have purchased, will it be possible for you to meet your
      all monthly bills with a car note of $200? Explain.




Blackline Masters, Mathematics, Grade 8                                            Page 19
Louisiana Comprehensive Curriculum, Revised 2008
Unit 1, Activity 12, My Dream House with Answers

                                      My Dream House


Budgeting your Income
      You work for a major company in ______(your city) ________and your salary is
      $45,000 a year. You get paid the first of every month. Your pay is equally distributed
      each month. Your employer must take 30% out of your check each month for taxes.

       You need to buy a home, a car and one big item.
       Your house payment cannot be over 25% of your take home pay.
       The down payment for your home must be 5%.
       Home interest rate is 6.5%.


       SALARY
       Yearly salary $45,000
       Monthly salary _______$3750_______________ (before taxes)
       Taxes taken out ____________30%________ (each month)
       Take home pay _______$2625____________ (each month)


       HOME
       Cost of home ________________________________
       Down payment (5%) ______________________
       Cost of home after down payment ___________________________

       Interest (6.5%) for (# of)_____________years
       Total Interest_________________
       Cost of home with interest ________________________________________
       Monthly note ______________________
       Is your house payment over 25% of your take home salary? If it is, you may need to
       refigure your house note for a longer period of time or buy a cheaper house.
       *IF you need to refigure, leave the other one alone, and refigure here.

       REFIGURING YOUR HOME, if needed
       Cost of home_________________________
       Down payment (5%) ______________________
       Cost of home with down payment_______________________

       Interest (6.5%) for (# of)_____________years
       Total Interest _______________
       Monthly note_____________________


       What are some of the other expenses that you may encounter in a month?



Blackline Masters, Mathematics, Grade 8                                             Page 20
Louisiana Comprehensive Curriculum, Revised 2008
Unit 1, Activity 12, My Dream House with Answers


      Suppose you have some unexpected expenses. Do you have enough monthly income to
      take care of these unexpected expenses? If not, you might need to refigure your expenses.



      Looking back at the house you have purchased, will it be possible for you to meet your
      all monthly bills with a car note of $200? Explain.




Blackline Masters, Mathematics, Grade 8                                            Page 21
Louisiana Comprehensive Curriculum, Revised 2008
Unit 1, Activity 12, My Dream House: Student Self Assessment Rubric

Name ________________________________ Date _____________ Hour ___________

Use this rubric to assess your project. Score yourself on each item listed. Staple all parts of the
project along with this rubric together, and turn in.

                                                       Student                   Teacher


House buying activity completed                        _______ (20 points)      __________

Salary completed                                       _______ (20 points)      __________

Refiguring of house (if needed)                        _______ (15 points) __________

Total monthly notes figured                            _______ (15 points)      __________

Explanation of your budget                             _______    (30 points) __________


Total Points                                           _______ (100 possible) _________


Grading Scale
      A = ________ points
      B = ________ points
      C = ________ points
      D = ________ points
      F = _________points




Blackline Masters, Mathematics, Grade 8                                                  Page 22
Louisiana Comprehensive Curriculum, Revised 2008
Unit 2, Activities 1 and 3, Percent Grid




Blackline Masters, Mathematics, Grade 8            Page 23
Louisiana Comprehensive Curriculum, Revised 2008
Unit 2, Activity 1, Practice with Percents

Name ___________________________________ Hour _____________ Date ____________

Solve the following percent problems. Make a diagram to show the solution.

   1. Sarah was practicing basketball with her younger sister. Her younger sister made three
      free throws out of the twenty-five that she tried. What percent of free throws did the
      younger sister make?




   2. Billy ran only eight of the 1760 yards in a mile during practice. He walked the remaining
      distance. What percent of the mile did Billy run?




   3. Billy‟s coach said if he wants to play football, he must run for 25% of the mile. How
      many feet should Billy be prepared to run?




   4. Jane calculated that she had made 150% of the cookie sales that she set for her goal. Her
      goal was to sell 45 dozen cookies. How many dozen cookies did she sell?




   5. Joe was going to pay for his Christmas chorus trip which cost $150. He lost $2 sometime
      during the day at school. He paid for most of his trip. What percent of the cost of the trip
      does he still need to pay?



Blackline Masters, Mathematics, Grade 8                                              Page 24
Louisiana Comprehensive Curriculum, Revised 2008
Unit 2, Activity 1, Practice with Percents with Answers

Name ___________________________________ Hour _____________ Date ____________

Solve the following percent problems. Make a diagram to show the solution

   1. Sarah was practicing basketball with her younger sister. Her younger sister made three
      free throws out of the twenty-five that she tried. What percent of free throws did the
      younger sister make?

                        12
              .3/25 =       = 12%
                        100

   2. Billy ran only eight of the 1760 yards in a mile during practice. He walked the remaining
      distance. What percent of the mile did Billy run?

         8
            = 0.45% He ran less than one-half of a percent of the mile.
       1760

   3. Billy‟s coach said if he wants to play football, he must run for 25% of the mile. How
      many feet should Billy be prepared to run?

          x     25
             
       5280 100
        5280( 25) = 100x
       132,000 = 100x
       x = 1320 feet

   4. Jane calculated that she had made 150% of the cookie sales that she set for her goal. Her
      goal was to sell 45 dozen cookies. How many dozen cookies did she sell?

         x 150
           
        45 100
       45(150) = 100x
       6750 = 100x
       x = 67.50 dozen

   5. Joe was going to pay for his Christmas chorus trip which cost $150. He lost $2 sometime
      during the day at school. He paid for most of his trip, what percent of the cost of the trip
      does he still need to pay?

         2     x
            
       150 100
       150x = 200
       x = 1.33%



Blackline Masters, Mathematics, Grade 8                                               Page 25
Louisiana Comprehensive Curriculum, Revised 2008
Unit 2, Activity 2, How Much Improvement?

Name ___________________________________ Date __________ Hour _________


   1. Use the chart to answer A – E.
  Pre       90 90 50 90 70               75    60    85    50    55    95 85      70    65    40
  Post      85 100 100 90 80             90    80    60    90    75   100 100     90    80    80
Student     A    B      C   D     E      F     G     H      I     J    K   L      M     N     O
   ID

      A. Did all students increase from the Pretest to the Post-test? Justify your answer with
         data.



      B. What percent of total students increased their test score?



      C. What percent decreased test scores?



      D. What was the percentage of increase or decrease for each student? (students A – O)



      E. Which student should be named most improved? Why?




      F. Suppose there is a student P and this student scores an 80% on the pretest and
         increases the score by 1 ½ % on the post-test. What did student P score on the post-
         test?



      G. Suppose student D showed a 2% decrease on the score of the post-test. What would
         have been student D‟s score on the post-test?




Blackline Masters, Mathematics, Grade 8                                             Page 26
Louisiana Comprehensive Curriculum, Revised 2008
Unit 2, Activity 2, How Much Improvement? with Answers

   1. Use the chart to answer A – E.
  Pre       90 90 50 90 70               75    60    85    50    55    95 85      70    65    40
  Post      85 100 100 90 80             90    80    60    90    75   100 100     90    80    80
Student     A    B      C   D     E      F     G     H      I     J    K   L      M     N     O
   ID

      H. Did all students increase from the Pretest to the Post-test? Justify your answer with
         data.
         No, Students A and H decreased from pre test to post test.

      I. What percent of total students increased their test score?
         About 88% of the class increased their score.

      J. What percent decreased test scores?
         About 12% decreased their scores.

      K. What was the percentage of increase or decrease for each student? (students A – O)
         Answers are estimates. A- 6% decrease; B –11% increase; C – 100% increase; D –
         0% growth or decrease; E 14% increase; F- 20% increase; G – 34% increase; H –
         30% decrease; I -80% increase; J – 36% increase; K – 5% increase; L – 18%
         increase; M – 29% increase; N – 23% increase; O – 100% increase

      L. Which student should be named most improved? Why?

          There are two students, C & O, who each had a 100% increase in their score, C was
          at 100%.

      M. Suppose there is a student P and this student scores an 80% on the pretest and
         increases the score by 1 ½ % on the post-test. What did student P score on the post-
         test?
         Student P would have made a score of 81.2%.

      N. Suppose student D showed a 2% decrease on the score of the post-test. What would
         have been student D‟s score on the post-test?
         Student D would have made a 88.2% on the post test if the score represented a 2%
         decrease.




Blackline Masters, Mathematics, Grade 8                                             Page 27
Louisiana Comprehensive Curriculum, Revised 2008
 Unit 2, Activity 4, Four’s a Winner Game Card


                            Four’s a Winner Game Card



          320 400 10 250 50 225
            90 20 270 100 150 15
          150 120 80 30 240 75
          180 60 25 200 5 125
            40 100 50 135 90 45
            75 10 360 20 60 300
 Paper clips go on one percent expression and one number in the list below. Solve
 the problem and place your marker on the game card above.

 Percent expressions – Place one paper clip over one of these expressions

     25% of                     25% increase                         25% decrease
     50% of                     50% increase                         50% decrease
 Numbers – Place one paper clip over one of these numbers.

20       40          60          80 100 120 160 180                               200


 Blackline Masters, Mathematics, Grade 8                                    Page 28
 Louisiana Comprehensive Curriculum, Revised 2008
Unit 2, Activity 5, The Better Buy



One potato chip costs $0.15




With your partner, choose at least two questions
that you would need answered before
determining whether or not the price of the
potato chip is reasonable.




Blackline Masters, Mathematics, Grade 8            Page 29
Louisiana Comprehensive Curriculum, Revised 2008
Unit 2, Activity 5, The Better Buy with Answers


One potato chip costs $0.15




With your partner, choose at least two questions
that you would need answered before
determining whether or not the price of the
potato chip is reasonable.
Possible questions (they will vary, depending
upon students):
Is one potato chip the same size as regular
potato chips?
How many chips come in one bag?




Blackline Masters, Mathematics, Grade 8            Page 30
Louisiana Comprehensive Curriculum, Revised 2008
Unit 2, Activity 5, Choose the Better Buy?

Name _____________________________________ Date _____________ Hour __________

Choose the better buy



                                1. Soda at Store A sells for $3.59 for six and at Store B the
                                   soda sells 12 for $7.15. Which is the better buy? Show
                                   your thinking.




          2. Candy bars are selling at Store A 10 for $5.50. At Store B the
             same candy bars are 5 for $2.30. Which is the better buy? Show
             your thinking.




                        3. Store A decides to sell socks in a package of 12 for $17.25.
                           Store B puts the same socks on sale for $1.40/pair. Which
                                   is the better buy? Show your thinking.




          4. Justin found a CD player at Store A for $79.98 and he gets a 30%
             discount off the price. At Store B, the CD player is marked
             $55.00. Which is the better buy? Why?




Blackline Masters, Mathematics, Grade 8                                             Page 31
Louisiana Comprehensive Curriculum, Revised 2008
Unit 2, Activity 5, Choose the Better Buy? with Answers

Choose the better buy



                                1. Soda at Store A sells for $3.59 for six and at Store B the
                                   soda sells 12 for $7.15. Which is the better buy? Show
                                   your thinking.


                                   At store A the unit price for one soda is $.60 (.595833) and
                                   store B the price would also be $.60 (.5983333) because
                                   the money is always rounded to the hundredths there would
                                   be no better buy.


          2. Candy bars are selling at Store A 10 for $5.50. At Store B the
             same candy bars are 5 for $2.30. Which is the better buy? Show
             your thinking.

             Store B has a unit price of $.46 per candy bars and Store A has a unit price of
             $.55. Store B has the better buy.


                               3. Store A decides to sell socks in a package of 12 for $17.25.
                                  Store B puts the same socks on sale for $1.40/pair. Which
                                  is the better buy? Show your thinking.

                               Store B has the better buy because the unit price for socks at
                              store A is $1.44/pair.


          4. Justin found a CD player at Store A for $79.98 and he gets a 30%
             discount off the price. At Store B, the CD player is marked
             $55.00. Which is the better buy? Why?

                    With the 30% discount off of $79.98 the sale price would be $55.99, so
                    Store B is the better buy at $55.00.




Blackline Masters, Mathematics, Grade 8                                             Page 32
Louisiana Comprehensive Curriculum, Revised 2008
Unit 2, Activity 6, Refreshing Dance

Name____________________________________ Date __________ Hour ________

Use the data in the chart below to determine the total cost of getting the concession stand ready
for the Friday night dance if there are 200 students predicted to attend.

     Item           Cost per unit         Amount            Price       Amount        Total cost
                                         needed per          per        needed         of item
                                          student          student                       (200
                                                                                      students)
    Soda            $1.19/2-liter          50 mL
                        soda


   Candy           $8.99/box of             1 bar
    bars             36 bars


 Popcorn             $1.19/bag             1 quart
                    which pops
                      about 5
                     gallons of
                      popcorn
    Pizza           $5.00/pizza            1 slice
                   divided into 8
                    equal slices


            1. If 250 students attend the dance and every student in attendance orders a slice of
               pizza, how many extra pizzas must be ordered?




            2. If there are only 150 students who want to purchase a box of popcorn, how much
               profit would be made if every box sells for $0.75?




Blackline Masters, Mathematics, Grade 8                                                Page 33
Louisiana Comprehensive Curriculum, Revised 2008
Unit 2, Activity 6, Refreshing Dance with Answers

Use the data in the chart below to determine the total cost of getting the concession stand ready
for the Friday night dance if there are 200 students predicted to attend.

     Item           Cost per unit            Amount         Price         Amount          Total cost
                                            needed per       per          needed           of item
                                             student       student                           (200
                                                                                          students)
     Soda            $1.19/2 liter soda        50 mL      $.03/student   10 2L bottles       $5.95


   Candy bars       $8.99/box of 36 bars       1 bar      $.25/student   must buy the
                                                                         6th box to get     $53.94
                                                                           200 bars
    Popcorn            $1.19/bag which        1 quart     $.06/student   Need 10 bags       $11.90
                    pops about 5 gallons
                          of popcorn
     Pizza           $5.00/pizza divided       1 slice    $.63/student   Need 25 pizzas      $125
                      into 8 equal slices




             1. If 250 students attend the dance and every student in attendance orders a slice of
                pizza, how many extra pizzas must be ordered?
                Must order 7 more pizzas because 8 is not a factor of 50.

             2. If there are only 150 students who want to purchase a box of popcorn, how much
                profit would be made if every box sells for $0.75?
                150 x $.06 = $9.00 to purchase the popcorn and if this sells for $.75/box, 150 x
                .75 = $112.50 therefore, 112.50 – 9.00 = $103.50 profit




Blackline Masters, Mathematics, Grade 8                                                   Page 34
Louisiana Comprehensive Curriculum, Revised 2008
Unit 2, Activity 7, My Future Salary


Wages and Benefits: Value of the Minimum Wage (1960-Current)

           Value of the Minimum Wage
                     1960-2003

               Min                            Min
       Min                            Min
              wage                           wage
       wage                           wage
Year          (Real            Year          (Real
     (Current                       (Current
              2003                           2003
        $)                             $)
                $)                             $)
1960 1.00      5.26            1982 3.35      6.11
1961 1.15      5.99            1983 3.35      5.87
1962 1.15      5.94            1984 3.35      5.64
1963 1.25      6.37            1985 3.35      5.46
1964 1.25      6.28            1986 3.35      5.39
1965 1.25      6.19            1987 3.35      5.19
1966 1.25      6.01            1988 3.35      5.01
1967 1.40      6.53            1989 3.35      4.80
1968 1.60      7.18            1990 3.80      5.19
1969 1.60      6.88            1991 4.25      5.60
1970 1.60      6.56            1992 4.25      5.46
1971 1.60      6.29            1993 4.25      5.33
1972 1.60      6.10            1994 4.25      5.22
1973 1.60      5.74            1995 4.25      5.09
1974 2.00      6.53            1996 4.75      5.54
1975 2.10      6.33            1997 5.15      5.89
1976 2.30      6.56            1998 5.15      5.80
1977 2.30      6.16            1999 5.15      5.68
1978 2.65      6.81            2000 5.15      5.50
1979 2.90      6.81            2001 5.15      5.35
1980 3.10      6.55            2002 5.15      5.27
1981 3.35      6.48            2003 5.15      5.15


Source: Economic Policy Institute




Blackline Masters, Mathematics, Grade 8                        Page 35
Louisiana Comprehensive Curriculum, Revised 2008
Unit 2, Activity 7, My Future Salary with Answers



                                          Minimum wage through the years


                  $7.00




                  $6.00




                  $5.00
                                                                                  x
     Amount
     of minimum
     wage                                                                  x
                  $4.00
                                                                     x

                                                              x
                  $3.00
                                                         x




                  $2.00
                                                 x

                                           x

                                    x
                  $1.00        x


                             1960         1970         1980         1990         2000
                                    '65          '75          '85          '95

                                                       Year




Blackline Masters, Mathematics, Grade 8                                                 Page 36
Louisiana Comprehensive Curriculum, Revised 2008
 Unit 2, Activity 9, Proportional Reasoning


 Name _______________________________ Date ___________ Hour _______

                                                              Proportional Reasoning
 1. Work in groups of four. You will need a yard stick that will be used to set up a proportion
    using shadows, a measuring tape, and two small objects to serve as markers.

 2. Mark a spot on the ground. Have group Member A stand at the marked spot and have
    Member B sit or kneel next to Member A. Person B should hold a yard stick perpendicular to
    the ground so that the shadow of the yard stick can be seen. Member C will mark the point at
    the end of the shadow of the Member A using one marker. Member D should mark the
    shadow at the end of the yard stick. See diagram below.




Person A
                                                                                 person A height                        36 inches
                                                                                                         =
                                                                           Length of Person A's shadow         length of yar dstick shadow
                                         yardstick




            Person A shadow                       yardstick shadow
           Distance to measure                   Distance to measure




                      Point on ground that should be mar ked by member C



 3. Find the lengths of the shadows and complete the chart below.

                 Height of            Shadow of                Ratio                    Decimal              Length of
                 group                member A                                          equivalent of        yard
                                                               height of person
                 member               (measure                 Shadow
                                                                                        height/shadow        stick’s
                 A                    to the ¼                                          ratio (nearest       shadow
                                      inch)                                             hundredth) use
                                                                                        a calculator




           5. Discuss in your group how you might be able to use the ratio to find the actual height
              of a tree that leaves a 17 foot shadow at the same time of the day that you measured
              the objects. Be ready to share your group‟s ideas in about 10 minutes.



 Blackline Masters, Mathematics, Grade 8                                                                                    Page 37
 Louisiana Comprehensive Curriculum, Revised 2008
Unit 2, Activity 10, Scaling the Trail

Name ________________________________ Date __________ Hour ____________

      1. The drawing below represents a hiking trail through the forest. For problems 1 – 4,
         use the drawing and a ruler to find the actual distances of the following.


 Scale
 2 inches = 5 miles                                 1) A to B

     C                       E
                                                    2) B to C
                        D


                                                    3) C to D



                                                    4) Total length of the trail
           A                       B


                                                       1
          5) The forest rangers asked that we add 1        miles to the hiking trail from point A.
                                                       4
               Use your ruler to sketch a possible path that will lead the hiker closest to point C
               (be sure to use the correct scale). Label the end of your path point F. The rangers
               need to know the shortest distance from the new beginning point F to the end
               point E of the trail for emergencies. Find the shortest actual distance from point F
               to point E and record the distance on the diagram above




Blackline Masters, Mathematics, Grade 8                                                Page 38
Louisiana Comprehensive Curriculum, Revised 2008
Unit 2, Activity 10, Scaling the Trail with Answers

    The drawing below represents a hiking trail through the forest. For problems 1 – 4, use the
    drawing and a ruler to find the actual distances of the following.


