Problems of the Week 28 -...

Grade 7 • Page 82

Geometry/Measurement

28Problems of the Week

Visual

Multi-Step

Make a Good"Expression"

Problem-SolvingStrategies

What Do You Say?

Study the graph. If the trend continues, what will be the

sales figures for May?

Jim has 35 quarters. He wants to put

them in equal stacks with an odd

number of quarters

in each stack. In

how many

ways can he do

this?

Write an inequality and solve:

A number decreased by seven is less than 10.

Use the Appropriate Formula

To make batik scarves, Anna paints hot

melted wax on white fabric. The directions

Anna follows state that the wax she uses

must be at least 170°F. Anna uses a

thermometer marked in degrees Celsius. At

what reading on her thermometer should the

temperature of the wax be?

There are 11 boys and 17 girls in a class.

Write at least 2 comparisons you can

make from this information. Describe

what each comparison shows.3 cm

7 cm

4 cm

What is the surface area of this

rectangular prism?

Jan Feb Mar Apr May

250

225

200

175

150

125

100

75

50

25

Sale

s (

Thousands o

f dolla

rs)

Sales at Sprocket Industries

Jan Feb Mar Apr May

Grade 7 • Page 83

MentalMath

28

Keeping Skills Sharp

1. 1% of 85

2. (–9)2

3. 1,0000

4. 5–3

5. 8 = ? %

6. Round 614 to the nearest hundred.

7.25

35 =

?

7

8. 50% of ? = 25

9. 152

10. 6 – 2.6

1. 215 – 148 =

2. 11.05 – 6.92 =

3. 12

3 ! 2

3

5 =

4. What is 15% of $30.00?

5. Give the prime factorization of 63.

6. Find the GCF and LCM of 36 and 48.

7. Find the area of the circle.

8. Simplify: 240 ÷ [21 – (3 + 8)]

9. 21

2 + 3

1

4 + 7

3

8 =

10. Estimate the measure of each angle:

9 cm

a. b. c.

*See answer key. The Mental Math section should not be duplicated for the students.

Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________

Grade 7 • Page 84

28Visual

Multi-Step

Make A Good "Expression"


Problem-Solving Strategies

What Do You Say?

Mental Math1. 0.85

2. 81

3. 1

4.1

125

5. 800

6. 600

7. 5

8. 50

9. 225

10. 3.4

Keeping Skills Sharp1. 67

2. 4.13

3. 41

3

4. $4.50

5. 32 ! 7

6. GCF = 12, LCM = 144

7. A = 63.6 cm2

8. 24

9. 131

8

10. a. 135° b. 60° c. 180°

35 stacks of 1

5 stacks of 7

7 stacks of 5

1 stack of 35

Answer: n – 7 < 10

n < 17

Answer: C = 5

9(F – 32)

= 5

9(170 – 32)

= 5

9(138) = 76.666659

C " 77°

The thermometer would read about 77°C.

11 to 17 Shows number of boys compared to

number of girls

17 to 11 Shows number of girls compared to

number of boys

Answer: 122 cm2

Answer: about $262,500

This section provides an

oral drill for sharpening

one's mental computation.

Before each session give

these directions, "Number

your paper from 1 to 10.

Write your answer as the

questions are called out.

Each question will be

repeated one time only."

Answer Key

Grade 7 • Page 85



Visual

Multi-Step



What Do You Say?

The chart shows the

percentage of the pigs’

time spent during certain

activities within a 24 hour

period. How much time

did they spend building?45%

Building12% Picking

at wolf

10% Sleeping33% Eating

If # = * + 7, then 4# + 6 + 3* = _______.

Draw a Diagram

Jake has five t-shirts, three pairs of pants and

four pairs of shorts. How many different 2-

piece outfits can he put together? How many

shirt-pants combinations? How many shirt-

shorts combinations?

Hot and cold are opposites. In

mathematics, 5 and –5 are opposites.

Explain why 5 and –5 are called opposites.

How do you know when two numbers are

opposites?

Three Little Pigs’ Adventures

In the board game “Clue,” the players

decide which of 6 suspects, which of 9

rooms, and which of 6 weapons were

used in a murder. You have the cards

for Miss Scarlett, the ballroom, and the

knife and you take a wild

guess that Professor Plum

did it in the hall with the

rope. What is the

probability that you

are correct?

6 cm

8 cm

4 cm

5 cm

What is the surface area of this

triangular prism?

