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7th grade warmups 2008

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					                            7th Grade Eligible Content
                                    Warm-ups

Variables & Patterns
M7.A.3.1.1
Use the table to the right to answer the question.          Movie Ticket Prices
The Smith family consists of two adults and two
children, Ryan, age 5, and Samantha, age 3. What is         Adults                 $9.50
a good estimate of what it will cost the family to go       Child (ages 4-11)      $6.50
to the movies?                                              Child (under age 4)    Free



Use the table to the right to answer the question.          Roller Coaster Ticket Prices
The Everet family consists of two adults and three
children, Chris, age 10, Jenny, age 8, and Billy, age 2.    Adults                 $9.50
What is a good estimate of what it will cost the family     Child (ages 4-11)      $6.50
to ride the roller coaster?                                 Child (under age 4)    Free


M7.B.1.1.1
At the state track meet, Steve averaged 1 minute, 28 seconds, per lap. How long did it
take him to finish the four-lap race?

Add.
Convert answer to largest whole unit. (Example: 90 minutes = 1 hour 30 minutes)

6 hours 35 minutes + 9 hours 40 minutes

Subtract. 4 feet – 2 feet 4 inches.


1 meter = 100 centimeters. 4 meters 15 centimeters = ___ centimeters


M7.D.1.1.1
Kristi placed four cards on the table. The numbers on the cards followed a pattern. If the
pattern continues, what should be the next number?


              3         8       23        68            ?
A pattern of numbers is shown below. The pattern continues. What is the next number in
the pattern?

                                1, 4, 9, 16, 25, …

A pattern is shown below. Draw the next figure in the pattern.




Look at the pattern formed by the following figures. Which figure will appear next in the
pattern?




Look at the following number pattern. What will be the next number in the pattern?

                     1       1       1
              1, 2     , 4, 5 , 7, 8
                     2       2       2
M7.D.2.1.1

Solve for the given variable.

17b  425

28  z  56

7  y 3

22  2a



M7.D.2.2.1

Billy is 11 years older than Katelyn. Write an expression that represents Katelyn’s age if
we express Billy’s age as b years?



Emily’s mother is selling hats at the school fair. The sign on her booth listing the prices
is shown below. Write an expression that represents the cost for x number of hats.



                                       Hats
                                     1 for $7
                                    2 for $14
                                    3 for $21
                                    4 for $28



Lisa has a $100 gift certificate for a mail-order video store. She will pay $18.99 for each
DVD and $5.95 in shipping charges. How many DVDs, d, can Lisa order with her gift
certificate? Write an inequality to represent this situation.
Peter gives Ian a clue to help him guess a number.


When the number (x) is doubled the result is less than 24.
Write an inequality that represents this clue.
     Algebraic Concepts Mini-unit
     M7.A.1.2.1
           Replace the ___ with >, <, or =.
               a. 8 ___ -5
               b. 6 + 7 x 4 ___ 5 x 7
               c. 12 – 4 ___ 2 3

     M7.D.1.1.1
                   Use the pattern below to answer the question.


                   What is the next figure in this pattern?


                           A.

                           B.

                           C.


                           D.


     M7.D.2.1.2
     What is the value of the expression when y = 12; 7 y  3  y  3 ?

     If x  3 , what is the value of 5x  3 ?

     If n  9 , what is the value of 3(n  2) ?

     M7.D.3.1.1
     Daniel drove 480 km in 4 hours. If Daniel continues driving at the same speed, how long
     will it take him to drive an additional 720 km?

     It takes Jan 10 minutes to skate downtown from school. Skating at the same speed, it
     takes about 38 minutes to skate home from downtown. About how far from downtown
     does Jan live?

                       ●Downtown Area
About 2 miles



                ●School                          ● Home
Comparing & Scaling

M7.A.1.1.1
                                  1
                                    off. What is the percent of the discount for the
James buys a book that is on sale for
                                  8
price of the book? _____________________

Fill in the missing fractions/decimals and percents: (put fractions in lowest terms)

Problem #    Fraction     Decimal       Percent
1.           1
             4
2.                            0.125
3.                                      80 %
4.           2
             5
5.                                      95 %


Fill in the missing fractions/decimals and percents: (put fractions in lowest terms)

Problem #    Fraction     Decimal       Percent
1.           3
             4
2.                            0.25
3.                                      60 %
4.           4
             5
5.                                      85 %


Sally buys a sweater that was originally priced $25.00, but is now on sale for $15.00.
What percent off of the original price was the sale price? ________________________