                                     1. A to B
                                     A to B is 1.5 inches which would represent 3.75 miles
Scale
2 inches = 5 miles                       2. B to C
                                     B to C is 2 3/8 inches which would represent about 5.9 miles
C                        E
                                         3. C to D
                                     C to D is 7/8 of an inch which would represent about 2.2 miles
    F                D
                                         4. Total length of the trail
                                     D to E is 7/16 of an inch and when all distances are added,
                                     the sum is 5.1875 inches or 5 3/16 inches which represents
                                     about 12.97 miles


                                                                                       1
                                         5. The forest rangers asked that we add 1        miles to the
        A                     B                                                        4
                                             hiking trail from point A. Use your ruler to sketch a
         possible path that will lead the hiker closest to point C (be sure to use the correct scale).
         Label the end of your path point F. The rangers need to know the shortest distance from
         the beginning point to the end point of the trail for emergencies. Find the shortest actual
         distance from point F to point E, and record the distance on the diagram above. It is 1.5
         inches from point F to point E representing 3.75 miles




Blackline Masters, Mathematics, Grade 8                                                   Page 39
Louisiana Comprehensive Curriculum, Revised 2008
Unit 2, Activity 11, How Many Outfits are on Sale?

Sketch a diagram to illustrate the different outfits that could be made from the clothing items
below. The outfits must include pants (skirt), shirt, and shoes. Determine which of the outfits
would cost the least and show your mathematical thinking.




     $11.50                    $17.90                   $22.75                  $30.99




 $20.89                    $15.00                    $24.30




      $19.50                   $18.25                  $9.99                        $13.80




Blackline Masters, Mathematics, Grade 8                                               Page 40
Louisiana Comprehensive Curriculum, Revised 2008
Unit 2, Activity 11, How Many Outfits are on Sale? with Answers




     $11.50                    $17.90                   $22.75                  $30.99




  $20.89                   $15.00                   $24.30




       $19.50                  $18.25                  $9.99                        $13.80


      There are 4 x 3 x 4 = 48 different combinations of shirt, shorts and shoes. The least
      expensive combination would be $11.50 + $15.00 + $9.99 = $36.49




Blackline Masters, Mathematics, Grade 8                                             Page 41
Louisiana Comprehensive Curriculum, Revised 2008
Unit 2, Activity 13, Tour Cost

      Name ____________________________________ Date _____________ Hour ____

      Read the following problem and work with your group members to complete the problem
      using a tree diagram. You will present your information to the class as you justify your
      solution.

      The choir has just won a superior rating and has been asked to perform in San Diego, CA;
      New Orleans, LA; Atlanta, GA; and New York City, NY. The company that is going to
      fund the trip has asked that the choir visit just three of the cities. The choir must decide
      the order of the cities that they will visit. The director told the group that they must allow
      for the 300 miles to get to New Orleans.

             a. Determine the different tour possibilities and the total cost of each tour if the
                funding company plans to spend about $8.90/mile.




      This problem involves only travel expenses. The distances between the cities compare as
      follows: New Orleans to Atlanta is about 500 miles; New Orleans to New York is about
      1250 miles; New Orleans to San Diego is about 1750 miles; New York to Atlanta is
      about 900 miles; New York to San Diego is about 3000 miles; San Diego to Atlanta is
      about 2250 miles.

             b. The funding company needs to know the order of the cities they will be
                touring.



             c. Use a graphic organizer and draw a tree diagram to determine the different
                routes. Remember that the group must start and end in New Orleans.



             d. Explain how you determined your answer. Research costs of plane fare, bus
                fare and train fare.



             e. Determine which of the methods of transportation will be acceptable to the
                sponsors.



             f. Prepare a presentation to justify your route and cost of the trip to the class.


Blackline Masters, Mathematics, Grade 8                                                Page 42
Louisiana Comprehensive Curriculum, Revised 2008
Unit 2, Activity 13, Tour Cost with Answers

      The choir has just won a superior rating and has been asked to perform in San Diego, CA;
      New Orleans, LA; Atlanta, GA; and New York City, NY. The company that is going to
      fund the trip has asked that the choir visit just three of the cities. The choir must decide
      the order of the cities that they will visit. The director told the group that they must allow
      for the 300 miles to get to New Orleans.

          a. Determine the different tour possibilities and the total cost of each tour if the
             funding company plans to spend about $8.90/mile.

             NO, Atlanta, SD,
             NO, Atlanta, NYC,
             NO SD, NYC
             NO SD, Atlanta,
             NO, NYC, Atlanta,
             NO, NYC, SD,

      This problem involves only travel expenses. The distances between the cities compare as
      follows: New Orleans to Atlanta is about 500 miles; New Orleans to New York is about
      1250 miles; New Orleans to San Diego is about 1750 miles; New York to Atlanta is
      about 900 miles; New York to San Diego is about 3000 miles; San Diego to Atlanta is
      about 2250 miles.

          b. The funding company needs to know the order of the cities they will be touring.
                                                                                                  Atlanta
          Atlanta, NYC, NO (either beginning or ending with the                      NYC
          concert in NO)                                                                          San Diego




          c. Use a graphic organizer and draw a tree diagram to                                   San Diego

             determine the different routes. Remember that the           New         Atlanta
                                                                         Orleans                  NYC
             group must start and end in New Orleans.
                                                                                                   NYC

                                                                                   San Diego
          d. Explain how you determined your answer. Research                                      Atlanta

             costs of plane fare, bus fare and train fare.

          Just use the cost given per mile which would be 2950 miles x $8.90 = $26,255.

          e. Determine which of the methods of transportation will be acceptable to the
             sponsors.

          Answers will vary

          f. Prepare a presentation to justify your route and cost of the trip to the class.




Blackline Masters, Mathematics, Grade 8                                                        Page 43
Louisiana Comprehensive Curriculum, Revised 2008
Unit 3, Activity 1, One Inch Grid




Blackline Masters, Mathematics, Grade 8            Page 44
Louisiana Comprehensive Curriculum, Revised 2008
Unit 3, Activity 1, Index Card Shapes

Shapes to use:


  A                                     B
                                            F
                                                            1.5"


                                                            E

                                                            1.5"
  D                                  C      G


          2"     L           M     1"
                                                                 H




      K                            N               2"   J        R




Blackline Masters, Mathematics, Grade 8                         Page 45
Louisiana Comprehensive Curriculum, Revised 2008
Unit 3, Activity 1, ¼ Inch Grid




Blackline Masters, Mathematics, Grade 8            Page 46
Louisiana Comprehensive Curriculum, Revised 2008
Unit 3, Activity 1, Transformations

Name __________________________________ Date ________________ Hour ___________

Give the coordinates of the vertices of the figure in its original position, and then give the
coordinates of the new vertices based on stated transformation. The rotation is 90°clockwise
about the origin. The reflection is across the y-axis.


     Shape              Original           Translate             Rotate          Reflect across
                        Position                                                     y-axis

   Rectangle            A( 2 , 3 )          A( , )              A(    , )           A(   , )
                        B( 2 , 6 )          B( 2 ,-4)           B(   , )            B(   , )
                        C( , )              C( , )              C(    , )           C(    , )
                        D( , )              D( , )              D(   , )            D(   , )

Right Triangle          H( 0 , 3 )          H( , )              H( , )             H( , )
                        R( 0 , 0 )          R(2 , -4)           R( , )             R( , )
                        J( , )              J( , )              J( , )             J( , )


   Isosceles           E(4, -3.5)           E( , )              E( , )              E( , )
   Triangle            F( , )               F( , )              F( , )              F( , )
                       G(-1, -5)            G(-1, -3)           G( , )              G( , )


   Trapezoid            K( , )              K( , )              K(    ,    )        K(    ,      )
                        L( 6 , -1)          L( , )              L(    ,    )        L(    ,      )
                        M( 8, -1)           M( , )              M(     ,   )        M(     ,     )
                        N( , )              N(-1 , -1)          N(    ,    )        N(    ,      )




Blackline Masters, Mathematics, Grade 8                                               Page 47
Louisiana Comprehensive Curriculum, Revised 2008
Unit 3, Activity 1, Transformations with Answers

    Shape            Original          Translate     Rotate       Reflect across
                     Position                                         y-axis

  Rectangle          A( 2 , 3 )        A(2 ,-7)     A(3 , -2 )      A(-2, 3 )
                     B( 2 , 6 )        B( 2 ,-4 )   B(6 , -2)       B(-2 , 6 )
                     C( 7 , 6 )        C( 7 ,-4 )   C(6 , -7)       C(-7 ,6 )
                     D( 7 ,3 )         D(7 , -7 )   D(3 , -7 )      D(-7 , 3 )

Right Triangle       H( 0 , 3 )        H(2 , -1 )    H(3 , 0)       H( 0, 3)
                     R( 0 , 0 )        R(2 , -4 )    R(0 ,0)        R(0 , 0 )
                     J(-3 , 0 )        J(-1 ,-4 )    J( 0 ,3 )      J( 3 , 0 )


   Isosceles         E(4, -3.5)       E(4 ,-1.5 )   E(-3.5 ,4 )    E(-4 , -3.5 )
   Triangle          F(-1 ,-2)         F(-1 ,0 )     F(2 , 1 )      F( 1 , -2 )
                     G(-1, -5)         G(-1, -3)     G(5 ,1 )       G(1 ,-5 )


  Trapezoid          K(4 , -4 )        K(-6 ,-1 )   K(-4 ,-4)       K(-4 ,-4 )
                     L( 6 , -1)        L(-4 , 2 )   L( -1, -6)      L( -6 ,-1)
                     M( 8, -1)         M(-2 ,2 )    M(-1 ,-8)       M(-8 ,-1)
                     N(9 , -4 )        N(-1 , -1)   N(-4, -9 )      N( -9, -4)




Blackline Masters, Mathematics, Grade 8                               Page 48
Louisiana Comprehensive Curriculum, Revised 2008
Unit 3, Activity 1, Transformation Review

Name __________________________________ Date ____________ Hour __________

Fill in the ‘bridge maps’ below to illustrate the resulting changes in the coordinates of polygons
in the transformation explained.

Example


                             A polygon is reflected
                             across y axis                          e
                                                                  th result
                                                                  is




   1.

                       a polygon reflection
                       across the x axis
                                                     the result
                                                     is




   2.
                                                                        The coordinates switch (x,
                                                                        y) becomes (-y, x)
                                                   the result
                                                   is




   3.

          with a translation down 2 and to the right 1
                                                         the result
                                                         is




   4.
                                                                        a polygon in quadrant 4
                                                     the result
                                                     is




                     A reflection across the
                     x-axis of a triangle
                     with point A located at        e
                                                  th result
                                                  is
                     (-1, 3)




Blackline Masters, Mathematics, Grade 8                                                              Page 49
Louisiana Comprehensive Curriculum, Revised 2008
Unit 3, Activity 1, Transformation Review with Answers


Fill in the ‘bridge maps’ below to illustrate the resulting changes in the coordinates of polygons
in the transformation explained.

Example:


                             A polygon is reflected across                              The opposite x value and
                             y axis                                th result
                                                                   is
                                                                     e                  the same y value


   1.

                               a polygon reflection across                              The same x value and the
                               the x axis                    th result
                                                               e
                                                                                        opposite y value.
                                                             is




   2.

                          With a 90 clockwise                                          The coordinates switch (x, y)
                          rotation about the origin                                     becomes (-y, x)
                                                             e
                                                           th result
                                                           is




   3.
                                                                                        The x value increases by 1
           with a translation down 2 and to the right 1                                 The y value decreases by 2
                                                             e
                                                           th result
                                                           is




   4. The answer below is only one possible solution. For example, a polygon in quadrant 1
      might have been reflected across the x-axis and end up in quadrant 1.

                   A polygon is rotated 180
                   about the origin from                                       a polygon in quadrant 4
                   quadrant 2                            e
                                                       th result
                                                       is




   5.


                     A reflection across the x-                                 The new coordinates will be
                     axis of a triangle with point A                            (-1, -3)
                     located at (-1, 3)                    e
                                                         th result
                                                         is




Blackline Masters, Mathematics, Grade 8                                                                                 Page 50
Louisiana Comprehensive Curriculum, Revised 2008
Unit 3, Activity 2, Dilations


Name ___________________________________ Date ___________________ Hour ______

      1. Plot the following points on the grid paper showing only quadrant I.
         A(4,16), B(8.16), C(12, 14), D(10,10) and E(6,10).
      2. Find the measure of each of the angles.
          a) m A
          b) m B
          c) m C
          d) m D
          e) m E
      3. Use a ruler and find the length of each side of the polygon.
          a) Length of AB
          b) Length of BC
          c) Length of CD
          d) Length of DE
          e) Length of EA
      4. Draw a dotted line from the origin through each of the five vertices of the polygon
          (i.e. you will have five dotted lines extending from the origin of the graph through the
          vertices of your polygon).
      5. You will plot a new polygon on your grid by doubling the length of each side of the
          original polygon. To do this, double the coordinates for x and y and plot the new
          point. How does the placement of the new point relate to the dotted lines you drew in
          step 4?
      6. Connect the points to form your new polygon. Measure the angle lengths.
          a) m A‟
          b) m B‟
          c) m C‟
          d) m D‟
          e) m E‟
      7. Measure the side lengths of your dilation (enlargement).
          a) Length of A' B'
          b) Length of B'C '
          c) Length of C ' D'
          d) Length of D' E '
          e) Length of E ' A'
      8. Dilate the original polygon by a scale factor of ½. Name points A‟‟, B‟‟, C‟‟, D‟‟, E‟‟
      9. How are the angles of a figure affected by a dilation? What is the relationship
          between the scale used for the dilation and the lengths of corresponding sides of an
          original to figure created by using dilation?
      10. Using the lines and the conjectures that you have developed, determine the new
          coordinates of ABCDE if it were dilated by a scale factor of 1 ½ without graphing the
          points. Will it fit on the grid? Why or why not?


Blackline Masters, Mathematics, Grade 8                                              Page 51
Louisiana Comprehensive Curriculum, Revised 2008
    Unit 3, Activity 2, Quadrant I Grid


    Name _________________________________ Date ______________ Hour ____________

y




                                                                                   x


    Blackline Masters, Mathematics, Grade 8                              Page 52
    Louisiana Comprehensive Curriculum, Revised 2008
Unit 3, Activity 5, The Theorem


Name ___________________________________ Date _______________ Hour ________

Work with your partner to complete these problems. Make scale drawings of the figures in
problems 1 – 3, and label sides of the right triangle that is being used to solve the problem.
Problem 4 has a diagram already drawn for you.

   1. James has a circular trampoline with a diameter of 16 feet. Will this trampoline fit
      through a doorway that is 10 feet high and 6 feet wide? Explain your answer.




   2. A carpenter measured the length of a rectangular table top he was building to be 26
      inches, the width to be 12 inches, and the diagonal to be 30 inches. Explain whether or
      not the carpenter can use this information to determine if the corners of the tabletop are
      right angles.




   3. For safety reasons, the base of a ladder that is 24 feet tall should be at least 8 feet from
      the wall. What is the highest distance that the 24 foot ladder can safely rest on the wall?
      Explain your thinking.




                                                        boards are 4 inches wide



   4. The wall of a closet in a new house is
      braced with a corner brace. The wall
      of the closet has three boards placed
      16 inches apart, and this corner brace
      becomes the diagonal of the rectangle
      formed. How long will the brace
      need to be for the frame at the right?




Blackline Masters, Mathematics, Grade 8                                                 Page 53
Louisiana Comprehensive Curriculum, Revised 2008
Unit 3, Activity 7, 2 cm Grid




Blackline Masters, Mathematics, Grade 8            Page 54
Louisiana Comprehensive Curriculum, Revised 2008
Unit 3, Activity 8, Rectangular Prism




Blackline Masters, Mathematics, Grade 8            Page 55
Louisiana Comprehensive Curriculum, Revised 2008
Unit 3, Activity 8, Triangular Prism




Blackline Masters, Mathematics, Grade 8            Page 56
Louisiana Comprehensive Curriculum, Revised 2008
Unit 3, Activity 8, Right Triangular Prism




Blackline Masters, Mathematics, Grade 8            Page 57
Louisiana Comprehensive Curriculum, Revised 2008
Unit 3, Activity 12, Scale Drawings



Name __________________________________ Date ______________ Hour _______

Complete each of the following situations:

   1. Sandy was given the assignment during a summer job to draw a map from the city
      recreational complex to the high school. Sandy started from the recreational complex and
      walked north 3.5 miles, west 10 miles, north 5.3 miles, and then east 3 miles. Sandy was
      given a space 3 1 inches x 4 inches to sketch the route on a brochure being made by the
                       2
      staff at the complex. Determine a scale that Sandy will be able to use and draw a map that
      can be used in the space provided. Explain how the scale was determined.




   2. Draw a diagram of a rectangular bedroom with dimensions of 24 feet by 15 feet. Use a
      scale of 1 inch = 6 feet.
               2




   3. The picture of the amoeba at the right shows a width of 2 centimeters. If
      the actual amoeba‟s length is 0.005 millimeter, what is the scale of the
      drawing?



Blackline Masters, Mathematics, Grade 8                                             Page 58
Louisiana Comprehensive Curriculum, Revised 2008
Unit 3, Activity 12, Scale Drawings with Answers

Complete each of the following situations:

   1. Sandy was given the assignment during a summer job to draw a map from the city
      recreational complex to the high school. Sandy started from the recreational complex and
      walked north 3.5 miles, west 10 miles, north 5.3 miles, and then east 3 miles. Sandy was
      given a space 3 1 inches x 4 inches to sketch the route on a brochure being made by the
                       2
      staff at the complex. Determine a scale that Sandy will be able to use and draw a map that
      can be used in the space provided. Explain how the scale was determined.

                      North 3.5 miles + 5.3 miles = 8 . 8 miles
                      West 10 miles and east 3 miles so she needs to show 10 miles east-west.

                      If 1 inch represents 3 miles then the map can be centered on the brochure,
                      with margins between ¾ and 1 inch. If 1 inch represents 2.75 miles, then
                      there will be a margin of about ½ inch around the map.

   2. Draw a diagram of a rectangular bedroom with dimensions of 24 feet by 15 feet. Use a
      scale of 1 inch = 6 feet.
               2
                          2 inches


           1 ¼ inch




   3. The picture of the amoeba at the right shows a width of 2 centimeters. If the actual
      amoeba‟s length is 0.005 millimeter, what is the scale of the
      drawing?

              1 cm represents 200 mm




Blackline Masters, Mathematics, Grade 8                                              Page 59
Louisiana Comprehensive Curriculum, Revised 2008
Unit 4, Activity 1, Volume and Surface Area


Name ________________________________ Date __________________ Hour ____________


                                Exploring Volume and Surface Area


# cubes used   Length of          Width of         Height of        Volume of       Surface Area
for model      rectangular        rectangular      rectangular      rectangular     of rectangular
               prism built        prism built      prism built      prism built     prism built
               (linear units)     (linear units)   (linear units)   (cubic units)   (square units)

     16




Blackline Masters, Mathematics, Grade 8                                              Page 60
Louisiana Comprehensive Curriculum, Revised 2008
Unit 4, Activity 1, Volume and Surface Area with Answers

                                Exploring Volume and Surface Area

# cubes used   Length of          Width of         Height of        Volume of       Surface Area
for model      rectangular        rectangular      rectangular      rectangular     of rectangular
               prism built        prism built      prism built      prism built     prism built
               (linear units)     (linear units)   (linear units)   (cubic units)   (square units)

     16           16 units            1 unit           1 unit            16 u3           66u2

     16            8 units            2 units          1 unit            16 u3           52u2

     16            4 units            4 units          4 units           16 u3           24u2

The number of cubes will vary as students
build other rectangular solids.