Grade 7 • Page 86

MentalMath

29


1. What percent of 15 is 6?

2. 2 yd. 1 ft. = _____ yd.

3. 32 – 12

4. 1.5(1.5 + 1.5)

5. 3.21 ! 104

6. 30% of 120

7. 125 ÷ 5 ! (#3) + 15

8. 0.125 = ? %

9. 21

2 + 3.25

10. 12.5 = ? %

1. 31 ! 14 ! 25 =

2. 0.38 ! 84.1 =

3.7

8

1

4÷ =

4. Solve for n: 17

3 =

51

n


6. Find the GCF of 32 and 48.

7. Find the area of a circle whose diameter is 42 cm.

8. Simplify: 291 – (36 – 87)7

9. Round 0.898 to the nearest tenth.

10. Estimate: )29 268


Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________

Grade 7 • Page 87

29Visual

Multi-Step




What Do You Say?

Mental Math1. 40%

2. 21

3

3. 8

4. 4.5

5. 32,100

6. 36

7. 60

8. 12.5

9. 5.75 or 53

4

10. 1,250

Keeping Skills Sharp1. 10,850

2. 31.958

3. 31

2

4. 9

5. 2 ! 32 ! 5

6. 16

7. 1,384.74 cm2

8. 648

9. 0.9

10. 9

Answer: 10 hours 48 minutes

Answer: 4(* + 7) + 6 + 3*

4* + 28 + 6 + 3*

7* + 34

1

SPSPSPSSSS

SSSS

2

SPSPSPSSSS

SSSS

3

SPSPSPSSSS

SSSS

4

SPSPSPSSSS

SSSS

5

SPSPSPSSSS

SSSS

35 outfits; 15 shirt-pants

combinations + 20 shirt-

shorts combinations.

5 and –5 are opposites because they are on

opposite sides of zero and are the same distance

from zero on the number line.

There are 5 choices of weapons, 8 choices of

rooms and 5 choices of suspects — 1

200.

Answer: 140 cm2











Answer Key

Grade 7 • Page 88



Visual

Multi-Step



What Do You Say?

Using the information

in the chart, create a

circle graph.

A rectangle has an area of 120 square

centimeters. What are the possibilities

for length and width if both are whole

numbers? Which pair gives the

smallest perimeter?

Write and solve an equation:

Juan collects stamps. A month ago he had

6 less than 2 times a dozen. How many

did he have a month ago?

Guess and Check

The volume of a rectangular prism is 36 m3.

The surface area is 72 m2. What are the

dimensions of the prism?

Without actually calculating the sum,

explain how you can decide whether the

sum of two integers is positive. How do

you decide whether the sum is negative?

How do you know when the sum will be

zero?

Colors of Pieces of Candy in a Bag

Colors

red

blue

green

purple

yellow

Frequency

III

II

IIII I

IIII

IIII II|

Find the surface area of this cylinder.

10 cm

7 cm

Grade 7 • 9

MentalMath

30


1. 2 lb. 2 oz. = ____ lb.

2. 70

3. 56.49 ÷ 7

4. 200% of 45

5. 30 ! ? = 270

6.1

2 ! 3 ! 6

7. ( - )

8. -14 + 21

9. Find the area of a triangle with base 9mm and height

16 mm.

10. 2(7 + 4)

1. 1,288 ÷ 161 =

2. 1.82 ÷ 0.28 =

3. Determine the missing number: 3, 9, 27, ____, 243

4. 125% of 104 is what number?

5. What is the prime factorization of 50?

6. Find the LCM of 45 and 50.

7. Solve for n: 40

160 =

5

n

8. Simplify: 98 – 17 – 10 + 48

9. Round 1.099 to the nearest hundredth.

10. About how many 45’s are in 6,500.


Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________

1

5

3

Grade 7 • 0

30Visual

Multi-Step




What Do You Say?

Mental Math

1. 21

8 or 2.125

2. 1

3. 8.07

4. 90

5. 9

6. 9

7. -

8. 7

9. 72 mm2

10. 22


2. 6.5

3. 81

4. 130

5. 2 ! 52

6. 450

7. 20

8. 119

9. 1.10

10. 144

Answer: 1 ! 120, 2 ! 60, 3 ! 40, 4 ! 30, 5 ! 24, 6 !20, 8 ! 15, 10 ! 12. 10 ! 12 gives the smallest

perimeter.

