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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) 7 654 = 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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