Blackline Masters, Mathematics, Grade 8                                              Page 61
Louisiana Comprehensive Curriculum, Revised 2008
Unit 4, Activity 2, cm Grid




Blackline Masters, Mathematics, Grade 8            Page 62
Louisiana Comprehensive Curriculum, Revised 2008
Unit 4, Activities 2, 5, and 8, LEAP Reference Sheet




Blackline Masters, Mathematics, Grade 8                Page 63
Louisiana Comprehensive Curriculum, Revised 2008
Unit 4, Activity 3, What’s the Probability?

Name _______________________________________ Date ________________ Hour ______


Answer each of the following probability questions.

   1. Under the best conditions, sunflower seeds have a 30% chance of growing. If you select
      two seeds at random, what is the probability that both will grow, under the best
      conditions? Explain your solution.




   2. You roll a number cube once. Then you roll it again. What is the probability that you get
      3 on the first roll and a number greater than 5 on the second roll? Explain your solution.




Blackline Masters, Mathematics, Grade 8                                             Page 64
Louisiana Comprehensive Curriculum, Revised 2008
Unit 4, Activity 3, What’s the Probability with Answers

Answer each of the following probability questions.
   1. Under the best conditions, sunflower seeds have a 30% chance of growing. If you select
      two seeds at random, what is the probability that both will grow, under the best
      conditions? Explain your solution.

       P(a seed grows) = 30% or 0.30
       P(two seeds grow) = P(a seed grows)  P(a seed grows)
                            = 0.30  0.30
                            = 0.09
                            = 9% probability

   2. You roll a number cube once. Then you roll it again. What is the probability that you get
      3 on the first roll and a number greater than 3 on the second roll? Explain your solution.

                1
       P(3) =                                 there is only one 3 on a number cube
                6
                            3 1
       P(greater than 3) =                   there are 3 numbers greater than 3 on a number
                            6 2
       cube and this simplifies to one half

       1 1 1                      1
         =   The probability is
       6 2 12                    12




Blackline Masters, Mathematics, Grade 8                                              Page 65
Louisiana Comprehensive Curriculum, Revised 2008
Unit 4, Activity 4, Spinner




                     2                             3
                      5                            4
    Length             Width             Height    Volume   POINTS




Blackline Masters, Mathematics, Grade 8                     Page 66
Louisiana Comprehensive Curriculum, Revised 2008
Unit 4, Activity 6, Volume Comparison of Pyramids and Rectangular Prisms

Name _______________________________ Date _______________ Hour ________

Fill in the chart below using at least 4 different measurements for area of base and heights of
pyramids and rectangular prisms. Assume that the area of the base and the height is the same for
each set of figures.

Area of square base     Height                 Volume of pyramid         Volume of Prism

         4 in2                   3 in




Blackline Masters, Mathematics, Grade 8                                             Page 67
Louisiana Comprehensive Curriculum, Revised 2008
Unit 4, Activity 6, Models of Rectangular Prism and Pyramid

Cut the patterns out on the bold lines. Fold on the dotted lines to make a rectangular prism and a pyramid.




Blackline Masters, Mathematics, Grade 8                                                                       Page 68
Louisiana Comprehensive Curriculum, Revised 2008
Unit 4, Activity 6, Models of Cylinder and Cone




Blackline Masters, Mathematics, Grade 8            Page 69
Louisiana Comprehensive Curriculum, Revised 2008
Unit 4, Activity 6, Models of Cylinder and Cone




 This cone was drawn so that it will fit inside of the
 cylinder for comparison. Popcorn kernels can be used to
 fill the cone and then poured into the cylinder to show the
 one-third relationship of the volume. Not for mastery at
 the eighth grade level.




Blackline Masters, Mathematics, Grade 8                        Page 70
Louisiana Comprehensive Curriculum, Revised 2008
Unit 4, Activity 7, Comparing Cones

Name ______________________________ Date ________________ Hour _____________

Cut out the Model for Cone BLM and make a slit for the radius.

Form a cone by sliding point „L‟ so that it touches point „A‟.
Measure the approximate diameter of the cone formed.
Measure the approximate height of the cone formed.
Record this information on the chart.

Complete the table below by sliding point „L‟ of the circle so that it lies on top of the points
listed in the table. Use your centimeter ruler to measure the approximate diameter of the cone
formed and the approximate height. (As you begin to make the cones from L to F and smaller
diameters, it is easier to form the cone if a section is cut off the circle by cutting from point D to
the center. This reduces the amount of the paper inside the cone.)


Point of intersection           Approximate             Approximate height           Approximate
                              diameter of cone            of cone formed             volume of the
                                  formed                                                 cone

        L to A

        L to B

        L to C

        L to D

        L to E

         L to F

        L to G

        L to H

        L to I
Use the data you collected in your chart to make the following observations:

   1. How does the change affect the volume of the cone?


   2. How do the changes in the diameter and height affect the surface area of the cone?


   3. Is there a maximum height of a cone formed from a circle? Explain.


Blackline Masters, Mathematics, Grade 8                                                   Page 71
Louisiana Comprehensive Curriculum, Revised 2008
Unit 4, Activity 7, Comparing Cones with Answers


Cut out the circle on the Model for Cone BLM and make a slit for the radius.

Form a cone by sliding point „L‟ so that it touches point „A‟.
Measure the approximate diameter of the cone formed.
Measure the approximate height of the cone formed.
Record this information on the chart.

Complete the table below by sliding point „L‟ of the circle so that it lies on top of the points
listed in the table. Use your centimeter ruler to measure the approximate diameter of the cone
formed and the approximate height.


Point of intersection          Approximate            Approximate height          Approximate
                             diameter of cone           of cone formed            volume of the
                                 formed                                               cone

        L to A                     15 cm                         3cm               177cm3

        L to B                     13cm                      4.5cm                 199cm3

        L to C                     12cm                      5.5cm                 207 cm3

        L to D                       11                          6                 190 cm3

        L to E                      9                            6.5               138 cm3

        L to F                      8                            7                 117cm3

        L to G                      7                            7.25               93cm3

        L to H                      5.5                          7.5                59cm3

        L to I                      4                        8                     34cm3
Use the data you collected in your chart to make the following observations:
   1. How does the change affect the volume of the cone?
           As the diameter decreases, the height increases and the volume decreases
   2. How do the changes in diameter of the cone and height affect the surface area of the
       cone?
           The surface area decreases as the diameter decreases.
   3. Is there a maximum height of a cone formed from a circle? Explain
           The height of a cone formed from a circle must be less than the radius of the circle. A
           cone cannot be formed with a height equal to the radius.




Blackline Masters, Mathematics, Grade 8                                                Page 72
Louisiana Comprehensive Curriculum, Revised 2008
Unit 4, Activity7, Model for Cone


                                        J
                                                     K
                     I


                                                         L
        H

                                                   TOP



    G
                                                                 A




         F                                                   B



                                                     C
                         E
                                             D




Blackline Masters, Mathematics, Grade 8                  Page 73
Louisiana Comprehensive Curriculum, Revised 2008
Unit 4, Activity 8, Common Containers

Name ____________________________ Date ______________ Hour ___________


   Container      Estimated         Volume in US Customary     Volume in metric
                  Volume            Measure ( write formula,   measure (write formula,
                                    show substitutions, and    show substitutions, and
                                    provide answer)            provide answer)

       A




       B




       C




       D




       E




       F




       G




Blackline Masters, Mathematics, Grade 8                                     Page 74
Louisiana Comprehensive Curriculum, Revised 2008
Unit 4, Activity 9, Changing Volumes

Name _________________________________ Date __________________ Hour __________

                                             Part 1
                             SURFACE AREA, VOLUME AND DIMENSIONS
          Volume                                            Dimensions
                                 Original: 4 units x 3 units x 2 units
                                 Double width:



                                             Part 2
          Volume                                            Dimensions
     8 cubic units (8 u3)        Cube:


                                 Double one side:


                                 Double two sides:


                                 Double three sides:


    27 cubic units (27 u3)       Cube:


                                 Double one side:


                                 Double two sides:


                                 Double three sides:




Blackline Masters, Mathematics, Grade 8                                  Page 75
Louisiana Comprehensive Curriculum, Revised 2008
Unit 4, Activity 9, Changing Volumes

      1. Think about the activity we have done, and explain the relationship that doubling one
         or more dimensions has on volume.


      2. Complete the table below using what you learned about the relationship of
         dimensions to volume. Show your work.

                                           Part 3
         Volume                                         Dimensions
                                                     1        1        1
                              Original Dimensions:     unit x   unit x   unit
                                                     4        4        4
                                                     1        1        1
                                                       unit x   unit x   unit
                                                     2        2        2
                                                     1        1
                                                       unit x   unit x 1 unit
                                                     2        2
                                                      1
                                                        unit x 1 unit x 1 unit
                                                      2




Blackline Masters, Mathematics, Grade 8                                            Page 76
Louisiana Comprehensive Curriculum, Revised 2008
Unit 4, Activity 9, Changing Volumes with Answers

                                                    Part 1
                                   SURFACE AREA, VOLUME AND DIMENSIONS
             Volume                                               Dimensions
                           3
       24 cubic units (24 u )          Original: 4 units x 3 units x 2 units
                           3
       48 cubic units (48 u )          Double width: 4 units x 6 units x 2 units

                                                    Part 2

             Volume                                               Dimensions
        8 cubic units (8 u3)           Original: 2 units x 2 units x 2 units
                           3
      16 cubic units (16 u )           Double one side: 2 units x 2 units x 4 units
                           3
      32 cubic units (27 u )           Double two sides: 2 units x 4 units x 4 units
                               3
      64 cubic units (216 u )          Double three sides: 4 units x 4 units x 4 units
                       3
    27 cubic units (1 u ) [cube]       Original: 3 units x 3 units x 3 units
      54 cubic units (54 u3)           Double one side: 3 units x 3 units x 6 units
     108 cubic units (108 u3)          Double two sides: 3 units x 6 units x 6 units
     216 cubic units (216 u3)    Double three sides: 6 units x 6 units x 6 units
         1. Think about the activity we have done, and explain the relationship that doubling one
            or more dimensions has on surface area and volume.
             Doubling only one dimension makes the volume twice as large.
             Doubling two dimensions makes the volume four times as large as the original..
            Doubling all three dimensions makes the volume 8 times large.
         2. Complete the table below using what you learned about the relationship of
            dimensions to surface area and volume. Show your work.
                                             Part 3
            Volume                                         Dimensions

               1 3                      1         1        1
                  u                       unit x unit x       unit
               64                       4         4        4
               1 3                      1          1        1
                 u                         unit x unit x unit Multiply original volume by 8 since
               8                        2          2        2
                                       all dimensions have been doubled.
                1 3                     1          1
                  u                        unit x    unit 1 unit Multiply original volume by 16 since
                4                       2          2
                                       two dimensions were doubled and one was quadrupled.
               1 3                      1
                 u                         unit x 1 unit x 1 unit Multiply original volume by 2 x 4 x 4
               2                        2
                                       or 32 since those are the factors.
.

Blackline Masters, Mathematics, Grade 8                                                      Page 77
Louisiana Comprehensive Curriculum, Revised 2008
Unit 4, Activity 9, Real Life Volume Situations

Name ____________________________ Date ___________________ Hour ______________

      1. Richard said that he constructed a rectangular prism that has the largest possible
         surface area with a volume of 48 ft3. Explain what the whole number dimensions of
         Richard‟s rectangular prism have to be to have the largest surface area.




      2. Daniel said that if the dimensions of Richard‟s rectangular prism were not whole
         numbers he could make a rectangular prism with a larger surface area. Is Daniel
         correct? Explain.




      3. Samantha said she built a rectangular prism with „snap cubes‟ that had one face with
         a surface area of 24 u2 and a volume of 216 u3. Find the dimensions of Samantha‟s
         rectangular prism, and sketch a diagram with dimensions labeled.




Blackline Masters, Mathematics, Grade 8                                           Page 78
Louisiana Comprehensive Curriculum, Revised 2008
Unit 4, Activity 9, Real Life Volume Situations with Answers

      1. Richard said that he constructed a rectangular prism that has the largest possible
         surface area with a volume of 48 ft3. Explain what the whole number dimensions of
         Richard‟s rectangular prism have to be to have the largest surface area.


          Dimensions would be 1 unit by 1 unit by 48 units, and all 48 cubes would be
          showing---SA = 2 ends + 48 + 48 + 48 + 48 = 194 unts²



      2. Daniel said that if the dimensions of Richard‟s rectangular prism were not whole
         numbers, he could make a rectangular prism with a larger surface area. Is Daniel
         correct? Explain.


          Yes. If you change the dimensions to ½u x 96u x 1u = 289u²




      3. Samantha said she built a rectangular prism with „snap cubes‟ that had one face with
         a surface area of 24 u2 and a volume of 216 u3. Find the dimensions of Samantha‟s
         rectangular prism, and sketch a diagram with dimensions labeled.

           Possible answers: 1x24x9, 2x12x9, 3x8x9, 4x6x 9




Blackline Masters, Mathematics, Grade 8                                           Page 79
Louisiana Comprehensive Curriculum, Revised 2008
Unit 4, Activity 11, Finding Density

                                   Finding Density

              L     W        H        Volume       Mass   Density
Station 1
rectangular
prism
Station 2
rectangular
prism
Station 3
rectangular
prism
                                                          Average Density




Blackline Masters, Mathematics, Grade 8                               Page 80
Louisiana Comprehensive Curriculum, Revised 2008
Unit 4, Activity 12, Density Experiments



                           Station 1 – Density of Candy
Item             Mass in              Volume in cubic cm         Density
                 grams           L       W        H     Volume
Musketeers®
Bar

Snickers ®
Bar



                 Station 2– Density of Soap and Pumice Stone
Item             Mass in              Volume in cubic cm         Density
                 grams           L       W        H    Volume
Soap


Pumice
Stone



                     Station 3– Density of Marble and Ball
Item             Mass in              Volume in cubic cm         Density
                 grams                         4
                                            V   r3
                                               3
Marble


Ball




Blackline Masters, Mathematics, Grade 8                             Page 81
Louisiana Comprehensive Curriculum, Revised 2008
Unit 4, Activity 12, Class Data Charts

                         Station 1 – Class Data Chart


Group          Density of Musketeers® Bar          Density of Snickers® Bar
Number
1


2


3


4


5


6


Average




Blackline Masters, Mathematics, Grade 8                                 Page 82
Louisiana Comprehensive Curriculum, Revised 2008
Unit 4, Activity 12, Class Data Charts



                         Station 2 – Class Data Chart


Group                 Density of Soap              Density of Pumice
Number                                                   Stone
1


2


3


4


5


6


Average




Blackline Masters, Mathematics, Grade 8                                Page 83
Louisiana Comprehensive Curriculum, Revised 2008
Unit 4, Activity 12, Class Data Charts


                         Station 3 – Class Data Chart


Group               Density of Marble                   Density of Ball
Number
1


2


3


4


5


6


Average




Blackline Masters, Mathematics, Grade 8                                   Page 84
Louisiana Comprehensive Curriculum, Revised 2008
Unit 4, Activity 14, Alligator

Directions: In Louisiana, there are many alligators. Use the information in the graph below to
write a paragraph describing whether or not there is a relationship between the length of an
alligator and the number of documented bites by alligators of each length. Justify your
conclusion with any information from the graph. Make a prediction as to the number of times an
alligator that is about five feet long bites, and explain why you think your prediction is correct.


                                         Number of Alligator bites
                                    (each point represents one alligator)
                           16



                           14



                           12
         Number of Bites




                           10



                           8



                           6



                           4



                           2



                           0
                                0    2       4            6           8           10          12


                                                  Length in Feet

                                                 The alligator at the left is a 10-foot alligator. What is the
                                                 scale used in the drawing? Explain.

                                                 Place a point on the graph above to represent the number
                                                 of projected bites from an alligator of this length.



                                         Give approximate dimensions of a rectangular prism or
solid that could be used to transport this gator. Explain why your dimensions will create a box to
contain this gator.




Blackline Masters, Mathematics, Grade 8                                                            Page 85
Louisiana Comprehensive Curriculum, Revised 2008
Unit 4, Activity 14, Alligator with Answers

The graph shows a definite negative trend that shows as the length goes down, the number of
bites go up and vice versa.

Make a prediction as to the number of times an alligator that is about five feet long bites and
explain why you think your prediction is correct
At 5 feet about 7 bites



                                        The alligator at the left is a 10-foot alligator. What is the
                                        scale used in the drawing? Explain.


                                        2 1/8” = 10’

                                        Place a point on the graph above to represent the number
                                        of projected bites from an alligator of this length.

                                      between 1 and 2 bites



Give approximate dimensions of a rectangular prism or solid that could be used to transport this
gator. Explain why your dimensions will create a box to contain this gator

Answers will vary depending on how thick they think an alligator is. A reasonable answer would
include the 10’ for the length. A student might measure the width of the alligator in the picture
                1                              .5"    x
(approximately ”) and use the proportion                 to find the width. This would give an
                2                            2.125" 10'
                         1
approximate width of 2 feet.
                         3




Blackline Masters, Mathematics, Grade 8                                                   Page 86
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activities 1, 2, 3, 4, and 17, Grid




Blackline Masters, Mathematics, Grade 8            Page 87
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 1, Camping Sounds!

Name ______________________________ Date ____________ Hour ________

   1. Raccoons ate 117 marshmallows total from three bags. The raccoons ate 47 from Sue‟s
      bag and 31 from Sam‟s bag. How many were eaten from Melissa‟s bag? Write your
      equation and solve.



   2. Melissa ate some marshmallows on Saturday and 3 less on Sunday. She ate four times as
      many on Friday as she did on Saturday. If Melissa ate a total of 33 marshmallows, how
      many marshmallows did Melissa eat on Saturday? Write your equation and solve.



   3. Jack wanted to go canoeing. He has carried the canoe for 14 minutes. The trip should take
      21 minutes for him to get to the lake. How much more time, t, does he have to walk?
                                                                                  1
      Write your equation. Make a graph of Jack‟s walk to the lake if he walks 4 mile every 3
      minutes.



   4. Sam is hiking on a trail that is 280 feet long. He has hiked 20 feet less than half the
      distance. How far, d, has he walked? Write your equation and solve. If Sam walks 10
      feet per second and completes the trail, make a graph of his hike along the trail.


   5. A bag of marshmallows has about 150 small marshmallows in each bag. Campers took
      marshmallows on a camping trip. A group of raccoons came to the campsite and ate
      about 20 marshmallows each hour. Make a table of values to find the length of time it
      took for the raccoons to eat the bag of marshmallows. Graph your values on the Grid for
      Questions 5 and 6 BLM.




   6. Jack wants to canoe down river. The guide told him that the average speed down river is
      20 mph. Jack will leave the campsite to canoe at 10:20 a.m. Make a table of values to
      find how far Jack will have gone by 5:00 p.m. Graph your values on the Grid for
      Questions 5 and 6 BLM.