Answer: 2(12) – 6 = n

24 – 6 = n

18 = n

Answer: 6 m ! 2 m ! 3 m

If the number with the greatest absolute value is

positive, the sum is positive.

If the number with the greatest absolute value is

negative, the sum is negative.

If the numbers have the same absolute value but one

is positive and the other is negative, the sum is zero.

Answer: approximately 377 cm2

yellow

purple

green

blue

red











1

125

Answer Key

Grade 7 • Page 91



Visual

Multi-Step



What Do You Say?

A goat is tied to a corner of a 20 ft by

35 ft barn in the center of a grassy

field. His rope is 50 ft long.

Approximately how much area does he

have to graze?

What is the measure of $BCG?

Write and solve an equation.

Three less than the product of five and a

number equals twelve.

Make a Table

There are 12 members in a checker match.

If each member plays one game with each

of the other

members, how

many games will

be played?

Explain the steps you would use to solve

this equation.

3x + 5 = 17

AD EH

BF CG

4 m

4 m

2 m

8 m

4 m

1 m

Which of the rectangular prisms

above has the largest volume?

Explain.

A

B

D

C

E

F

G

H

95°

Grade 7 • Page 92

MentalMath

31


1. 81 + 14 + 29

2. 0.12 + 0.05 + 3.01

3.17

5

2

5–

4. 15 is what percent of 150?



7. Find the area of a 14 m by 9 m rectangle.

8. Evaluate: (86 ! 3) + (4 ! 3)


10. Estimate how far you can go on 9.6 gallons of gasoline

if your car gets 30 miles per gallon.

.


Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________

1-5 Order from least to greatest.

1. 10.1, 10.01, 11.01, 11.101, 10.101

2. 12, –3, 22, –14, 5, 0

3. 22

3

1

2, , , 2 – 2

1

4, – 2

7

12 2

5

6

4. 6.2, 6.3, –6.1, –6.01, 6.4

5. 53%, –1

2, 0.51, 50%, –0.05, –55

6-10 Compare. Write <, >, or =.

6. 6.1 61

9

7. –1.5 –1.8

8. 42 24

9.1

2

2%&'(

1

6

10. 35 53

Grade 7 • Page 93

31Visual

Multi-Step




What Do You Say?

Mental Math


Answer: 6,774 square feet

Answer: 85°

Answer: 5n – 3 =12

5n = 15

n = 3

Members Games

2 1 (1) From the table you

3 3 (2 + 1) can see the pattern.

4 6 (3 + 2 + 1)

12 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 1 =

66 games

Work backwards, subtract 5 from 17, then divide

the difference by 3.

Students could also use trial and error to solve the

equation.

Answer: Neither. They both have a volume of

32 m3. This section provides an










1. 124

2. 3.18

3. 3

4. 10%

5. 24

6. 12

7. 126 m2

8. 270

9. 1.1

10. 300 miles

1. 10.01, 10.1, 10.101, 11.01, 11.101

2. –14,–3, 0, 5, 12, 22

3. – , , ,27

12 – 2

1

4, 2

1

2 2

2

3 2

5

6

4. –6.1, –6.01, 6.2, 6.3, 6.4

5. –55, –1

2, –0.05, 50%, 0.51, 53%

6. <

7. >

8. =

9. >

10. <

Answer Key

Grade 7 • Page 94



Visual

Multi-Step



What Do You Say?

How is this graph

misleading?

90

80

70

60

50

40

30

20

0

Miles p

er

Ho

ur

Fri. Sat. Sun. Mon.

Roger babysits for 43

4 hours each

Saturday and each Sunday. He plans to

babysit for 31

2 weekends next month.

What is the total number of hours he

will babysit next month?

Write an equation and solve:

A number minus the difference of 6 and 4 is 8.

During a 10-minute period in a busy office

building, an elevator started at the ground

floor, rose 8 floors, rose 7 floors, descended

3 floors, rose 5 floors, descended 1 floor,

rose 2 floors, rose 8 floors, and descended

11 floors. On which floor was the elevator

at the end of the 10-minute period?

Your first grade little brother tells you:

“Zero is the smallest number.” Is zero the

smallest number? Are there any numbers

smaller than zero? How do you know?

Explain your answer.

What is the area of a square

with side x?

x

Daily Driving Speeds

Grade 7 • Page 95

MentalMath

32


1.3

4 1

1

3!