M7.A.1.2.1
Order the following numbers from least to greatest:
          1             3
        2                                 0.643                1                  2.03
          4             8

                              2                               10
     0.99                 3                 1                                  0.875
                              3                               16
M7.A.1.2.2
Order the following numbers from greatest to least:

          52              -18               125                  1              -227

          -95              95               5                  -33              33


M7.A.1.2.3
Use the number line below to answer the question.
               A       B C D
                                                                1   7 19
                                                           2      ,   ,1    , 0.43
                                                               17   3    20
                0     1      2         3     4

Match the points on the number line with the numbers in the box


Group the equivalent fractions together (3 groups of 3 fractions)

Group A. _________,___________,______________                  12         16            3
                                                               24         24            6
Group B. _________,___________,______________                   2          6            3
                                                                3          8            4
Group C. _________,___________,______________
                                                               18          2            3
                                                               24          4           12

In the sets of numbers below, one number is not equivalent to the others. Tell which one
is not like the others and explain why.

A. 0.60         0.6             6%
B. 1/25         25%             0.25
C. 0.75         34%             ¾


M7.A.2.2.1
Write a ratio for each of the following groups of items:
Triangles to Circles            Smiley Faces to Hearts                Circles to All Shapes
M7.A.2.2.2
Solve for the variable in the following proportions.

1. 14 = _A             2. 2 = B           3.   C_ = 8__       4. _15_ = _3_
   25   100               3   27               36   24            25     D

A = _______           B = _______         C = _______      D = ______


Solve for the variable in the following proportions.
1. 8 = _A              2. 1 = B           3. C_ = 4__         4. _15_ = _3_
   25     100              3      27         56      24           45     D

A = _______           B = _______         C = _______      D = ______


Solve for the variable in the following proportions.

1. 8 = _A              2. 2 = B           3.   C_ = 4__       4. _15_ = _5_
  15   75                 3   24               56   12            75     D

A = _______           B = _______         C = _______      D = ______


M7.A.2.2.3
Which of the following proportions represent equivalent fractions?

2   30           6   24         12 140
  =                =              =
3   45          12 50           25 300


 6   27         8   72           14   75
   =              =                 =
18   81         9   64           24 120


M7.A.2.2.4
Find the unit price for each product. If the unit prices are different, indicate which
product has the lower unit price.

   1. George’s Groceries sells a half-gallon of mild for $1.75 and a full gallon of the
      same milk for $3.50

   2. S-Mart has 12-packs of Cola on sale for $2.88. Brick-Mart has 24-packs of the
      same cola at the regular price of $5.28
     3. An 8-ounce can of Tom’s Tomato Sauce is $0.48, a 15-ounce can is $0.75, and a
        29-ounce can is $1.74. Which can has the lowest unit price?
           A. the 8-ounce can
           B. the 15- ounce can
           C. the 29- ounce can
           D. Each can has the same unit price

M7.A.2.2.5
If Bobby spends $5.00 on one hat, how much would eight hats cost?

If Jill spends $15 for two shirts, how much will five shirts cost?

M7.A.3.2.1
Find the sum or difference.
 3     1               1    2                   2   1                 5   2
                                                                     
 4     6               2    7                   3   4                 6   5

 0.25 + 1.254          1.263 + 0.1              12.3-1.256             10 – 3.6

 1  3                  3 1                  3 1                   2 4
 2 1               2    3                                        
 2  4                  4 5                  5 2                   5 7

     3 2                      4
                      34 
    16 5                      5


                                        2
A blueberry muffin recipe calls for 1     cups of flour. A banana muffin recipe calls for
                                        3
    2
2     cups of flour. How much flour do you need to make both recipes?
    3


Newly cut lumber contains a lot of moisture. Before the wood is used for carpentry or
                                                                        1
construction, it is usually dried. Suppose a freshly cut board weighs 10 pounds. After
                                                                        2
                              2
drying, the board weighs 4 pounds. What was the weight of the water evaporated?
                              3

                                                 1              2
Of the three different types of horses on a ranch, are Arabians, are Thoroughbreds,
                                                 4              5
and the rest are Morgans. What fraction of the horses are Morgans?
In the 2002 World Cup, 5 of the 32 soccer teams that competed were from South
America. What percent of the teams were from South America?

An adult cat has a body mass of 3500 grams. It can eat up to 8% of its body mass in food
each day. How many grams of food can the cat eat each day?