Blackline Masters, Mathematics, Grade 8                                               Page 88
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 1, Camping Sounds! with Answers


   1. Raccoons ate 117 marshmallows total from three bags. The raccoons ate 47 from Sue‟s
      bag and 31 from Sam‟s bag. How many were eaten from Melissa‟s bag? Write your
      equation and solve. Solution: 117 = 31+47 +n; n = 39

   2. Melissa ate some marshmallows on Saturday and 3 less on Sunday. She ate four times as
      many on Friday as she did on Saturday. If Melissa ate a total of 33 marshmallows, how
      many marshmallows did Melissa eat on Saturday? Write your equation and solve.
      Solution 33 = 4(x)+ x+(x - 3); x = 6                                           2                                     Canoe Trip




                                                               Distance

   3. Jack wanted to go canoeing. He has carried the           (miles)




      canoe for 14 minutes. The trip should take 21                                  1

      minutes for him to get to the lake. How much more
      time, t, does he have to walk? Write your equation.
      Solution: 21 – 14 = t ; Make a graph of Jack‟s walk
                               1                                                     0
                                                                                                 3                6        9
                                                                                                                      Time (minutes)
                                                                                                                                     12        15     18        21


       to the lake if he walks 4 mile every 3 minutes.
   4. Sam is hiking on a trail that is 280 feet long. He has
                                                                           280


      hiked 20 feet less than half the distance. How far, d,               260
                                                                                                         Hiking
                                                                           240


      has he walked? Write your equation and solve.                        220


                                                                           200



      Solution: 280 - 20 = d; d = 120 feet If Sam walks 10
                   2
                                                                           180


                                                                           160




      feet per second and completes the trail, make a graph
                                                                           140


                                                                            120
                                                                Distance
                                                                (feet)
                                                                           100


      of his hike along the trail.                                          80


                                                                            60


                                                                            40


                                                                            20



     5. A bag of marshmallows has about 150 small                                0
                                                                                         2   4       6

                                                                                             Time (seconds)
                                                                                                              8       10   12   14   16   18    20   22    24   26   28




         marshmallows in each bag. Campers took
         marshmallows on a camping trip. A group of raccoons came to the campsite and ate
         about 20 marshmallows each hour. Make a table of values to find the length of time it
         took for the raccoons to eat the bag of marshmallows. Graph your values on the Grid for
         Questions 5 and 6 BLM.
Hours                 0         1         2        3       4       5      6        7        8
Marshmallows         150      130        110      90      70      50     30       10     Finished
left in bag                                                                               bag in
                                                                                         about ½
                                                                                           hour

    6. Jack wants to canoe down river. The guide told him that the average speed down river is
        20 mph. Jack will leave the campsite to canoe at 10:20 a.m. Make a table of values to
        find how far Jack will have gone by 5:00 p.m. Graph your values on the Grid for
        Questions 5 and 6 BLM.
Time         10:20    11:20     12:20     1:20      2:20     3:20     4:20        5:00
              a.m.     a.m.      a.m.     p.m.      p.m.      p.m.    p.m.        p.m.
Distance       0        20        40       60        80       100      120         1
(miles)                                                                        133 miles
                                                                                   3



Blackline Masters, Mathematics, Grade 8                                                                                                                         Page 89
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 1, Grid for Questions 5 and 6
Grid for #5




 Grid for #6




Blackline Masters, Mathematics, Grade 8            Page 90
Louisiana Comprehensive Curriculum, Revised 2008
   Unit 5, Activity 1, Grid for Questions 5 and 6 with Answers
Graph for question 5

                 150

                 140                                                      Marshmallows Eaten on Trip
       #
                130
       m        120
       a
       r        110
       s
                100
       h
       m        90
       a
       l        80
       l
       o        70
       w
       s        60

                50
       e
       a        40
       t
       e        30
       n
                20

                10

                          0           1           2           3       4        5        6        7      8




   Graph for question 6


                 140
                                                                    Canoe Trip


                 120
        D
        I
        S
                  100
        T
        A
        N
        C            80
        E
      (miles)


                      60



                     40



                     20



                      0
                              10:20       11:20       12:20        1:20     2:20     3:20      4:20    5:20
                                                                  Time (m inutes)




   Blackline Masters, Mathematics, Grade 8                                                                    Page 91
   Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 2, Patterns and Graphing

Name ___________________________________ Date _______________ Hour __________

Pattern 1




       Arrangement    Arrangement       Arrangement
            1              2                 3


   a) Sketch the 4th and 5th arrangement in the pattern.
   b) Make a table that shows the arrangement number and the total number of tiles in the
      pattern.


   c) Describe a „rule‟ for determining the number of tiles in the 25th pattern, 100th pattern.



   d) Is the rate of change in this pattern linear? Explain why or why not.



Pattern 2

        Ar r #1      Ar r #2         Ar r #3




   a) Sketch the 4th and 5th arrangement in the pattern.
   b) Make a table that shows the arrangement number and the total number of tiles in the
      pattern.

Blackline Masters, Mathematics, Grade 8                                                Page 92
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 2, Patterns and Graphing




   c) Describe a „rule‟ for determining the number of tiles in the 25th pattern, 100th pattern.


   d) Is the rate of change in this pattern linear? Explain why or why not.




Blackline Masters, Mathematics, Grade 8                                                Page 93
Louisiana Comprehensive Curriculum, Revised 2008
    Unit 5, Activity 2, Patterns and Graphing with Answers

    Pattern




Arrangement    Arrangement      Arrangement             Arrangement            Arrangement
  1                 2                3                      4                      5



        a) Sketch the 4th and 5th arrangement in the pattern.
        b) Make a table that shows the arrangement number and the total number of tiles in the
           pattern.
                                        Arrangment #        Total tiles
                                               1                 4
                                               2                 7
                                               3                10
                                               4                13
                                               5                16
        c) Describe a „rule‟ for determining the number of tiles in the 25th pattern, 100th pattern.
                            3 times the arrangement number plus 1
                            3x + 1
        d) Is the rate of change in this pattern linear? Explain why or why not? Linear, no
           exponents.



    Pattern 2
                                                             Arr # 4                  Arr # 5
              Ar r #1     Ar r #2         Ar r #3




                                                               Arrangement #          Total # of tiles
                                                                     1                       1
                                                                     2                       4
                                                                     3                       9

    Blackline Masters, Mathematics, Grade 8                                                  Page 94
    Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 2, Patterns and Graphing with Answers

   a) Sketch the 4th and 5th arrangement in the                 4                       16
      pattern.                                                  5                       25
   b) Make a table that shows the arrangement
      number and the total number of tiles in the pattern.
   c) Describe a „rule‟ for determining the number of tiles in the 25th pattern, 100th pattern.
               Rule: The arrangement number times itself, or the arrangement number squared
               produces the number of tiles needed.
   d) Is the rate of change in this pattern linear? Explain why or why not? This arrangement
      number is not linear because it is a square.




Blackline Masters, Mathematics, Grade 8                                             Page 95
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 2, More Practice with Patterns


Name ___________________________Date __________________ Hour _____________

Sketch the 4th and 5th arrangements in each of the patterns below. Answer the questions that
follow.

1.




                     Arrangement
        #1           #2          #3

       a) How many tiles will be in the 10th arrangement?


       b) One arrangement in this pattern has 86 tiles. Explain how you will determine the
          arrangement number that this number of tiles represents. Which arrangement is it?


       c) There are two consecutive arrangements of this pattern that contain a total of 128
          tiles. What are the two consecutive arrangements?



       d) Explain which consecutive arrangements contain exactly this number of tiles.



       e) Write an equation to represent this pattern.



       f) Make a table and graph this equation on a coordinate grid.




Blackline Masters, Mathematics, Grade 8                                              Page 96
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 2, More Practice with Patterns

Name _________________________________
.
2. Sketch the 4th and 5th arrangements in each of the patterns below. Answer the questions that
follow.



                      Arrangement Number
            #1            #2         #3


       a) Make a table of values with the x value representing the arrangement number and the
          y value representing the perimeter of the figures 1 - 5 (the sides of the equilateral
          triangle represent 1 unit).




       b) Plot the coordinates of the pattern on grid paper. Use the grid paper to determine
          which arrangement will have a perimeter of 57 units. Explain how you determined
          this.




       c) Write an equation to represent the growth represented in this pattern. Explain how
          you determined this.




Blackline Masters, Mathematics, Grade 8                                              Page 97
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 2, More Practice with Patterns with Answers

Sketch the 4th and 5th arrangements in each of the patterns below. Answer the questions that
                                                                                                Arrangement 5


follow.                                                         Arrangement 4




1.




                       Arrangement
       #1              #2          #3

          a. How many tiles will be in the 10th arrangement? 42 tiles


          b. One arrangement in this pattern has 86 tiles. Explain how you will determine the
             arrangement number that this number of tiles represents. Which arrangement is it?
             (86 – 2) ÷4 = 21      21 is the arrangement number

              There is a constant of 2 squares in the center---and
              each leg is the arrangement number.



          c. There are two consecutive arrangements in this pattern that contain a total of 128
             tiles. What are the two consecutive arrangements?

              Arrangements 15 and 16

          d. Explain which consecutive arrangements contain exactly this number of tiles.
             One possible explanation: Arrangement 15 will contain 4(15) + 2 and arrangement
             16 will contain 4(16) + 2 tiles. These two arrangements would give the exact 128
             tile. 15 tile in 3 of the four legs of the 15th and 16 tile in 3 of the 4 legs of the 16th and
             the 2 extra center tiles.

          e. Write an equation to represent this pattern.
                Total = 4 times the arrangement number plus 2, T = 4n + 2


          f. Make a table and graph this equation on a
                                                                                Arrangement #                   total tile
             coordinate grid.
                                                                                    x                               y
                                                                                1                  6
                                                                                2                  10
                                                                                3                  14
                                                                                4                  18
                                                                                5                  22

Blackline Masters, Mathematics, Grade 8                                                                         Page 98
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity2, More Practice with Patterns with Answers

2. Sketch the 4th and 5th arrangement in each of the patterns below. Answer the questions that
follow.

                                                           4TH arrangement has 4 hexagons and
                                                           4 equilateral triangles.
                     Arrangement Number
                                                           5th arrangement has 5 hexagons and
           #1           #2          #3
                                                           5 equilateral triangles

       a. Make a table of values with the ‘x’ value represent the arrangement number and the
          ‘y’ value represent the perimeter of the figures 1 - 5 (the sides of the equilateral
          triangle represent 1 unit).


                       arrangement Perimeter
                       number
                            x          y
                            1            7
                            2           12
                            3           17
                            4           22
                            5           27
       b. Plot the coordinates of the pattern on grid paper. Use the grid paper to determine
          which arrangement will have a perimeter of 57 units. Explain how you determined
          this.
              (57 – 2)÷ 2 = 11, the 11th arrangement has 57 units.
              Continued the line on the graph and found the coordinates of the line on the grid.

       c. Write an equation to represent the growth shown in this pattern. Explain how you
          determined this.

Perimeter = arrangement number times 5 plus 2, y = 5x + 2




Blackline Masters, Mathematics, Grade 8                                              Page 99
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 2, Patterns and Graphing Practice

Name _________________________________ Date ____________ Hour _____


      1. While performing an experiment in Mr. Knight‟s science class, the students noticed a
         pattern was formed when a certain ingredient was added to a solution. From the table
         below, choose an equation that best generalizes the pattern.


                         Amount of x (mL)        Amount of y (mL)
                                 5                     32
                                 6                     29
                                 7                     26


          a) y = -3x + 47           b) y = 3x – 47        c) y = 3x +47       d) y = 3x


      2. Mona is saving money for college. Each week she doubles the amount of her deposit.
         She began her account with just $5.


          a. Make a table representing Mona‟s savings.




          b. How much money will Mona deposit into her account after 5 weeks?




          c. Predict how much money Mona deposited into her account after 10 weeks?

      3. Sketch the 4th and 5th arrangements in the pattern below.




          Arr. # 1       Arr. #2               Arr. #3

Blackline Masters, Mathematics, Grade 8                                         Page 100
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 2, Patterns and Graphing Practice

          4. How many tiles will there be in the 10th arrangement? Explain in words what it
             will look like.


          5. How many tiles will there be in the 27th arrangement? Sketch a diagram that
             shows what it will look like.




          6. Which arrangement will have 133 tiles? Explain how you determined the answer.




          7. Write an expression that would help you determine the total number of tiles in the
             nth arrangement.




          8. Make a table of values with x being the arrangement number and y being the total
             number of tiles. Graph your table values on a coordinate grid.




Blackline Masters, Mathematics, Grade 8                                           Page 101
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 2, Patterns and Graphing Practice with Answers

      1. While performing an experiment in Mr. Knight‟s science class, the students noticed a
         pattern was formed when a certain ingredient was added to a solution. From the table
         below, choose an equation that best generalizes the pattern.
                          Amount of x (mL)        Amount of y (mL)
                                  5                     32
                                  6                     29
                                  7                     26
          a) y = -3x + 47             b) y = 3x – 47           c) y = 3x +47         d) y = 3x

      2. Mona is saving money for college. Each week she doubles the amount of her deposit.
         She began her account with just $5.

          a. Make a table representing Mona‟s savings.
              x=       0        1       2       3      4               5
                week
                Amount    5      10        20         40       80      160
                of
                deposit
          b. How much money will Mona deposit into her account after 5 weeks?
             $160 deposit week 5
          c. Predict how much money Mona deposited into her account after 10 weeks?
             About $5000 – if student figures out pattern, the amount will be $5120

      3. Sketch the 4th and 5th arrangements in the pattern below.

                                                                               3 tiles on each leg




                                                                               3 tiles on each leg
     Arr. # 1        Arr. #2                Arr. #3


  Arrangement 5 has a center tile, with 4 tiles on each leg.

      4. How many tiles will there be in the 10th arrangement? Explain in words what it will
         look like.
        The 10th arrangement has 37 tiles. There will be one tile in the center and nine tiles on
        each of the 4 legs.
      5. How many tiles will there be in the 27th arrangement? Sketch a diagram that shows
         what it will look like. There will be 26 tile on each of the 4 legs and one in the middle
         for a total of 105 tiles.




Blackline Masters, Mathematics, Grade 8                                                Page 102
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 2, Patterns and Graphing Practice with Answers

       6. Which arrangement will have 133 tiles? Explain how you determined the answer.
       The 34th arrangement has 133 tiles. 133 – 1(center tile) = 132. 132 ÷4 legs) = 33+ 1=34
       7. Write an expression that would help you determine the total number of tiles in the nth
            arrangement.
       4(n – 1) + 1 or 4n - 3
       Make a table of values with x being the arrangement number and y being the total number
       of tiles. Graph your table values on a coordinate grid.

                                           x              y
                                           2              5
                                          10             37
                                          27            105
                                          34            133
Student answers will vary.




Blackline Masters, Mathematics, Grade 8                                            Page 103
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 3, Circles and Patterns


Name __________________________ Date ____________________ Hour _____________


Below are sketches of three circles. The radius of each successive circle is one unit longer than
the previous. Make a table of values for circles 1 – 5 in this same pattern for which the radius
increases in the same manner.




   Circle #1                     Circle #2                             Circle #3



Complete the table of values below: Use  = 3.14
                        r        r2   Observations:




Blackline Masters, Mathematics, Grade 8                                              Page 104
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 3, Circles and Patterns with Answers

Below are sketches of three circles. The radius of each successive circle is one unit longer than
the previous. Make a table of values for circles 1 – 5 in this same pattern for which the radius
increases in the same manner.




    Circle #1                    Circle #2                              Circle #3



Complete the table of values below: Use  = 3.14
                                                                                        16




      r2
                                                                                        14



r                 Area of Circle with      Observations:
                  given radius                                                          12




1    (3.14)(12)   3.14 square units        Student answers will vary.                   10




2    (3.14)(22)   12.56 square units       Examples of student                          8




3    (3.14)(32)   28.26 square units       observations might be as                     6




4    (3.14)(42)   50.24 square units       follows: Not a linear pattern.
     (3.14)(52)
                                                                                        4


5                 78.5 square units        If the radius is doubled, the
                                           area of the circle is 4 times as             2




                                           large. For example, the circle                           5   10




                                           with the radius of 2 has an
                                           area of 12.56 square units,
                                           and the circle with a radius of
                                           4 units has an area of 4 x
                                           12.56 or 50.24 square units.




Blackline Masters, Mathematics, Grade 8                                              Page 105
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 6, Graph Situations

   This is the sheet you need to cut into strips to distribute to the students

A) Joe left his room walking slowly, stopped at the refrigerator to get a
  snack, and then he went quickly into the backyard.

B) Sally ran quickly to the dressing room after the ball game. She
  stopped at the door and went back to speak to her parents.


C) Stephanie receives $25 a week for allowance, and she spends only
  $15 a week.


D) Jeremy has $200 in his savings account and puts $15 a week in his
  account, but he spends $10 a week for snacks after school.


E) The rental car company charges $30/day to rent a small car.


F) Danny rode his bicycle fast and then stopped for a few minutes to
  rest before beginning to ride at a slow, steady pace.


G) The bus was stalled at the intersection for about 10 minutes before
  the driver started the engine and moved the bus slowly out of the way.

H) Jonathan drives slowly until he gets on the interstate. He speeds up
  until he gets to an area of construction where he slows down once
  more.


I) Derrick walks to the store, stops to buy a soda, and then he runs back
   home.


Blackline Masters, Mathematics, Grade 8                                          Page 106
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 6, Graph Situations for Students

Name(s) ________________________ Date ______________ Hour _______

Write the letter from the graph on the wall next to the situation.

____ 1.) Sally ran quickly to the dressing room after the ball game. She stopped at the door and
went back to speak to her parents.

____ 2.) Derrick walks to the store, stops to buy a soda, and then he runs back home.

____ 3.) Danny rode his bicycle fast and then stopped for a few minutes to rest before
beginning to ride at a slow, steady pace.

____ 4.) Jeremy has $200 in his savings account and puts $15 a week in his account, but he
spends $10 a week for snacks after school.

____ 5.) Joe left his room walking slowly, stopped at the refrigerator to get a snack, and went
quickly into the backyard.

____6.) Jonathan drives slowly until he gets on the interstate. He speeds up until he gets to an
area of construction where he slows down once more.

____ 7.) The rental car company charges $30/day to rent a small car.

____ 8.) Stephanie receives $25 a week for allowance, and she spends only $15 a week.

____ 9.) The bus was stalled at the intersection for about 10 minutes before the driver started the
engine and moved the bus slowly out of the way.




Blackline Masters, Mathematics, Grade 8                                              Page 107
Louisiana Comprehensive Curriculum, Revised 2008
         Unit 5, Activity 6, Graph Situations with Possible Graph Sketches


(A) Distance from starting point         (B) Distance from starting point            (C)   amount of $




                          time                            time                                weeks




  (D) amount of $                         (E)   amount of $                   (F) distance from starting point



                          weeks                           days                                time




  (G) Distance from starting point        (H) Distance from starting point   (I) Distance from starting point



                          time                            time                                time




         Blackline Masters, Mathematics, Grade 8                                        Page 108
         Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 6, Graph Situations Process Guide

                               Graphs needed to represent situations


Sketch a graph illustrating the difference in a   Sketch a graph illustrating running fast and
graph for walking slowly and running              coming to a stop.




Sketch a graph illustrating a deposit into a      Sketch a graph that compares the speed of a car
bank account of the same amount each week.        traveling on the interstate and a second car
                                                  traveling on a busy city street.




Sketch a graph that illustrates the speed of a    Sketch a graph that illustrates the speed of a
car on the interstate and exiting onto a busy     runner during a 10 mile marathon.
street as the light turns red.