2. (–3)3

3. 75% of ? = 9

4. 10(2.5 + 1.5)

5. 48.6 ! 10,000

6. 42 – (–32) + 11

7. 1.6 ! 0.03

8. Simplify: 49

63

9.1

2(9 ! 8 ! 0.5)

10. Estimate: 42 ! 58

1. 305 – 249 =

2. 8.75 – 3.04 =

3. Solve for n: 30 = n

12

4. 20% of 220 is what number?



7. A parallelogram has a base of 16 meters and a height of 4 meters.

Find the area.

8. Simplify: (7 + 4 ! 3)2


10. 140 inches = ____ feet


Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________

Grade 7 • Page 96

32Visual

Multi-Step




What Do You Say?

Mental Math1. 1

2. –27

3. 12

4. 40

5. 486,000

6. 85

7. 0.048

8.7

9

9. 18

10. 2,400


2. 5.71

3. 360

4. 44

5. 23 ! 3

6. 150

7. 64 m2

8. 361

9. 3.0

10. 11 feet

The mph scale is deceptive. Because 10 is missing,

the relationship among the days is misleading. Also

the value for Friday might appear to be smaller than

it actually is.

1 weekend = 43

4 + 4

3

4 = 8

6

4 = 9

1

2 hours

31

2 weekends = _____ hours

91

2 ! 3

1

2 =

19

2

7

2 =

133

4 = 33

1

4 ! hours

Answer: n – (6 – 4) = 8

n – 2 = 8

n = 10

Answer: + 8 + 7 – 3 + 5 – 1 + 2 + 8 – 11 =

+ 8 + 7 + 5 + 2 + 8 = +30

–3 – 1 – 11 = –15

+30 – 15 = 15th floor

Zero is not the smallest number because all the

negative integers are smaller than zero. Temperature

readings below zero could be used for explanation.

Answer: 25 square units











2

3

Answer Key

Grade 7 • Page 97



Visual

Multi-Step



What Do You Say?

José and Manuel went to a restaurant to

celebrate Manuel's birthday. Manuel

ordered a $2.98 cheeseburger, a $0.99

soda and a $1.12 order of fries. José

ordered the same as Manuel. If the tax is

5% and José is paying for the entire meal,

how much will José spend all together?

Mrs. Murray’s science class is building

an uncovered compost box. How many

square feet of plywood are needed if

the box is 15 feet wide, 10 feet long

and 2 feet tall? How many square feet

of plastic are needed to cover the box?

Write and solve an equation:

Half a number is seven less than 12.

Working Backwards

Alex is conditioning for basketball. He

runs in place for 8 minutes, then does

push-ups for 2 minutes and 4 minutes of

sit-ups. Then he does ball-handling drills

for 15 minutes. If he is all finished at

3:25 p.m., when did he start?

Write a problem you can solve by making

a list. Explain why making a list is a

good strategy to use to solve the problem

you wrote.

Boy

Girl

Boy

Girl

Boy

Girl

Boy

GirlBoy

Girl

Boy

Girl

Boy

Girl

Create a story problem to match the given tree diagran.

Grade 7 • Page 98

MentalMath

33


Estimate each sum, difference, product or quotient

1. 172.5 + 25.6

2. 12.2 – 4.5

3. 123 + 270 + 698

4. 92

3 • 4

2

3

5. 151

5 – 5

4

7

6. 72 ! 49

7. 11.7 ÷ 2.8

8. 3.02 ! 15.1

9. 170 ÷ 11

10. 621

2 ÷ 12

2

3

1. 58 ! 19 =

2. 83.6 ! 42 =

3. 62

7 ÷

2

7 =

4. 21 is what percent of 60?



7. A circle has a diameter of 18 cm. Find the area (to the

nearest whole number).

8. Simplify: 16.25 – (2.5 + 3.85) ! 2.01

9. Round 3.009 to the nearest hundredth.

10. Ryan is on page 32 of a 275 page novel. If he reads 30

pages per day, about how many days will it take him to

complete the novel?


Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________

Grade 7 • Page 99

33VisualAnswers may vary.

Multi-Step




What Do You Say?

Mental MathAnswers may vary.

1. 200

2. 7

3. 1,100

4. 50

5. 9

6. 3,500

7. 4

8. 45

9. 17

10. 5


2. 3,511.2

3. 22

4. 35%

5. 22 ! 3 ! 7

6. 12

7. 254 cm2

8. 3.4865

9. 3.01

10. 8 days

3

8

Answer: $10.69

Answer: 250 ft2 – plywood

150 ft2 – plastic

Answer:1

2n = 12 – 7

1

2n = 5

n = 10

3:25 p.m. – 15 min. = 3:10 p.m.