A camel that weighs 1500 pounds can drink up to about 20% of its weight in water at one
time. About how many pounds of water can a camel that weights 1500 pounds drink at a
time?

Ms. Francis drove her car 427 miles on 15.8 gallons of gas.
To the nearest mile, how many miles per gallon is this?
What was the cost of the gasoline she used if the price was $1.96 per gallon?

M7.B.2.3.1

A map has a scale of 1 inch : 40 miles. Use the given map distance to find the actual
distance.
1) 5 inches
2) 12 inches
3) 32 inches
4)1 foot


Write the scale without units (i.e. convert to same unit of measure)
Example: 1 inch : 1 foot       Answer: 1 :12
   1) 1 inch : 4 feet
   2) 1 cm: 1 meter
   3) 1 feet : 2 yards.


You are building a model of the Viper roller coaster in California using a scale of 1 : 47.
The model is 4 feet high. How many feet high is the Viper?


M7.B.2.3.2

You are enlarging a photograph to make a poster. The poster will be similar to the
original photograph. The photograph is 6 inches tall and 4 inches wide. The poster will
be 2.5 feet wide. How tall will the poster be?

In a scale drawing, a wall is 8 centimeters long. The actual wall is 20 meters long. Find
the scale of the drawing.

A sofa is 8 feet long. In a scale drawing, the sofa is 3 inches long. Find the scale of the
drawing.
Accentuate the Negative

M7.A.2.1.1
Evaluate the expression. 87 + (36 - 11) ∙ (3 + 9)


Which of the following expressions has a value of 50?
A.    25 – 5 ÷1 + 4 - 3

B.       30 ∙ (3 ∙ 7) ÷ 10
                                   3
C.       158 – (12 + 36) ÷ 4 ∙ 3
              3
D        2 +5 ÷ 25 – 7


Simplify the expression.
                             2
9 ∙ (24 – 18) + (20 ÷ 8)

M7.A.3.2.1

4 + -6            -8 + -3              -14 – 2       14 – (-5)

5
   8           -56 ÷ -8
6


At 8 a.m. on Wednesday, the temperature was -8º. During the next 6 hours it dropped
10º. Then, during the next 6 hours it rose 3º. What was the temperature at 8 p.m.?

On Friday, the temperature changed by an average of 4º per hour for 5 hours. What was
the total temperature change during those five hours?

On Sunday, the temperature rose 2º per hour during the day. If the temperature at 6 a.m.
Sunday was 50º, what was the temperature at 2 p.m.?

Alice and Zake decided to set up for a lemonade stand. They bought lemonade mix for
$5.00, paper cups for $2.00 and one piece of poster board for $0.25. They decided to sell
their lemonade for $0.50 per cup. How many cups do they need to sell to make any profit
at all?

Walmat dropped its prices on everything in the store by $0.25 per hour for the 6 hours of
its Midnight Madness Sale. How much did the prices drop during the sale?
Megan has $80 to spend on clothes for school. After looking at the ads, she decides to
buy two pairs of jeans for $29.99 each and two tank tops for $8.18 each. Does she have
enough money to buy three new hair clips that are on sale 3 for $10?


Paula calls her grandparents long distance in California and talks for 45 minutes. The
phone company charges $0.05 per half—minute. How much does the call cost?



M7.C.3.1.1
Give the coordinates of the point
1) A                  2) B                   3) C
                                                             A




                                                                                    •B

                                                                                 •C




Plot the points in a coordinate plane.
1) P(-1, 0)

2) Q(-3,-6)

3) R (2, -4)
Identify the following
Quadrant I
Quadrant II
Quadrant III
Quadrant IV
X-Axis
Y-Axis
Origin




Name the quadrant where each point is located.

   1) S

   2) T
                                                 •S   •
                                                      U
   3) U




                                                          T•
Data Analysis & Probability Mini-unit
M7.E.1.1.1
                              Estimated Population of New Hampshire
                                         From 1630-1720
                               10
                                                                                According to this graph, during
                                                                                which 20-year period did the
                                                                                colonial population of New
      Population (in 1000s)




                                                                                Hampshire grow fastest?
                                                                                       a. 1700-1720
                                                                                       a. 1670-1690
                                                                                       b. 1650-1670
                                                                                       c. 1630-1650

                               0                                      x
                               1630                            1720
                                           Year
M7.E.2.2.1
What is the median of the following data?                       Hits per game: 0, 0, 0, 0, 1, 1, 2, 2, 3

What is the mean of the following set of data?
Points scored in 6 games: 54, 63, 81, 72, 93, 78

Fruit bars have the following prices: $0.69, $0.93, $0.66, $0.70, $0.73, $0.59, $0.70,
$0.61, $0.66, and $0.67. What is the mode?