Blackline Masters, Mathematics, Grade 8                                              Page 109
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 7, Inequality Situations and Graphs

Name ______________________________ Date ___________________ Hour ___________

a. Jamie went to the mall and found a pair of in-line skates that he wanted to buy for $88. He
   makes $5.50/hour babysitting his little brother. He already has $13.25. Write and solve an
   inequality to find how many hours and minutes he must baby-sit to buy the skates. Graph the
   solution set.




b. A group of 8 students could not spend more than $78.50 when they went to the movies. If the
   tickets cost $6.50 each and snacks were $1.50 each, how many snacks could the students
   buy?




c. Coach told the team members that they must each earn at least $30 this week for a weekend
   tournament. Tim knows his dad will give him $12 to mow his grandmother‟s lawn and $8
   for each car he washes. If Tim mows his grandmother‟s lawn, write and solve an inequality
   to find how many cars he needs to wash to earn at least $30. Graph the solution set.




d. Sam wants to go to Washington D.C. in the spring. The trip will cost him $380 to go with
   his 8th grade class. Sam has saved $150 and he makes $5.25/hour when he works with his
   dad after school. Write and solve an inequality to find how many hours Sam must work with
   his dad to have at least $380. Graph the solution set.




Blackline Masters, Mathematics, Grade 8                                          Page 110
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 7, Inequality Situations and Graphs with Answers

a. Jamie went to the mall and found a pair of in-line skates that he wanted to buy for $88. He
   makes $5.50/hour babysitting his little brother. He already has $13.25. Write and solve an
   inequality to find how many hours and minutes he must baby-sit to buy the skates. Graph the
   solution set.
               5.5 x ≥88 – 13.25                                        Number of hours
               x ≥73.25/5.5
               x ≥ 13.5 hours                                      13.0     14.0
               He must work at least 13 hours and 30
               minutes.

c. A group of 8 students could not spend more than $78.50 when they went to the movies. If the
   tickets cost $6.50 each and snacks were $1.50 each, how many snacks could the students
   buy?

              $78.50 ≤ 8(6.50) +
              1.5x
              $78.50 – 52.00 ≤ 1.5x
              26.50 ≤ 1.5x
              17.7 ≤ x
              x≥ 17.7 snacks

c. Coach told the team members that they must each earn at least $30 this week for a weekend
   tournament. Tim knows his dad will give him $12 to mow his grandmother‟s lawn and $8
   for each car he washes. If Tim mows his grandmother‟s lawn, write and solve an inequality
   to find how many cars he needs to wash to earn at least $30. Graph the solution set.
              12 + 8x ≥ 30
              8x ≥ 30 – 12
              8x ≥ 18
              x ≥ 2 1/9 or he must wash
              at least 3 cars
              He must wash at least 3
              cars.

d. Sam wants to go to Washington D.C. in the spring. The trip will cost him $380 to go with
   his 8th grade class. Sam has saved $150 and he makes $5.25/hour when he works with his
   dad after school. Write and solve an inequality to find how many hours Sam must work with
   his dad to have at least $380. Graph the solution set.
                                                            Number of hours
              150 +5.25x ≥380
              5.25x ≥ 380 – 150                         42  43 44    45   46   47   48   49
              5.25x ≥ 230
              x≥ 230 /5.25
              x ≥43.80952381
              He must work at least 44 hours to have enough money.




Blackline Masters, Mathematics, Grade 8                                             Page 111
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 9, T-Shirt Auction Word Grid

Name ______________________________ Date ____________ Hour ________

Original Cost of the T-            $10             $11.50              $9
shirt
twice the square of the
price of the T-shirt


one-half the cube of the
price of the T-shirt


5 times the cost of the T-
shirt


the square of the cost of
the T-shirt plus $15


one hundred times the cost
of the T-shirt


the cost of the shirt x 104



$15 less than the cost of
the shirt squared


$250 less than the cube of
the price of the T-shirt




Blackline Masters, Mathematics, Grade 8                               Page 112
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 9, T-shirt Auction Word Grid with Answers

Name ______________________________ Date ____________ Hour ________

Original Cost of the T-               $10                $11.50                $9
shirt
                              2(102) = $200        2(11.52) =$264.50   2(92) =$162
twice the square of the
price of the T-shirt


one-half the cube of the      10 3                 11 .53              93
                                   = $500                 =$760.44        = $364.50
price of the T-shirt           2                     2                 2

                              5(10) = $50          5(11.5) = $57.50    5(9) = $45
5 times the cost of the T-
shirt

                              102 + 15= $115       11.52 + 15          92+ 15 =$96
the square of the cost of
                                                   =$147.25
the T-shirt plus $15

                              100(10) = $1000      100(11.5) =         100(9) = $900
one hundred times the cost
                                                   $1150.00
of the T-shirt

                              10(104) = $100,000   11.5(104)           9(104) = $90,000
the cost of the shirt x 104
                                                   =$115,000


                              (102)-15 = $85       (11.52)- 15 =       (92)- 15 = $66
$15 less than the cost of
                                                   $117.25
the shirt squared

                              (103) – 250 = $750   (11.53) – 250       (93) – 250 =$479
$250 less than the cube of
                                                   =$1270.88
the price of the T-shirt




Blackline Masters, Mathematics, Grade 8                                      Page 113
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 10, Reporting Results

Name ___________________________________ Date _____________ Hour ______

  Rule used for         Auctioned price of   Number of T-shirts Amount made on the
 Auctioned price        the $11.50            sold for this price $11.50 T-shirt following
                        originally priced                         each rule
                        T-shirt.
twice the square of
 the price of the T-                                  4
        shirt




one-half the cube of
 the price of the T-                                  2
        shirt




 5 times the cost of
     the T-shirt                                     15




  the square of the
 cost of the T-shirt                                  3
      plus $15




 one hundred times
  the cost of the T-                                  1
        shirt




the cost of the shirt
       x 104                                          1




Blackline Masters, Mathematics, Grade 8                                         Page 114
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 10, Reporting Results with Answers

  Rule used for         Auctioned price of     Number of T-shirts Amount made on the
 Auctioned price        the $11.50              sold for this price $11.50 T-shirt following
                        originally priced T-                        each rule
                        shirt.
twice the square of     $264.50                         4           $648
 the price of the T-
        shirt




one-half the cube of    $760.44                         2           $1520.88
 the price of the T-
        shirt




 5 times the cost of    $57.50                         15           $862.50
     the T-shirt




  the square of the     $147.25                         3           $441.75
 cost of the T-shirt
      plus $15




 one hundred times      $1150                           1           $1150
  the cost of the T-
        shirt




the cost of the shirt   $115,000                        1           $115,000
       x 104




Blackline Masters, Mathematics, Grade 8                                           Page 115
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 11, Rate of Change Grid




Blackline Masters, Mathematics, Grade 8            Page 116
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 11, Rate of Change Grid With Answers


                                            10




                                                   y = x3



                                                        y = 2x


                        y = x2



      -10                                  0                        10
                                                    y=x-2




Blackline Masters, Mathematics, Grade 8                          Page 117
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 12, Scientific Notation

Set up each of the problems in scientific notation and then solve the problems.

   1. The planet Mercury is 58,000,000 kilometers from the sun. The planet Pluto is 102 times
      further from the sun than the planet Mercury. About how far is the planet Pluto from the
      sun?




   2. Samantha‟s bicycle tire has a diameter of 65 centimeters. She figured the circumference
      was about 204 centimeters. She used a counter on her front bicycle tire that counts each
      time the tire makes one rotation to determine the distance she traveled. The counter said
      106 when she stopped. She decided that she had traveled 204,000,000 cm but her
      calculator said 2.04 x 108. Use your calculators to determine how the calculator
      representation relates to Samantha‟s or give an example of how Samantha‟s calculator
      represents 204 million centimeters.



   3. How old is a person who is one billion seconds old? Explain your reasoning. Represent
      your answer using the number of seconds and represent the one billion seconds in
      scientific notation. Next, simplify your answer using years, months, weeks, days,
      minutes, and/or seconds.




   4. In a FoxTrot cartoon the character refers to her excitement over summer vacation by
      cheering that since it is summer vacation she has 8,121,600 seconds without homework!
      Write the number in scientific notation and determine the number of hours that she is
      referring to.




Blackline Masters, Mathematics, Grade 8                                            Page 118
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 12, Scientific Notation with Answers

Set up each of the problems in scientific notation and then solve the problems.

   1. The planet Mercury is 58,000,000 kilometers from the sun. The planet Pluto is 102 times
      further from the sun than the planet Mercury. About how far is the planet Pluto from the
      sun?

       5,800,000,000 = 5.8 x 109km


   5. Samantha‟s bicycle tire has a diameter of 65 centimeters. She figured the circumference
      was about 204 centimeters. She used a counter on her front bicycle tire that counts each
      time the tire makes one rotation to determine the distance she traveled. The counter said
      106 when she stopped. She decided that she had traveled 204,000,000 cm but her
      calculator said 2.04 x 108. Use your calculators to determine how the calculator
      representation relates to Samantha‟s or give an example of how Samantha‟s calculator
      represents 204 million centimeters.

       The calculator was giving the answer in scientific notation.

   2. How old is a person who is one billion seconds old? Explain your reasoning. Represent
      your answer using the number of seconds and represent the one billion seconds in
      scientific notation. Next, simplify your answer using years, months, weeks, days,
      minutes, and/or seconds.
      1 billion seconds in scientific notation would be 1.0 x 109
      1,000,000,000seconds/60 seconds in a minute ≈ 16,666,666.67min
      About 16,666,666.67minutes/60 minutes in an hour ≈ 277,777.7778 hours
      About 277,777.78 hours/ 24 hours in a day ≈ 11574.0741 days
      1157.4075 days/365 days in a year (not a LEAP year) ≈ 31.7098 years
      About 31.7098 years ≈ 3 years, 259 days


   3. In a FoxTrot cartoon the character refers to her excitement over summer vacation by
      cheering that since it is summer vacation she has 8,121,600 seconds without homework!
      Write the number in scientific notation and determine the number of hours that she is
      referring to.

       8.1216 x 10 6seconds
       8,121,600 seconds = 2256 hours




Blackline Masters, Mathematics, Grade 8                                            Page 119
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 15, Inequality Cards



Sally wants to buy a new jacket that costs
$85 with her baby-sitting money. She
makes $5.25 an hour baby-sitting. How                           5.25n  85
many whole hours must she baby-sit to
buy the jacket.




           15       16       17       18        19   20    n  17; at least 17 hours




Kyle mows lawns for $5.25/hour. He does
not charge any customer more than $42.
What is the maximum number of hours it                          5.25n  42
takes Kyle to mow a lawn?




                                                          n  8; no more than 8 hours
       6        7        8        9        10




Blackline Masters, Mathematics, Grade 8                                        Page 120
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 15, Inequality Cards



A city bus charges $2.50 per trip. It also
offers a monthly pass for $85. How many
times must a person use the bus so that the
pass is less expensive than individual
                                                                   85 < 2.50n
tickets.




                                                             n > 34; more than 34 times

                32        33        34        35        36




Monroe needs more than 45 cubic feet of
soil to fill the planter he built. Each bag of                      2.5n > 45
soil contains 2.5 cubic feet. How many
bags of soil will Monroe need?




                                                              n > 18; at least 18 bags
           16        17        18        19        20




Blackline Masters, Mathematics, Grade 8                                          Page 121
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 15, Formula Madness BLM

Name _____________________________ Date ____________ Hour __________

   1. A rectangular sandbox has measurements of 6.5 feet x 4.8 feet. Don wants to completely
      fill the sandbox with sand. Find the volume of sand that Don needs to completely fill the
      sandbox if the height of the sandbox is 9 inches.




   2. Sam found a beach ball that was advertised as having a diameter of 48 inches. What is
      the circumference of the beach ball? Describe your method.



   3. Joseph was planning a trip to south Florida. The average low temperature is 56 F and
      the average high temperature is 88 F. The formula for converting Fahrenheit to Celsius
             5
      is C  ( F  32) . Find these temperatures in Celsius. Explain your thinking.
             9




                              1                                          13
   4. A stack of nickels is 2   inches tall. The diameter of a nickel is    in. find the volume
                              2                                          16
      of the stack of nickels. Be sure to label your steps. Make a table of values for stacks of
                            1
      nickels that are 2, 2 , and 3 inches tall. Graph these points and determine whether the
                            2
      relationship is linear.




   5. Betty wanted to cover a circular area of the counter that was 38.465 square feet. She had
      to buy the marble in square pieces. What would be the smallest square that she could buy
      that would cover this area? How does the diameter of the circular area relate to the size
      of the square she must buy?




Blackline Masters, Mathematics, Grade 8                                             Page 122
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 16, Formula Madness BLM with Answers

   1. A rectangular sandbox has measurements of 6.5 feet x 4.8 feet. Don wants to completely
      fill the sandbox with sand. Find the volume of sand that Don needs to completely fill the
      sandbox if the height of the sandbox is 9 inches.
               V = lwh
               V = (6.5)(4.8)(9)
               V =23.4 cubic feet

   2. Sam found a beach ball that was advertised as having a diameter of 48 inches. What
      would be the circumference of the beach ball? Describe your method. Use 3.14 for .
               C=d
               C = (3.14)(48)
               C = 150.72 inches
      If the diameter is given, multiply the diameter times pi. This time I used 3.14 for pi.

   3. Joseph was planning a trip to south Florida. The average low temperature is 56 F and
      the average high temperature is 88 F. The formula for converting Fahrenheit to Celsius
              5
      is C  ( F  32) . Find these temperatures in Celsius. Explain your thinking.
              9
                           1
              56 F = 13  C
                           3
                           1
              88 F = 31  C
                           9
                               1                                        13
   4. A stack of nickels is 2 inches tall. The diameter of a nickel is      in. find the volume
                               2                                        16
      of the stack of nickels. Be sure to label your steps. Make a table of values for volumes
                                        1
      of stacks of nickels that are 2, 2 , and 3 inches tall. Graph
                                        2
      these points and determine whether the relationship is                       2




      linear.
              B =  r2                                                volume
                                                                      of stack
                                                                      of nickels
                                                                                   1



                           6.5 2
              B = (3.14) ( )
                            16
              B = (3.14)(.17)                                                          0   1                 2
                                                                                               height of stack of nickels
                                                                                                                            3




              B = 0.53 square units
              V = B(h)
              V  .53(2.5)  1.325 cubic inches

              2 inches  1.06 cubic inches
              3 inches  1.59 cubic inches

   5. Betty wanted to cover a circular area of the counter that was 38.465 square feet. She had
      to buy the marble in square pieces. What would be the smallest square that she could buy
      that would cover this area? How does the diameter of the circular area relate to the size
      of the square she must buy?

Blackline Masters, Mathematics, Grade 8                                                               Page 123
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 16, Formula Madness BLM with Answers

      A =  r2                                               12 .25 = (r2)
                      2
      38.465 = 3.14(r )                                    3.5 feet =r
      38.465/3.14 = (r2)                                   D = 2r or 2(3.5) = 7 feet.
      12.25 = (r2)
      The diameter is the same length as the side of the square needed.




Blackline Masters, Mathematics, Grade 8                                           Page 124
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 17, Constant and Varying Rates of Change

Name _______________________________ Date __________________ Hour ___________

1. Complete the table of values.
                                                                                           2
                                                                             x      y=       x
2. What do you know about the relationship shown by your completed                         3
   chart?                                                                     -2
                                                                              -1
3. What is the rate of change?                                                 0
                                                                               1
                                                                               2
4. Plot these coordinates on grid paper. Is the change constant or             3
   varying? Explain.




5. Complete the table of values.                                           x       y= 3x
                                                                            -2
6. What do you know about the relationship shown by your completed          -1
   chart?                                                                    0
                                                                             1
7. What is the rate of change?                                               2
                                                                             3

8. Plot these coordinates on grid paper. Is the change constant or varying? Explain.




9. Complete the table of values.

                                                                           x       y= x2 + 2
10. What do you know about the relationship shown by your completed         -2
    chart?                                                                  -1
                                                                             0
                                                                             1
11. Plot these coordinates on grid paper. Is the change constant or          2
    varying? Explain.                                                        3




Blackline Masters, Mathematics, Grade 8                                             Page 125
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 17, Constant and Varying Rates of Change with Answers

1. Complete the table of values.
                                                                                          2
                                                                             x      y=      x
2. What do you notice about the relationship shown by your completed                      3
   chart?                                                                     -2       -1.333
              Increasing by .666 each time                                    -1        -.666
3. What is the rate of change?                                                 0          0
              .666 or 2/3                                                      1        .666
                                                                               2       1.333
4. Plot these coordinates on grid paper. Is the change constant or             3       1.999
   varying? Explain.
               Constant rate of change----linear


5. Complete the table of values.                                           x       y= 3x
                                                                            -2         -6
6. What do you notice about the relationship shown by your completed        -1         -3
   chart?                                                                    0         0
      Increasing by 3 each time                                              1         3
7. What is the rate of change?                                               2         6
      Rate of change of is 3                                                 3         9

8. Plot these coordinates on grid paper. Is the change constant or varying? Explain.
               Constant rate of change ---linear




9. Complete the table of values.

10. What do you notice about the relationship shown by your completed      x       y= x2 + 2
    chart?                                                                  -2          6
       They do not increase by the same amount each time                    -1          3
                                                                             0          2
11. Plot these coordinates on grid paper. Is the change constant or          1          3
    varying? Explain.                                                        2          6
                Varying rate of change---nonlinear                           3         11




Blackline Masters, Mathematics, Grade 8                                             Page 126
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 17, Situations with Constant or Varying Rates of Change


Name ______________________________ Date ___________________ Hour ____________

Create a table of values, write equations, sketch a graph and identify the rate of change for the
situations. Tell whether the rate of change is constant or varying and explain how you know.

     1. Sam gets $5.75 an hour for babysitting his baby brother.




     2. Roderick‟s mom gives him $2 for the first hour of babysitting and then doubles his pay
        each hour he baby-sits.




     3. Ellen walks every day. It takes her fifteen minutes to walk one mile, 30 minutes to walk
        2 miles, 45 minutes to walk 3 miles.




     4. Denise started a science experiment measuring the growth of a bean plant. The plant
        grew 2 inches the first week, 9 inches the second week and 16 inches the third week.




Blackline Masters, Mathematics, Grade 8                                               Page 127
Louisiana Comprehensive Curriculum, Revised 2008
Unit 5, Activity 17, Constant and Varying Rates of Change with Answers

Create a table of values, write equations, sketch a graph and identify the rate of change for the
situations. Tell whether the rate of change is constant or varying and explain how you know.

     1. Sam gets $5.75 an hour for babysitting his baby brother.             x                 y
                                                                             1               5.75
         Constant rate of change—we added 5.75 to each ‘y’                   2              11.50
         value each time.                                                    3              17.25
                                                                             4              23.00
     2. Roderick‟s mom gives him $2 for the first hour of babysitting and then doubles his pay
        each hour he baby-sits.
                                                                          x              y
                                                                          1              2
        Rate of change varies each time—we add a different
                                                                          2              4
        number to the ‘y’ value each time.
                                                                          3              8
                                                                          4             16
     3. Ellen walks every day. It takes her fifteen minutes to            5             32
         walk one mile, 30 minutes to walk 2 miles, 45 minutes to walk 3 miles, etc.

                                                                       x               y
       Constant rate of change—we added 15 each time.                  1               15
                                                                       2               30
                                                                       3               45
     4. Denise started a science experiment measuring the
        growth of a bean plant. The plant grew 2 inches the first week, 9 inches the second
        week and 16 inches the third week.
                                                                           x              y
        Constant rate of change—we subtracted 7 each time.                 1              2
                                                                           2              9
                                                                           3             16




Blackline Masters, Mathematics, Grade 8                                                Page 128
Louisiana Comprehensive Curriculum, Revised 2008
Unit 6, Activity 1, Find that Rule




Draw the 5th arrangement in each of these patterns and complete the table of values.




      x              y
(arrangement    (perimeter)
      #)
      1
      2
      3
      4
      5




      x              y
(arrangement    (perimeter)
      #)
      1
      2
      3
      4
      5




      x              y
(arrangement    (perimeter)
      #)
      1
      2
      3

Blackline Masters, Mathematics, Grade 8                                                Page 129
Louisiana Comprehensive Curriculum, Revised 2008
Unit 6, Activity 1, Find that Rule

     4
     5                     A

                                1            2           3            4




                            B



                                    1         2      3                4




                            C

                                        1        2
                                                         3
                                                                  4




Blackline Masters, Mathematics, Grade 8                      Page 130
Louisiana Comprehensive Curriculum, Revised 2008
    Unit 6, Activity 1, Find that Rule




    D



                                     2                     3
             1



          x                 y
    (arrangement       (perimeter)
          #)
          1
          2
          3
          4
          5




E


    1              2                 3                 4



          x                 y
    (arrangement       (perimeter)
          #)
          1
          2
          3
          4
          5




    Blackline Masters, Mathematics, Grade 8                    Page 131
    Louisiana Comprehensive Curriculum, Revised 2008
Unit 6, Activity 1, Find that Rule


Complete the tables below using the patterns A, B, C, and E. Notice that y is the area of the
arrangement in this section

     Pattern A                 Pattern B                 Pattern C                Pattern E
      x        y               x         y               x         y              x         y
(arrangement (area       (arrangement (area)       (arrangement (area)      (arrangement (area)
      #)       )               #)                        #)                       #)
      1                        1                         1                        1
      2                        2                         2                        2
      3                        3                         3                        3
      4                        4                         4                        4
      5                        5                         5                        5


Review the values in the tables, then write the rules for finding perimeter and/or area below.


  Pattern   Rule for pattern for       Rule for pattern for
            finding perimeter          finding area


    A


    B


    C

            Rule for finding the number of dots in pattern
    D


    E




Blackline Masters, Mathematics, Grade 8                                         Page 132
Louisiana Comprehensive Curriculum, Revised 2008
     Unit 6, Activity 1, Find that Rule with Answers


       Pattern    Sketch the 5th arrangement     Rule for pattern for      Rule for pattern for
                                                 finding perimeter         finding the area


         A                                       y = 2x + 2                y=x


         B                                       y = 2x + 8                y=x +3


         C                                       y = 4x + 8                y = 2x + 1



                                                 y = 2x + 3
         D



         E                                       y = 4x + 2                y = x2 + 1




     Perimeters
   Pattern A             Pattern B                Pattern C              Pattern D              Pattern E
     x        y           x         y               x        y           x          y            x         y
(arrang. #) (P)      (arrang. #) (P)           (arrang. #) (P)      (arrang. #) (#dots)     (arrang. #) (P)
     1        4           1        10               1        8           1          5            1         6
     2        6           2        12               2       12           2          7            2        10
     3        8           3        14               3       16           3          9            3        14
     4       10           4        16               4       20           4         11            4        18
     5       12           5        18               5       24           5         13            5        22

     Areas

          Pattern A              Pattern B                     Pattern C                Pattern E
          x         y            x         y                   x          y             x          y
     (arrang. #) (area)     (arrang. #) (area)            (arrang. #) (area)       (arrang. #) (area)
          1         1            1         4                   1          3             1          2
          2         2            2         5                   2          5             2          5
          3         3            3         6                   3          7             3         10
          4         4            4         7                   4          9             4         17
          5         5            5         8                   5         11             5         26


     Blackline Masters, Mathematics, Grade 8                                              Page 133
     Louisiana Comprehensive Curriculum, Revised 2008
Unit 6, Activity 1, More Patterns and Rules

Name ______________________________ Date _____________ Hour __________




   A

        1                     2                         3                4




   B


        1                 2                                 3

x (arr. #)   y (# tile)           x (arr. #)   y (# tile)
    1                                 1
    2                                 2
    3                                 3
    4                                 4
    5                                 5


1. How many tiles will be in the 5th arrangement of pattern „A‟? Explain.



2. Explain the rule for the number of tiles that will be in the nth arrangement of pattern „A‟?



3. How many tiles will be in the 4th arrangement of pattern „B‟?



4. Explain the rule for the number of tiles that will be in the nth arrangement of pattern „B‟?


5. Make a graph of one of these patterns. Explain the pattern that the graph of the pattern
   creates (i.e., linear or not).

Blackline Masters, Mathematics, Grade 8                                               Page 134
Louisiana Comprehensive Curriculum, Revised 2008
Unit 6, Activity 1, More Patterns and Rules with Answers


                                                                                          x (arr. #)        y (#
                                                                                                            tile)
                                                                                                1              2
                                                                                                2              4
   A                                                                                            3              8
                                                                                                4             16
        1                                           3                     4
                                                                                                5             25
                            2




                                                                                          x (arr. #)        y (#
                                                                                                            tile)
   B                                                                                            1              3
                                                                                                2              9
                                                                                                3             27
         1              2                                  3                                    4             81
                                                                                                5            243



1. How many tiles will be in the 5th arrangement of pattern „A‟? Explain.

There will be 32 tiles in the 5th arrangement.

2. Explain the rule for the number of tiles that will be in the nth arrangement of pattern „A‟?

The rule is powers of 2 and the nth arrangement the number of tiles would be 2n.

3. How many tiles will be in the 4th arrangement of pattern „B‟?

There will be 81 tiles in the 4th arrangement.

4. Explain the rule for the number of tiles that will be in the nth arrangement of pattern „B‟?
                                                                           16




                                     n
The rule is the powers of 3 so y = 3                                       14




5. Make a graph of one of these patterns. Explain the                      12




   pattern that the graph of the pattern creates (i.e., linear             10




   or not). The graph is not linear.                                       8




                                                                           6




                                                                           4




                                                                           2




                                                                   -5              5       10          15




Blackline Masters, Mathematics, Grade 8                                                Page 135
Louisiana Comprehensive Curriculum, Revised 2008
Unit 6, Activity 2, Use That Rule

Name _______________________________ Date _______________ Hour ________


   a.   Write the rule that represents each of the phrases below.
   b.   Sketch the first three figures in an arrangement that represents the rule.
   c.   Make a table of values to represent the first 10 arrangements in each pattern.
   d.   Identify and graph one linear and one exponential pattern.

   1. Four times a number plus one.




   2. A number squared minus one.




   3. Two raised to the power of the figure number plus three.




   4. A number plus five.




   5. Three times a number minus two




Blackline Masters, Mathematics, Grade 8                                                  Page 136
Louisiana Comprehensive Curriculum, Revised 2008
Unit 6, Activity 2, Use That Rule with Answers

   a.   Write the rule that represents each of the phrases below.
   b.   Sketch the first three figures in an arrangement that represents the rule.
   c.   Make a table of values to represent the first 10 arrangements in each pattern.
   d.   Graph one linear and one exponential pattern.

   1. Four times a number plus one.

Rule: 4x + 1
Answers for chart: (1,5); ( 2,9); (3,13); (4,17); (5,21); (6,25); (7,29); (8,33); (9,37);
(10,41)

   2. A number squared minus one.

Rule: x2 - 1
Answers for chart: (1,0); (2,3); (3,8); ( 4,15); (5,24); (6,35); (7,48); (8,63); (9,80); (10,99)

   3. Two raised to the power of the figure number plus three.

Rule: 2x + 3
Answers for chart: (1,5); (2, 7); (3,12); ( 4, 19);( 5,28); ( 6, 39);( 7, 52);( 8, 76); (9, 84); (10,
103)

   4. A number plus five.

Rule: x + 5
 Answers for chart: ( 1, 6);   (2, 7); (3,8); (4, 9); ( 5, 10); (6, 11); (7, 12); (8, 13); ( 9, 14);
(10, 15)

   5. Three times a number minus two

Rule: 3x -2
Answers for chart: (1, 1); ( 2, 4); ( 3, 7); ( 4, 10); (5, 13); (6,16); ( 7,19); (8,22); ( 9, 25);
(10, 28)




Blackline Masters, Mathematics, Grade 8                                                  Page 137
Louisiana Comprehensive Curriculum, Revised 2008
Unit 6, Activity 3, Practice with Rules

Name ______________________________ Date _______________ Hour ______________

Find the missing numbers in each sequence below. Write a rule that could represent the
sequence. HINT: Make a table with the x values representing the arrangement numbers.

   a) 3, 5, 9, 17, ______, ______, ______, ______      RULE:




   b) 2, 5, 8, 11, ______, ______, ______, ______      RULE:




   c) 3, 6, 11, 18, ______, ______, ______, ______     RULE:




   d) 6, 7, 8, 9, 10, ______, ______, ______, ______     RULE:




   e) ______, ______, ______, ______ , 18, 22, 26, 30, ______, ______, ______, ______


   RULE:




Blackline Masters, Mathematics, Grade 8                                           Page 138
Louisiana Comprehensive Curriculum, Revised 2008
Unit 6, Activity 3, Practice with Rules with Answers

Find the missing numbers in each sequence below. Write a rule that could represent the
sequence. HINT: Make a table with the x values representing the arrangement numbers.

   a) 3, 5, 9, 17,           33, 65, 129, 257              RULE: times 2 minus 1


   b) 2, 5, 8, 11,           14, 17, 20, 23                RULE: add three to previous value


   c) 3, 6, 11, 18,          27, 38, 51, 67                RULE: add the next odd number


   d) 6, 7, 8, 9, 10,        11, 12, 13, 14, 15,           RULE: add one to each number


   e) 2, 6, 10, 14,          18, 22, 26, 30,               34, 38, 42, 46

   RULE:
The numbers differ by 4. Subtract 4 to find numbers to the left of a given number. Add 4 to find
numbers to the right of a given number.




Blackline Masters, Mathematics, Grade 8                                             Page 139
Louisiana Comprehensive Curriculum, Revised 2008
Unit 6, Activity 4, Real Rules Car Mileage Chart

http://www.fueleconomy.gov/feg/FEG2004_GasolineVehicles.pdf

      Type of vehicle                  Trans   Engine   Mileage/   Annual      Abbreviation
                                       type/   size     city/hwy   fuel cost   s/codes
                                       speed




Blackline Masters, Mathematics, Grade 8                                            Page 140
Louisiana Comprehensive Curriculum, Revised 2008
 Unit 6, Activity 4, Real Situations with Sequences

 Name ___________________________ Date _________________ Hour _____________

    1. Sam‟s dad drives an Acura NSX that can go 255 miles on
       a tank of gas. Suppose Sam‟s dad‟s car has a 15 gallon
       tank. Make a table to show how many miles he can travel
       on 5, 10, 15, 20, and 25 gallons of gasoline. Write a rule
       and graph your results.




    2. Julie‟s dad drives a BMW Roadster, and he can travel
       324 miles on a tank of gas. The table below shows the number of miles he can travel at
       given distances. Determine the size of his gasoline tank. Complete the chart, write a rule
       and graph your results.
                                                   #gallons     5    8       11      14       18
                                                    # miles    90   144     198
                                                   traveled




    3. Jeremy wanted to mail a letter that weighed 10 ounces. He
       looked up the charges for the US Post Office and found that they
       charged $0.37 for the first ounce and $0.23 for each additional
       ounce for first class mailings. Make a table, then write the rule
       that will help Jeremy find the amount he will have to pay. Plot a
       graph showing the cost for a letter weighing 1 ounce, 5 ounces,
       10 ounces, and 15 ounces.

    4. Susan wanted to go on a trip with her friend‟s family over spring
       break. Her parents told her she could if she worked to earn part
       of the money. Susan needs $500 to go on the trip and she
       already has $25.00. Her parents told her that they would double the amount she makes
       each week babysitting. If Susan makes $8.25/hour babysitting and works 4 hours the first
       week, 5 hours the second week, 3 hours the third week, 6 hours the fourth week, 5 hours
       the fifth week and 7 hours the sixth week, will she have enough money for the trip?

Week #          0          1         2          3          4          5          6
Amount $
   Susan‟s total

 Blackline Masters, Mathematics, Grade 8                                             Page 141
 Louisiana Comprehensive Curriculum, Revised 2008
Unit 6, Activity 4, Real Situations with Sequences


   5. The U. S. Post Office will not accept a letter that weighs more than 13 ounces using first
      class rates given in problem #3. Any package or letter weighing more than 13 ounces
      will be charged priority mail rates. The rates for local zones are given below:
  Weight in         1 pound        2 pounds           3 pounds         4 pounds       5 pounds
   pounds
   Charge            $3.85            3.95              4.75              5.30          5.85
      Write a rule and make a graph of the charges per pound for priority mailing. Describe the
      relationship.

   6. Find the slope or rate of change of each linear graph below.




                 (-1, 1)
                                                                                            (3, 1)




                (-2, -2)

                                                                        (-2, -4)




                                                             y




   7. The roof of an A-frame cabin slopes from
      the peak of the cabin down to the ground.
      It looks like the letter A when viewed
      from the front or the back. The equation y
      = -3x + 15 can model the relationship                          Model of one half of roof
      formed by one side of the roof. For a                          of an A-frame house.

      point (x,y) on the roof, x is the horizontal
      distance in feet from the center of the base
      of the house, and y is the height of the roof
      in feet. Make a table to represent different
      points along the roof and graph the
      equation. Find the slope or rate of change.


                                                                                                     x




Blackline Masters, Mathematics, Grade 8                                                  Page 142
Louisiana Comprehensive Curriculum, Revised 2008
Unit 6, Activity 4, Real Situations with Sequences with Answers


1. Sam‟s dad drives an Acura NSX that can go 255 miles on a tank of gas. Suppose Sam‟s
   dad‟s car has a 15 gallon tank. Make a table to show how many miles he can travel on 5, 10,
   15, 20, and 25 gallons of gasoline. Write a rule and graph your results.
                                   Changed by 5
                                             # gallons      5      10       15  20     25
                                             (x)
                                             # miles (y) 85        170      255 340    425
                                    Changed by 85
       CONSTANT RATE OF CHANGE              change in y value = Slope Slope = 85/5
                                            change in x value


2. Julie‟s dad drives a BMW Roadster, and he can travel 324 miles on a tank of gas. The table
   below shows the number of miles he can travel at given distances. Determine the size of his
   gasoline tank. Complete the chart, write a rule and graph your results.
                                                    Number of          5       8      11       14  18
                                                       gallons
                                                    Number of         90      144    198      252 324
                                                   miles traveled
       CONSTANT RATE OF CHANGE                change in y value = Slope Slope = 54/3
                                              change in x value
3. Jeremy wanted to mail a letter that weighed 10 ounces. He looked up the charges for the US
   Post Office and found that they charged $0.37 for the first ounce and $0.23 for each
   additional ounce for first class mailings. Make a table then write the rule that will help
   Jeremy find the amount he will have to pay. Plot a graph showing the cost for a letter
   weighing 1 ounce, 5 ounces, 10 ounces, and 15 ounces

Ounces        1             5             10            15            20
Amt paid      .37           1.29          2.44          3.59          4.74

   Expression .37 + .23(x -1) Notice The rate of change is not the same(for the x value) from 1
   ounce to 5 ounces and 5 to 10, but it is constant from 5 to 10 and 15 to 20, therefore the( y
   value) is not constant from .37 to 1.29, but becomes constant from 1.29 to 2.44 and 3.59 to
   4.74.
   4. Susan wanted to go on a trip with her friend‟s family over spring break. Her parents told
       her she could if she worked to earn part of the money. Susan needs $500 to go on the trip
       and she already has $25.00. Her parents told her that they would double the amount she
       makes each week babysitting. If Susan makes $8.25/hour babysitting and works 4 hours
       the first week, 5 hours the second week, 3 hours the third week, 6 hours the fourth week,
       5 hours the fifth week and 7 hours the sixth week, will she have enough money for the
       trip. Yes, she would have enough money.
   5.
   Week #             0          1          2          3          4          5          6
   Amount $          25         66       82.50       49.50       99        82.50     115.50
        Susan‟s total           91      173.50      223.00      322       404.50       520

Blackline Masters, Mathematics, Grade 8                                            Page 143
Louisiana Comprehensive Curriculum, Revised 2008
Unit 6, Activity 4, Real Situations with Sequences with Answers


   5. The U. S. Post Office will not accept a letter that weighs more than 13 ounces using first
      class rates given in problem #3. Any package or letter weighing more than 13 ounces
      will be charged priority mail rates. The rates for local zones are given below:
  Weight in         1 pound        2 pounds           3 pounds         4 pounds          5 pounds
   pounds
   Charge            $3.85            3.95              4.75              5.30             5.85
      Write a rule then make a graph of the charges per pound for priority mailing. Describe
      the relationship.
      Varying rate of change---pounds have a constant rate of change, but the change does
      not---3.85 to 3.95 is a change of .10, 3.95 to 4.75 is a change of .80, 4.75 to 5.30 is a
      change of .55 and 5.30 to 5.85 is a change of .55

   6. Find the slope or rate of change of each linear graph below.




                     (-1, 1)
                                                                                     (3, 1)




                    (-2, -2)

                                                                   (-2, -4)




                 Slope of 1                                                   Slope of 1

   7. The roof of an A-frame cabin slopes from the peak of            y

      the cabin down to the ground. It looks like the letter A
      when viewed from the front or the back. The equation
      y = -3x + 15 can model the relationship formed by one
      side of the roof. For a point (x,y) on the roof, x is the
      horizontal distance in feet from the center of the base              Model of one half of roof
                                                                           of an A-frame house.
        X        Y              of the house, and y is the
                                height of the roof in feet.
        5         0
                                Make a table to represent
        4         3             different points along the roof
                                and graph the equation. Find
        3         6
                                the slope or rate of change.
        2         9                                                                                  x



        1        12     The x value goes down 1 each time, the y value goes up 3. The slope is
                        -3.
        0        15

Blackline Masters, Mathematics, Grade 8                                                       Page 144
Louisiana Comprehensive Curriculum, Revised 2008
Unit 6, Activity 5, Name that Term

Name _______________________________ Date ______________ Hour ______

1. Dominique sketched the following dot pattern to represent the number of quarters he saved by
the end of each week during the summer. Make a table to represent the weeks w and the number
of quarters q.

       a) Find the number of quarters Dominique will save during the 5th week.




      arrangement       arrangement             arrangement                    arrangement
      1                 2                       3                              4




       b) Write a rule to represent Dominique‟s savings plan.




       c) During which week will Dominique save 122 quarters? Explain.




       d) How much money will Dominique have at the end of 12 weeks if he does not spend
       any of his savings? Explain.




       2. 68 is what term of the sequence given by –2, 3, 8, . . .? Explain.




Blackline Masters, Mathematics, Grade 8                                               Page 145
Louisiana Comprehensive Curriculum, Revised 2008
Unit 6, Activity 5, Name that Term with Answers

1. Dominique sketched the following dot pattern to represent the number of quarters he saved by
the end of each week during the summer. Make a table to represent the weeks w and the number
of quarters q.

                                                                                            x      y
                                                                                        (week)   # quarters

                                                                                            1     2
                                                                                             2   5
                                                                                             3   10
     arrangement     arrangement          arrangement                   arrangement
                                                                                            4    17
     1               2                    3                             4




       a) Find the number of quarters Dominique will save during the 5th week.
       He will save 26 quarters
       b) Write a rule to represent Dominique‟s savings plan.
       The number of the week times itself plus one

       c) During which week will Dominique save 122 quarters? Explain.

       11th week. 11 x 11 = 121 + 1 = 122

       d) How much money will Dominique have at the end of 12 weeks if he does not spend
       any of his savings? Explain.

       12 x 12 + 1 = 145 quarters. 145/4 = 36 ¼ or $36.25

2. 68 is what term of the sequence given by –2, 3, 8, . . .? Explain.

   The sequence increases by 5 each time and the equation would be y = 5x – 7.
   Therefore if 68 = 5x – 7 then 75 = 5x and it would be the 15th term in the sequence.