M7.E.2.2.2
Students’ hourly wage for Burger Hut: $5.25, $5.25, $5.25, $5.25, $5.25, $6.00, $6.00,
$6.00, $6.25, $7.00, $7.00, $7.00, $13.00. Jake said that the average hourly wage is
$6.50. Some of the students disagree. They say that they make an hourly wage of $5.25.
Which better represents the ―average‖ hourly wage? Explain.

M7.E.3.1.1
A bag contains 3 red marbles and 2 blue marbles. A marble is drawn at random and
replaced. A second marble is drawn at random. What is the probability that both marbles
are red?

M7.E.3.1.2
What is the probability that the spinner will NOT land on A?

                                                   B   A
                                               B           A

                                               A           B
                                                   C   B
What is the probability of NOT rolling a 1 on a number cube?


M7.E.3.1.3
A paper bag contains 10 marbles. A marble is drawn from the bag, its color is recorded
in the chart below, and it is put back in the bag. This is repeated 20 times. Using the
results shown, what is the experimental probability of drawing a blue marble?
                           Outcome           Results from 20
                                                 Draws
                            Red                    12
                            Blue                    8

M7.E.4.1.1
This table lists the average temperatures recorded on Mount Washington over a 30-year
period. Based on the table, what is the most likely average temperature on Mt.
Washington in October?

Month                           Temperature
January                         -15
March                           -10
May                             1
July                            9
September                       4
November                        -6


Use the graph below to answer the question.

                             Cost of Popcorn
                       y
              10

              8
Cost (in $)




              6

              4

              2

              0                                          x
                   0        2        4   6     8    10
                   Number of Bags of Popcorn

According to the graph, estimate how much four bags of popcorn would cost?
     Stretching & Shrinking
     M7.A.2.2.7
     The following figures are similar. Calculate the missing side lengths.
                                                                           C


                               18
                                                             5
24            12
              in                                   6

       16               A              B      2              1            8

     M7.B.2.1.1
     Find the perimeter of the trapezoid                           8 in


                                                    3.2 in                               3.2 in


                                                                   4 in
     Find the perimeter and area of the parallelogram
     A  bh

                                                        4.2 m


                                                        8.3 m
     The square chessboard shown below has an area of 144 square inches




                                                                               What is the length, in inches,
                                                                               of one side of the chessboard?
M7.A.3.2.1
                                   3                 1
You want to paint a wall that is 8 feet high and 11 feet long. You have a can of paint
                                   4                 4
that will cover 200 square feet with one coat. Find the area of the wall. If you want to
apply two coats of paint, do you have enough paint? Explain.


M7.B.2.1.3
Perimeter of a Rectangle
P = 2l + 2w
Area of a Rectangle
A = lw

Find the perimeter and area of the rectangle


             1 cm

                                          7 cm



Find the perimeter and area of the equilateral triangle
Area of a triangle
     bh
A=
      2




Find the area of the triangle.   8 feet
    bh
A
      2

                                                                  5 ft


                                          6 ft
M7.C.1.2.1

Which of these rectangles are similar?




Name 2 figures that are congruent


        A             B         C                      E
                                          D




M7.C.1.2.2

In this diagram,   ABC and     XYZ are similar triangles. Which segment corresponds
to AC?
Which side corresponds to BC?




Triangles ABC and DEF are similar. Which side corresponds to AC ?
Filling & Wrapping
M7.B.2.1.2
What is the circumference of the circle?
C  d
                                              12 yds.




What is the area of the circle?
A  r 2                                   5 mm




What is the area of the circle?


                                             8 in




M7.C.1.1.1
Circle O is shown below.
Name a radius of this circle.




M7.C.1.1.2

The diameter of a circle is 2 in. What is the radius?

The radius of a circle is 15mm. What is the diameter?

The diameter of a circle is 20cm. What is the radius?

The radius of a circle is 9ft. What is the diameter?
M7.C.1.1.3

Name a segment parallel to AD.

        G               F

A                   D




                        E


B                   C


Name a segment perpendicular to KJ

            N                            M

    H                                K


                                         L
    I                                J

Name a segment that is skew to FG
    F            G

    A           D

                    E
 B              C

				
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