Blackline Masters, Mathematics, Grade 8                                               Page 146
Louisiana Comprehensive Curriculum, Revised 2008
Unit 6, Activity 7, Generally Speaking

Name _________________________________ Date ________________ Hour ___________

Complete the following math grid using the sequences in column on the left.


Sequence               Rule in words         Equation       Could ‘0’ be part of the    Arithmetic
                                                            sequence?                   or
                                                                                        Geometric
2, 4, 8, 16. . .



3, 7, 11, 15, . . .



400, 299, 198, . . .



1, 4, 7, 10 . . .



3, 9, 27, 81 . . .




Blackline Masters, Mathematics, Grade 8                                                Page 147
Louisiana Comprehensive Curriculum, Revised 2008
Unit 6, Activity 7, Generally Speaking with Answers

Sequence               Rule in words            Equation             Could ‘0’ be       Arithmetic
                                                                     part of the        or
                                                                     sequence?          Geometric
2, 4, 8, 16. . .       multiply previous term   y = 2x               ‘0’ term would     geometric
                       by 2 or powers of 2                           work it would
                                                                     start the
                                                                     sequence with
                                                                     1.
3, 7, 11, 15, . . .    add four to previous      y = 4(x - 1)+3 or   ‘0’ would not      arithmetic
                       term                     y= 4x-1              work if the
                                                                     first term is 3
                                                                     because 0 + 4
                                                                     = 4.
400, 299, 198, . . .   subtract 101 from the     y = -101(x - 1)+400 ‘0’ will not be    arithmetic
                       previous term            or                   a term in the
                                                 y = -101x + 501     sequence
1, 4, 7, 10 . . .      triple the previous      y = 3x + 1           ‘0’ would          arithmetic
                       term and add 1                                work in the
                                                                     sequence
                                                                     because 0(3) +
                                                                     1=1
3, 9, 27, 81 . . .     Three raised to the      y = 3x               ‘0’ would          geometric
                       power of the term                             work in the
                                                                     sequence
                                                                     because 30 = 1




Blackline Masters, Mathematics, Grade 8                                                Page 148
Louisiana Comprehensive Curriculum, Revised 2008
Unit 6, Activity 8, Are You Sure?




             8, 10, 12…                                          5, 9, 13…




           2, 4, 8, 16. . .                                    4,7, 12, 19. . .




           2, 5, 8, 11. . .                                   4, 10, 16, 22. . .




                                              arrangement 1       arrangement 2   arrangement 3
    Arrangement   Arrangement   Arrangement
       #1             #2           #3




Blackline Masters, Mathematics, Grade 8                                           Page 149
Louisiana Comprehensive Curriculum, Revised 2008
Unit 6, Activity 8, Are You Sure? Directions for Activity

   1) Find the value of the 7thand 10th terms in the sequence you
      were given.

   2) Sketch a tile or dot pattern that represents your sequence.

   3) Write a rule to represent the nth term in the sequence you
      were given.

   4) Make a graph of your sequence.

   5) Write two questions from your sequence where the solution
      will be the „y’ value. Show your work on another sheet of
      paper with your correct answer.

   6) Write two questions from your sequence where the solution
      will be the „x‟ value. Show your work on another sheet of
      paper with your correct answer.




Blackline Masters, Mathematics, Grade 8                     Page 150
Louisiana Comprehensive Curriculum, Revised 2008
Unit 7, Activity 1, Family Data

 Student initials   Number of family     Age of oldest      Number of pets     Number of
                       members         child in family in                    hours you watch
                                            months                            TV in a week




Blackline Masters, Mathematics, Grade 8                                                Page 151
Louisiana Comprehensive Curriculum, Revised 2008
Unit 7, Activity 3, Graph Characteristic Word Grid

Read each descriptor and determine which type of graph can be used to determine the
information stated. Place a „Y‟ for yes and „N‟ for no in each cell.

                          Circle     Line      Box and      Scatter Bar         Stem
                          Graph      Plot      Whisker      Plot    Graph       and
                                               Plot                             Leaf
Can easily determine
percent of data
occurrences
Can easily determine
the most frequent
occurrence
Can easily determine
the median of the data

Can easily determine
the mode of the data

Can compare
relationships in data
sets
Can easily determine
where the top 25% of
the data set falls
Can identify each data
entry

Can be used to
determine the ratios

Can determine the
range of the data set

Can be used to make
predictions of
relationships in data
Can easily compare
parts of a data set to
the whole




Blackline Masters, Mathematics, Grade 8                                          Page 152
Louisiana Comprehensive Curriculum, Revised 2008
Unit 7, Activity 4, Reaction

Name ___________________________________ Date __________ Hour _________

Record the location where the meter or yard stick is caught after being dropped. Once three
times have been recorded, predict your reaction mark for trial 4 and write your prediction on the
chart. Take the 4th trial and record your reaction. Find the mean of your reaction marks for all 4
trials.

   Student        Reaction 1        Reaction 2       Reaction 3        Prediction      Reaction 4
    Name                                                               Reaction 4




What information did you use make your prediction of what would happen in the 4th trial?
Record this in your math learning log.

Use the grid on the next page to make a histogram of the class data. Put all labels on your
histogram so that it clearly represents the class data.

   .




Blackline Masters, Mathematics, Grade 8                                              Page 153
Louisiana Comprehensive Curriculum, Revised 2008
Unit 7, Activity 4, Reaction Time


                                            Reaction




         0-10 cm                 21-30 cm               41-50 cm              61-70 cm              >80 cm

                     11-20 cm                31-40 cm              51-60 cm              71-80 cm


Blackline Masters, Mathematics, Grade 8                                                              Page 154
Louisiana Comprehensive Curriculum, Revised 2008
Unit 7, Activity 5, High Cost of College

Use the data in the chart below to make a circle graph that illustrates the cost of college for the
year 2002-2003. Be sure to include tuition, books, rent, meals and personal expenses on your
circle graph.
    1) Use your protractor to draw the sections of your circle graph to the nearest degree
        measurement.
    2) Find the percent of increase in each category and determine which category had the
        greatest percent of increase from 1994 -1995 cost to the 2002 – 2003 cost.



     The table below gives detailed information on average costs for the 1994-1995
     academic year compared to the 2002-2003 academic year. The cost of attending this
     school in 2002-2003 was almost twice as much as it was eight years earlier in the
     1994-1995 academic year. Out-of-state students pay almost twice as much as state
     residents.




Blackline Masters, Mathematics, Grade 8                                                 Page 155
Louisiana Comprehensive Curriculum, Revised 2008
Unit 7, Activity 5, High Cost of College with Answers

Use the data in the chart below to make a circle graph that illustrates the cost of college for the
year 2002-2003. Be sure to include tuition, books, rent, meals and personal expenses on your
circle graph.
    1) Use your protractor to draw the sections of your circle graph to the nearest degree
        measurement.
    2) Find the percent of increase in each category and determine which category had the
        greatest percent of increase from 1994 -1995 cost to the 2002 – 2003 cost.


The table below gives detailed information on average costs for the 1994-1995
academic year compared to the 2002-2003 academic year. The cost of attending this
school in 2002-2003 was almost twice as much as it was eight years earlier in the
1994-1995 academic year. Out-of-state students pay almost twice as much as state
residents.




                                                                                               190.3% increase
                                                                                               40% increase

                                                                                               127.3% increase
                                                                                               32% increase
                                                                                               15% increase



                                                10%
                                                Personal Expenses




                                                                    33%
                                     22%                            Tuition and Fees
                                     Meals




                                                                         6%
                                                   29%                   Books and Supplies
                                                   Room Rent




                                             High Cost of College

Blackline Masters, Mathematics, Grade 8                                                       Page 156
Louisiana Comprehensive Curriculum, Revised 2008
Unit 7, Activity 6, Test Score Data

Name ____________________________ Date ___________________ Hour _________


                                                                   Student
                                                                   Number       Score
                                                                      1          77
                                                                      2          65
                                                                      3          88
                                                                      4          98
                                                                      5          78
                                                                      6          86
                                                                      7          88
                                                                      8          93
                                                                      9          91
                                                                     10          88
1) Make a stem-and-leaf plot of the data at the right.               11          83
                                                                     12          81
                                                                     13          74
2) Which measure(s) of central tendency is/are easily determined
   using a stem-and-leaf plot? Explain.
                                                                     14          62
                                                                     15          86
                                                                     16          67
                                                                     17          81
                                                                     18          85
                                                                     19          95
                                                                     20          99




Blackline Masters, Mathematics, Grade 8                                      Page 157
Louisiana Comprehensive Curriculum, Revised 2008
Unit 7, Activity 6, Test Score Data with Answers



                                                                     Student
                                                                     Number          Score
                                                                         1            77
                                                                         2            65
                                                                         3            88
                                                                         4            98
                                                                         5            78
                                                                         6            86
                                                                         7            88
                                                                         8            93
                                                                         9            91
                                                                        10            88
                              stem   leav es                            11            83
1) Make a stem-and-leaf          6 2, 5, 7                              12            81
   plot of the data at the       7 4, 7, 8                              13            74
   right.
                                 8 1, 1, 3, 5, 6, 6, 8, 8, 8            14            62
                                 9 1, 3, 5, 8, 9
                                                                        15            86
                                                                        16            67
                                      9/1 represents a score of 91
                                                                        17            81
                                                                        18            85
2) Which measure(s) of central tendency is/are easily determined
   using a stem-and-leaf plot? Explain.
                                                                        19            95
                                                                        20            99
   Mode is easily determined by the repeating digits in the leaves column. The median can be
   determined by counting the leaves and dividing by two and then finding the middle value.




Blackline Masters, Mathematics, Grade 8                                          Page 158
Louisiana Comprehensive Curriculum, Revised 2008
Unit 7, Activity 7, Reading Box and Whiskers Plots

Name ________________________________ Date ____________________ Hour ________

1. The plot below shows the number of questions that were correctly answered on a 30 question
   social studies test. Explain what you know about the results of the test from the box-and-
   whiskers plot.




                   4        10                  20
                                                                    30                  40




2. The plot below shows the results of try-outs for the marathon swim team. The participants
   had to swim laps of the pool until they were tired. Explain the results shown in the plot.




              10                    15                    20                    25




Blackline Masters, Mathematics, Grade 8                                              Page 159
Louisiana Comprehensive Curriculum, Revised 2008
Unit 7, Activity 7, Reading Box and Whiskers Plots

The following list of test scores represents the scores of the class on a recent quiz. Make a box-
and-whiskers plot that represents the data set.

        100, 70, 70, 90, 50, 90, 50, 90, 100, 50, 90, 100, 90, 50, 25, 80




4. Make two mathematical statements about the box-and-whiskers plot you drew in #3.




5. Add one or more data entries to the set of data in #3 so that the median and the lower quartile
   increase. Explain your thinking.




Blackline Masters, Mathematics, Grade 8                                               Page 160
Louisiana Comprehensive Curriculum, Revised 2008
Unit 7, Activity 7, Reading Box and Whiskers Plots with Answers

       1. The plot at the right shows the number of questions that were correctly answered on a
          40 question social studies test. Explain what you know about the results of the test
          from the box-and-whiskers plot.




              4          10                  20
                                                                 30                 40




The box-and-whiskers plot shows that the minimum number of questions missed was 0 because at
least one person got 40 correct. 50% of the class missed between 6 and 18 questions on the test,
and the median was 21 questions missed. The 25% that scored high were closer scores than the
25% that scored in the lower quartile.


       2. The plot at the left shows the results of try-outs for the marathon swim team. The
          participants had to swim laps of the pool until they were too tired. Explain the results
          shown in the plot.




             10                  15                  20                  25




The results show that 50% of the people got tired after 17 laps. The median was 17 laps, and
there must have been a large gap between the people that swam between 19 and 25 laps, because
the upper quartile shows a range of 8 laps. The least number of laps anyone swam was 10 laps.

Blackline Masters, Mathematics, Grade 8                                              Page 161
Louisiana Comprehensive Curriculum, Revised 2008
Unit 7, Activity 7, Reading Box and Whiskers Plots with Answers

      3. The following list of test scores represents the scores of the class on a recent quiz.
         Make a box-and-whiskers plot that represents the data set.

       100, 70, 70, 90, 50, 90, 50, 90, 100, 50, 90, 100, 90, 50, 25, 80




           20      30      40      50      60      70       80     90      100




      4. Make two mathematical statements about the box-and-whiskers plot you drew in #3.

          Answers will vary but should contain information about the 5 data points and the
          percent of data within the quartiles.

      5. Add one or more data entries to the set of data in #3 so that the median and the lower
         quartile increase. Explain your thinking.

          Two 100 scores would make the median increase but the lower quartile would remain
          the same. When four 100 scores are added, the median increases to 90 and the lower
          quartile increases to 60




Blackline Masters, Mathematics, Grade 8                                              Page 162
Louisiana Comprehensive Curriculum, Revised 2008
Unit 7, Activity 9, Which Display is Appropriate?


Name _________________________________ Date ________________ Hour __________




                                                             i nt erval l abel s


                                                                                   x
                                                                                   x
    1   2, 2, 4                                                                    x       x
    2   4, 5, 6                                                                    x   x   x




Choose an appropriate graph type for each of the situations below. Explain your choice.

   1. Susie wants to display the amount of money spent each month on snacks. She wants her
      display to be used to find the median and the range of money spent on snacks. Which
      type of data display will be appropriate? Explain.


   2. Mrs. Smith wants the students to show the test scores for the class, arranged in intervals.
      Which type of data display will be appropriate? Explain.



   3. Jerrika wants to show that the heights of students in her class are related to their shoe
      size. Which type of data display will be appropriate? Explain.



   4. Coach wants to display the number of 2-point shots scored by individual members of the
      basketball team as compared to the whole team through the first half of the season.
      Which type of data display will be appropriate? Explain.




Blackline Masters, Mathematics, Grade 8                                                        Page 163
Louisiana Comprehensive Curriculum, Revised 2008
Unit 7, Activity 9, Which Display is Appropriate with Answers

Name _________________________________ Date ________________ Hour __________




                                                             i nt erval l abel s


                                                                                   x
                                                                                   x
    1   2, 2, 4                                                                    x       x
    2   4, 5, 6                                                                    x   x   x




Choose an appropriate graph type for each of the situations below. Explain your choice.

   1. Susie wants to display the amount of money spent each month on snacks. She wants her
      display to be used to find the median and the range of money spent on snacks. Which
      type of data display will be appropriate? Explain.

        She can use a stem and leaf plot, a line plot, or a box-and-whiskers plot . The box and
        whiskers will easily show the median and range because they are data points. The line
        plot and the stem and leaf both show individual data values chronologically and can be
        used to find the mean and range.

   2. Mrs. Smith wants the students to show the test scores for the class, arranged in intervals.
      Which type of data display will be appropriate? Explain.

        The plot that shows intervals is the histogram.

   3. Jerrika wants to show that the heights of students in her class are related to their shoe
      size. Which type of data display will be appropriate? Explain.

        A scatterplot compares two variables and would be best.

   4. Coach wants to display the number of 2-point shots scored by individual members of the
      basketball team as compared to the whole team through the first half of the season.
      Which type of data display will be appropriate? Explain.

        A circle graph would compare the parts to the whole with percentages of the whole.




Blackline Masters, Mathematics, Grade 8                                                        Page 164
Louisiana Comprehensive Curriculum, Revised 2008
Unit 7, Activity 10, Match the Data and Situation - Set A

Cut the cards apart for activity 6
1                                            2


                                                   distance from home




                                                                               time


3                                            4


                                                           Time it Takes to Walk to School (minutes)

                                                    F                                                  M   F
                                                  F F                                                  M F M
water                                        F F M M                     F                             F M M
                                             M F F M F           F    M M            M                 M F M
level
                                             5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22          23 24 25




                          tim e


5                                            6



             dis tance from hom e
                                                              dis tance from hom e




                                    tim e
                                                                                      tim e




Blackline Masters, Mathematics, Grade 8                                                           Page 165
Louisiana Comprehensive Curriculum, Revised 2008
Unit 7, Activity 10, Match the Data and Situation- Set B

A                                            B

     I had just left home for
     school when I realized that I                       I started out calmly
     had left my books. I                                but I sped up
     returned home to get them                           when I realized I
     and hurried off to school.                          was going to be late.




C                                            D



                                                     #
                                                          12

                                                     s    10
                                                     t
                                                          8
                                                     u
                                                     d    6
                                                     e
                                                     n     4
                                                     t
                                                     s    2

                                                          0
                                                               0-9   10 - 19 20 - 29

                                                                 tim e (minutes )




E                                            F

    I left home walking at a steady pace,          I began to run water for my dog‟s
    and then I sped up before stopping to          bath when I realized the water was
    rest. I started walking again before I         a little too warm. I let the water
    looked at my watch and realized I had          cool off briefly before putting the
    better get home soon.                          dog into the water and bathing
                                                   him. The dog got out of the tub,
                                                   and I let the water out.




Blackline Masters, Mathematics, Grade 8                                                Page 166
Louisiana Comprehensive Curriculum, Revised 2008
Unit 7, Activity 11, Situations to Graphs

   Situations 1 – 6 for one group (remind them not to use numbers on their graphs because they
   will want another group to match the graph and situation)
   1. She walked slowly for 3 seconds. Then she stood still for 4 seconds. Suddenly, during
      the last 3 seconds, she went quite fast.
   2. She ran fast for 3 seconds, then slowly for 4 seconds. I took her 5 seconds to return to
      her starting point.
   3. He waited for 4 seconds before starting to walk slowly. He walked for a few seconds and
      then stopped.
   4. She left home running really fast. She went at that rate for 3 seconds, but then she
      realized that she had forgotten her book. She stopped for a couple of seconds to decide
      what to do. Then she decided that it would be too late anyway, so she went back home
      slowly.
   5. From his house to the corner store is 10 meters. He ran to the store, spent 1 second
      looking at the CLOSED sign, and walked slowly back to his house.
   6. She decided to cross the park walking slowly at first but going faster and faster each step.
      It took her 5 seconds to get to the other side.


   Situations 7 - 12 for one group (remind them not to use numbers on their graphs because they
   will want another group to match the graph and situation)
   7. He was going home, not in a rush. As he stepped into the street, he realized that a car
      was coming. He waited for the car, then ran across the street. As soon as he got to the
      other side of the street, he walked slowly again.
   8. At first the old man walked very slowly, as if he were tired. Suddenly, when he was next
      to us, he started to run amazingly fast. After a few seconds he stopped and walked back
      to say, “I surprised you, didn‟t I?”
   9. The dog ran off to catch the stick that his owner had thrown. As the dog grabbed the
      stick, he saw a rabbit. The dog held very still for a moment. Then, instead of running
      back to his owner, he crept very slowly toward the rabbit. When the dog was close to the
      rabbit, he jumped forward at great speed.
   10. First she went fast, at a steady pace. Then, at around 5 meters, she started to slow down.
       She went slower and slower until she stopped. She stood still for 4 seconds. Finally she
       walked slowly and steadily for a while.
   11. Trying not to wake anyone up, she walked very slowly with small steps. Once she got to
       the door, she began to run faster and faster. After 3 seconds of running, she stopped and
       sat down.
   12. Imagine someone walking back and forth two times between the chalkboard and her
       desk. She always walks quickly toward the board and slowly toward the desk. At the
       end, she stands for 3 seconds.




Blackline Masters, Mathematics, Grade 8                                             Page 167
Louisiana Comprehensive Curriculum, Revised 2008
Unit 7, Activity 11, Graphing Situations Opinionnaire



             What are Your Opinions About Graphs Representing Situations?

Directions: After each statement, write SA (strongly agree), A (agree), D (disagree), or SD
(strongly disagree). Then in the space provided, briefly explain the reasons for your opinions.


   1. The scale used on graphs can make the representation appear to show very different
      interpretations of data.

       Your reasons:




   2. A data set can be used to show the median best would be the box-and-whiskers plot.

       Your reasons:




   3. There is not a graph that easily shows the mode of data.

       Your reasons:




Blackline Masters, Mathematics, Grade 8                                              Page 168
Louisiana Comprehensive Curriculum, Revised 2008
Unit 7, Activity 12, Data Extremes

Name _______________________________________ Date _____________ Hour _________

Solve the following.

   1. Samantha can watch only 50 hours of television every fourteen days. On school nights
      she can watch television for no more than 3 hours. Make a table showing possible
      numbers of hours that Samantha watches television each night. Use at least 4 different
      lengths of time she watches television each day in your table.


           a. What are the mean, median and mode of the length of time Samantha watches
              television in 14 days?


           b. Will the mean, median and/or mode be the same no matter what the list of hours
              as long as the total is 50 hours? Explain your answer.


   2. The set of numbers below represents the number of pets that each student in Mr. Daily‟s
      homeroom has at home.

              7, 7, 3, 0, 8, 4, 3, 0, 0, 1, 2, 7, 0, 7, 4, 1, 0, 2, 4, 2, 3

       a. Add one number to the data that will increase the mean so that it is greater than the
          median of the data for Mr. Daily‟s class. Explain how you know your choice satisfies
          the requirements.



       b. Which of these measures of central tendency would best represent the number of pets
          that the students have in Mr. Daily‟s class? Explain why.

   3. Grace counted the number of blooms on each of the rose bushes in her grandmother‟s
      garden. The number of blooms on each of the bushes are listed below.
             10, 15, 11, 14, 12, 10, 15, 11, 12, 13, 14

         a.   When Grace showed her grandmother the mean average of the number of blooms
              was about 12 ½ blooms, her grandmother said that it could not be true because
              she had determined the mean average number of blooms to be 20 blooms. She
              asked Grace if she had checked the one bush on the back side of the garage. Find
              the number of blooms that the one remaining rose bush must have had if
              grandmother were correct.




Blackline Masters, Mathematics, Grade 8                                           Page 169
Louisiana Comprehensive Curriculum, Revised 2008
Unit 7, Activity 12, Data Extremes with Answers

Solve the following.

   1. Samantha can watch only 50 hours of television every fourteen days. On school nights
      she can watch television for no more than 3 hours. Make a list showing possible numbers
      of hours that Samantha watches television each night. Use at least 4 different lengths of
      time she watches television each day in your table.

       One possible solution: 2, 1, 2, 3, 3, 6, 6, 3, 3, 3, 2, 3, 7, 6
          a. What are the mean, median and mode of the length of time Samantha watches
             television in 14 days? Mean  3.57; median = 3; mode =3
          b. Will the mean, median and/or mode be the same no matter what the list of hours
             as long as the total is 50 hours? Explain your answer.
             The mean will stay the same, but the median and mode can be different.

   2. The set of numbers below represents the number of pets that each student in Mr. Daily‟s
      homeroom has at home.

              7, 7, 3, 0, 8, 4, 3, 0, 0, 1, 2, 7, 0, 7, 4, 1, 0, 2, 4, 2, 3

       a. Add one number to the data that will increase the mean so that it is at least 2 more
          than the median of the data for Mr. Daily‟s class. Explain how you know your choice
          satisfies the requirements.
          One solution: If 45 is added to the list, the mean is 5 and the median is 3.


       b. Which measure of central tendency would best represent the number of pets that the
          students have in Mr. Daily‟s class? Explain why.
          Answers will vary, student must justify his/her choice correctly.

   4. Grace counted the number of blooms on each of the rose bushes in her grandmother‟s
      garden. The number of blooms on each of the bushes are listed below.
             10, 15, 11, 14, 12, 10, 15, 11, 12, 13, 14

         a.   When Grace showed her grandmother the mean average of the number of blooms
              was about 12 ½ blooms, her grandmother said that it could not be true because
              she had determined the mean average number of blooms to be 20 blooms. She
              asked Grace if she had checked the one bush on the back side of the garage. Find
              the number of blooms that the one remaining rose bush must have had if
              grandmother were correct.
              If grandmother is correct, there must be about 103 blooms on the one bush behind
              the garage.




Blackline Masters, Mathematics, Grade 8                                           Page 170
Louisiana Comprehensive Curriculum, Revised 2008
Unit 8, Activity 1, Random or Biased Sampling Opinionnaire

Name _____________________________________________ Hour __________

Directions: Read each statement below and indicate whether you agree (A) or disagree (D).
Write your reason for your opinion.

__________________ A survey as to which of two playoff teams will win the championship
can never be a random sample.

Your reason:



__________________ A survey as to which movie the 8th grade students at your school would
rather watch could be a random sample if the 8th grade students in your homeroom were allowed
to vote.

Your reason:




__________________ A survey as to which lunch menu is the favorite of the middle school
students can be random if every 10th student to enter the school on Monday morning is surveyed.

Your reason:



__________________ A survey as to which type of music is the favorite of students at your
school can be random if the student council is surveyed.

Your reason:



__________________ A survey as to which type of fund raiser the 8th grade class wants to have
could be random if the PTO discussed and voted at the PTO meeting.

Your reason:




Blackline Masters, Mathematics, Grade 8                                           Page 171
Louisiana Comprehensive Curriculum, Revised 2008
Unit 8, Activity 1, Random or Biased Sampling


Directions: Determine whether statements 1 – 5 represent a method of gathering data from a
survey in a manner that is random or biased. Justify why you think the method is random or
biased.


   1. To determine which school lunches students like most, every 20th student to walk into the
      cafeteria is surveyed.


       Why?


   2. To determine what sports teenagers like, the student athletes on the girls‟ field hockey
      team are surveyed.


       Why?

   3. To evaluate the quality of their product, a manufacturer of cell phones pulls every 50th
      phone off the assembly line to check for defects.

       Why?

   4. To determine whether the students will attend a spring music concert at the school, Rico
      surveys her friends in the chorus.


       Why?


   5. To determine the most popular television stars, a magazine asks its readers to complete a
      questionnaire and send it back to the magazine.

       Why?

Directions: Answer the following questions.

   6. Brett wants to conduct a survey about who stays for after-school activities at his school.
      Who should he ask? Explain how you know that your choice is unbiased.



   7. Suppose you are writing an article for the school newspaper about some proposed
      changes to the cafeteria. Describe an unbiased way to conduct a survey of students.



Blackline Masters, Mathematics, Grade 8                                             Page 172
Louisiana Comprehensive Curriculum, Revised 2008
Unit 8, Activity 1, Random or Biased Sampling with Answers


Directions: Determine whether statements 1 – 5 represent a method of gathering data from a
survey in a manner that is random or biased. Justify why you think the method is random or
biased.

The answers given are possible answers, students may justify answer correctly looking
differently at the sample.

1. To determine which school lunches students like most, every 20th student to walk into the
   cafeteria is surveyed. random
   Why?


2. To determine what sports teenagers like, the student athletes on the girls‟ field hockey team
   are surveyed. biased

   Why?

3. To evaluate the quality of their product, a manufacturer of cell phones pulls every 50th phone
   off the assembly line to check for defects. random
   Why?

4. To determine whether the students will attend a spring music concert at the school, Rico
   surveys her friends in the chorus. biased

   Why?


5. To determine the most popular television stars, a magazine asks its readers to complete a
   questionnaire and send it back to the magazine. biased

   Why?

Directions: Answer the following questions.

6. Brett wants to conduct a survey about who stays for after-school activities at his school.
   Who should he ask? Explain how you know that your choice is unbiased.

       Student responses will vary



7. Suppose you are writing an article for the school newspaper about some proposed changes to
   the cafeteria. Describe an unbiased way to conduct a survey of students.
   Student responses will vary



Blackline Masters, Mathematics, Grade 8                                              Page 173
Louisiana Comprehensive Curriculum, Revised 2008
Unit 8, Activity 2, How Many Ways?

Name __________________________________ Hour ___________

Directions: Think back to the lesson on permutations and answer each of the following. You
can prove your answer with a tree diagram, a chart, or by counting.


A. The flag of Mexico is shown at the right. How many ways could the
Mexican government have chosen to arrange the three colors (green,
white, and red) on the flag? Prove your answer.




B. A security system has a pad with 9 digits. How many four-number “passwords” are available
if no digit is repeated?




C. Of the 10 games at the theater‟s arcade, Tyrone plans to play 3 different games. In how many
orders can he play 3 games?




D. Jack wants to play all 10 games at the theater arcade. In how many orders can he play all 10
games?




Blackline Masters, Mathematics, Grade 8                                             Page 174
Louisiana Comprehensive Curriculum, Revised 2008
Unit 8, Activity 2, How Many Ways? with Answers

Directions. Think back to the lesson on permutations and answer each of the following. You
can prove your answer with a tree diagram, a chart, or by counting.


A. The flag of Mexico is shown at the right. How many ways could the
Mexican government have chosen to arrange the three colors (green,
white, and red) on the flag? Prove your answer.

                Tree diagram
                               white        red
                   green       red          white
                                                        List
                               green        red                                                      red
                                                        green   green    white   white       red
 order of          white
                                            green       white   red     green    red         green   white
 f lag colors                  red
                                                        red     white    red     green       white   green
                               green        white
                   red
                               white        green



3x 2 x 1=
6 ways

B. A security system has a pad with 9 digits. How many four-number “passwords” is available if
no digit is repeated?

There are 9 possible 1st digits, 8 possible 2nd digits, 7 possible 3rd, and 6 possible 4th
9x8x7x6=
3,024 passwords

C. Of the 10 games at the theater‟s arcade, Tyrone plans to play 3 different games. In how many
orders can he play 3 games?

10 possible 1st, 9 possible 2nd, and 8 possible 3rd
10 x 9 x 8 =
720 orders

D. Jack wants to play all 10 games at the theater arcade. In how many orders can he play all 10
games?

10! or 3,628,800 ways




Blackline Masters, Mathematics, Grade 8                                                  Page 175
Louisiana Comprehensive Curriculum, Revised 2008
Unit 8, Activity 3, Which is it?

Name ____________________________________ Hour _____________

     Directions: Determine whether each of the following situations is a permutation or
     combination. Explain your decision on at least 5 of the situations.

  1. Choosing the arrangement of 6 glass animals on a shelf.


  2. Choosing 3 Chinese dishes from a menu.


  3. Choosing 5 friends to invite to a birthday party.


  4. Choosing a president, vice president, treasurer, and secretary from the members of the
     student council.


  5. Choosing 2 colors of paint from a paint chart to blend together for the walls in your room.


  6. Choosing the order in which to watch 3 videotapes you rented from the video store.




     Directions: Determine whether each of the following is a permutation or combination.
     Solve the problem. You may use calculators.

  7. How many ways can a coach choose the 6 starting players from a volleyball team of 13
     players?




  8. How many three-card hands can be dealt from a deck of 52 cards?




  9. You have 7 clean shirts in a laundry basket. How many ways can you fold 4 shirts and
     stack them in a drawer?




Blackline Masters, Mathematics, Grade 8                                             Page 176
Louisiana Comprehensive Curriculum, Revised 2008
Unit 8, Activity 4, Who Stole the Cookies?

     Directions: Determine whether each of the following situations is a permutation or
     combination. Explain your decision on at least 5 of the situations.

  1. Choosing the arrangement of 6 glass animals on a shelf.
     permutation

  2. Choosing 3 Chinese dishes from a menu.
     combination

  3. Choosing 5 friends to invite to a birthday party.
     combination

  4. Choosing a president, vice president, treasurer, and secretary from the members of the
     student council.
     permutation

  5. Choosing 2 colors of paint from a paint chart to blend together for the walls in your room.
     combination

  6. Choosing the order in which to watch 3 videotapes you rented from the video store.
     permutation



     Directions: Determine whether each of the following is a permutation or combination.
     Solve the problem. You may use calculators.


  7. How many ways can a coach choose the 6 starting players from a volleyball team of 13
     players?
      Combination (1716 ways) 13  12  11  10  9  8
                                  6  5  4  3  2 1



  8. How many three-card hands can be dealt from a deck of 52 cards?
     Combination (22,100 – 3 card hands)
                                               52  51  50
                                                             22,100
                                                 3  2 1

  9. You have 7 clean shirts in a laundry basket. How many ways can you fold 4 shirts and
     stack them in a drawer?
     Permutation (840 ways)

     7 654 = 840



Blackline Masters, Mathematics, Grade 8                                             Page 177
Louisiana Comprehensive Curriculum, Revised 2008
Unit 8, Activity 4, Who Stole the Cookies?

Name ___________________________________________ Hour ________________

     Jackie worked at a restaurant in the evening. She had a locker in the back where she put all
     of her personal belongings. One night she bought a big box of cookies to take to her
     grandmother the next day. She put this box of cookies in her locker so that she could take
     it home after work. When she went back to the locker at 10:00 P.M. after work, the
     cookies were gone! One of her friends saw a stranger at the lockers about 9:30 P.M.
     Jackie and her friend talked to the store manager and they were given a list of possible
     characteristics to help in identification. The list of characteristics looked like the one
     below.

     Work with your partner and determine how many different descriptions were possible for
     the cookie thief. Put your findings on a sheet of newsprint to share with the class. Make
     sure your descriptions are organized in a list, chart or diagram and that you can justify the
     total.

              Hair                           Eyes                            Height
  curly                           dark and sad                    short
  straight                        small and beady                 tall
  bald                            droopy                          average
                                  wide open and excited




Blackline Masters, Mathematics, Grade 8                                               Page 178
Louisiana Comprehensive Curriculum, Revised 2008
Unit 8, Activity 7, Dependent Events

Name _____________________________________ Hour _________________

Directions: Using the two spinners that you have made, one with three numbers and the other
with the names of four coins written in the spaces, complete the following questions.

   1. Determine the theoretical probability of spinning less than fifty cents. Show your
      thinking.


   2. Determine the theoretical probability of spinning more than fifty cents. Show your
      thinking.



   3. Determine the theoretical probability of spinning exactly fifty cents. Show your thinking.


   4. Use your two spinners and complete the experimental probability chart below.
Spin # # of      Coin     Total    >, < or Spin # # of         Coin      Total     >, < or
       coins     value    Value = to                 coins     value     Value = to
                          of spin $0.50                                  of spin $0.50

  1                                               9
  2                                              10
  3                                              11
  4                                              12
  5                                              13
  6                                              14
  7                                              15
  8                                              16
   5. Compare your experimental and theoretical results. Write a summary statement about
      how these results compare.
   6. Compare your summary statement with that of another group. How are they different?
   7. What do you think would happen to the experimental probability results if we gathered
      the results from all of the groups? Write your prediction below.




Blackline Masters, Mathematics, Grade 8                                            Page 179
Louisiana Comprehensive Curriculum, Revised 2008
Unit 8, Activity 7, Dependent Events with Answers

Name _____________________________________ Hour _________________

Directions: Using the two spinners that you have made, one with three numbers and the other
with the names of four coins written in the spaces, complete the following questions.

1. Determine the theoretical probability of spinning less than fifty cents. Show your thinking..
   The theoretical probability of spinning less than fifty cents if the suggested numbers are used
       6 1
   is     or 50%
      12 2
2. Determine the theoretical probability of spinning more than fifty cents. Show your thinking.
       The theoretical probability of spinning more than fifty cents if the suggested numbers are
                3 1
       used is  or 25%
               12 4
3. Determine the theoretical probability of spinning exactly fifty cents. Show your thinking.
       The theoretical probability of spinning exactly fifty cents if the suggested numbers are
                3 1
       used is     or 25%
               12 4

   Use your two spinners and complete the experimental probability chart below.
Spin # # of      Coin      Total   >, < or Spin # # of          Coin      Total        >, < or
        coins    value     Value = to                 coins     value     Value        = to
                           of spin $0.50                                  of spin      $0.50

   1                                                9
   2                                               10
   3                                               11
   4                                               12
   5                                               13
   6                                               14
   7                                               15
   8                                               16
               4. Compare your experimental and theoretical results. Write a summary
                  statement about how these results compare.
               5. Compare your summary statement with that of another group. How is it
                  different?
               6. What do you think would happen to the experimental probability results if we
                  gathered the results from all of the groups? Write your prediction below.




Blackline Masters, Mathematics, Grade 8                                              Page 180
Louisiana Comprehensive Curriculum, Revised 2008
Unit 8, Activity 9, Who Did It?

Name ___________________________________________ Hour_________

Devise a plan to sample contents of the bags without replacement in order to make the best
prediction based on experimental probability without looking at the contents of the bags.

When samples are examined without replacement, the sample size is constantly changing.
Suppose a red tile is selected from Bag A on the first selection, a red tile from Bag B on the first
selection, a green tile from Bag 3 on the first selection and a red tile from Bag 4 on the first
selection. Based on the information collected so far, can a good prediction be made as to the
matching bags?

1. Students record their results in the chart below by placing the color drawn from each bag and
   make a prediction after the 6th selection from each bag, justifying which bag would be
   identical to Bag A.

2. Are six trials or draws enough to give enough information to make a valid prediction? Why
   or why not?

3. Do all four bags have to be completely empty to make a valid prediction? Explain your
   thinking and results.
             Number of            Bag A        Bag B           Bag C            Bag D
               Trails
                 1
                 2
                 3
                 4
                 5
                 6
           With Replacement – Activity 10 chart. When results are gathered with
           replacement, the sample size remains the same. You will remove a tile, and
           replace that tile in the same bag.




Activity 10 questions
   4. Were your predictions the same when you collected data with replacement? Why or
       why not?



   5. Do you think you could ever get a certain prediction with replacement of the sample?
      Why?


Blackline Masters, Mathematics, Grade 8                                                Page 181
Louisiana Comprehensive Curriculum, Revised 2008
Unit 8, Activity 9, Who Did It? with Answers

Devise a plan to sample contents of the bags without replacement in order to make the best
prediction based on experimental probability without looking at the contents of the bags.

When samples are examined without replacement, the sample size is constantly changing.
Suppose a red tile is selected from Bag A on the first selection, a red tile from Bag B on the first
selection, a green tile from Bag 3 on the first selection and a red tile from Bag 4 on the first
selection. Based on the information collected so far, can a good prediction be made as to the
matching bags?

1. Students record their results in the chart below by placing the color drawn from each bag and
   make a prediction after the 6th selection from each bag, justifying which bag would be
   identical to Bag A.
2. Are six trials or draws enough to give enough information to make a valid prediction? Why
   or why not? there are only ten tiles and six of the ten out of the bag will not be enough
   unless you know what was in the bag to begin with.

3. Do all four bags have to be completely empty to make a valid prediction? Explain your
   thinking and results. For your prediction to be 100% valid, yes

             Number of            Bag A        Bag B          Bag C             Bag D
               Trails
                 1
                 2
                 3
                 4
                 5
                 6
           With Replacement – Activity 10 chart. When results are gathered with
           replacement, the sample size remains the same. You will remove a tile, and
           replace that tile in the same bag.




Activity 10 questions
   4. Were your predictions the same when you collected data with replacement? Why or
       why not? No. If percent predictions were used all were out of 10, if fractions, the
       denominator stayed the same with replacement sampling.

   5. Do you think you could ever get a certain prediction with replacement of the sample?
      Why? Answers will vary. Students should understand that unless we actually take them
      out of the bag and look at all of them, we can not make a certain prediction.



Blackline Masters, Mathematics, Grade 8                                                Page 182
Louisiana Comprehensive Curriculum, Revised 2008

				
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