3:10 p.m. – 4 min. = 3:06 p.m.

3:06 p.m. – 2 min. = 3:04 p.m.

3:04 p.m. – 8 min. = 2:56 p.m.

or

Add the minutes for all the activities and then subtract the

total number of minutes from the finishing time.

Answers will vary.

Example: List the lunches that can be made from

these choices: 2 meats, 3 vegetables, and 2 desserts.











If there are three children in a family, what is

the probability that there are two boys and one

girl?

Probability =

Answer Key

Grade 7 • Page 100



Visual

Multi-Step



What Do You Say?

If you can have one drink, one sandwich and one

cookie, how many different combinations could you

make from this menu, without repeating?

Drink

Milk

Juice

Water

Sandwich

Tuna

Ham

Chicken

Cookie

Chocolate Chip

Peanut Butter

Sugar Cookie

Steve picked out three items at the store.

They were a shirt for $16.95, a hat for

$12.50 and shoes for $49.99. He had to

pay 6% sales tax on the items. If he

paid with a $100 bill, how much change

should he have received?

If this pool is to be 4 feet deep on one

curved end, 8 feet deep on the other

curved end and 6 feet deep elsewhere,

how many cubic feet of water is

needed to fill the pool?

Translate into an equation and solve:

Three times the sum of 5 and a number

equals eighteen.

Make a Chart

One clock chimes every 5 hours. Another

clock chimes every 6 hours. If both clocks

begin ticking at the same time, how many

hours until both clocks chime at the same

time?

Laura Jane says that 0.25 and 0.250 have

the same value. Betty Ann says they do not

have the same value. Who is correct?

Explain your choice.

5 yd.

5 yd.

5 y

d.

5 y

d.


MentalMath

34



Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________

Use the set of given measurements to answer questions 1-6.

{15 m, 11m, 10m, 16m, 11m, 10m, 13m, 14m}

1. What is the mean?

2. What is the median?

3. What is the mode?

4. What is the range?

5. If an additional measurement of 13.5 m is added to the set, how

would this affect the median?

6. How would this additional measurement affect the mode?



9. Simplify: (3.8)2 – (3.2 + 0.8) ÷ 0.4

10. 250% of 650 =

1. 42 + 53

2. 27 ÷ (-3) ! 4 + 8.5

3.5

6 +

7

12

4. 300% of 18

5. A triangle has a base of 14 meters and a height of 10 meters. Find

the area.

6. Round 11,998 to the nearest hundred.

7. 8 ! 5

8. What is 75% of 800?

9. What is the perimeter of a parallelogram with sides of 25 feet and

30 feet?

10. 169

1

4


34Visual

Multi-Step




What Do You Say?

Mental Math

Keeping Skills Sharp1. 12.5 m

2. 12 m

3. two modes 10 and 11 (bimodal)

4. 6 m

5. the median changes to 13 m

6. no change

7. 2 ! 3 ! 11

8. 90

9. 4.44

10. 1,625

Answer: 27 combinations

Answer: $15.79

Answer: 2,409.75 ft3

Answer: 3(5 + n) = 18

n = 1

Clock 1 5 10 15 20 25 30 35

Clock 2 6 12 18 24 30 36 42

30 hours until the clocks chime simultaneously.

An alternative strategy for solving the problem

would be to determine the LCM.

Laura Jane is correct. Students may use a fraction to

show the equivalence or they may mention that the

zero in the thousandths place means no thousandths

and there are also no thousandths in 0.25.











1. 141

2. -25.5

3. 15

12

4. 54

5. 70 m2

6. 12,000

7. 42

8. 600

9. 110 feet

10. 13

Answer Key




Visual

Multi-Step



What Do You Say?

What is the probability of

picking a triangle out of the

bag?

A store sells one model of a 10-speed

bicycle for $200. Write a variable

expression for the amount of money

the store will receive if it sells b of

these bicycles. If b = 6, how much

will the store receive from the sales?

Write an equation represented by the

problem and solve:

Alice is 22 years old. She is eight years

older than Jim who is twice Sam’s age.

How old is Sam?

Working Backwards

Find the starting number on this flow chart:

??

÷ 2

– 1 7

A 15 foot ladder is propped against

the top of a house that is 12 feet tall.

How far from the house is the base

of the ladder?

Write an explanation of how to find the

surface area of a cylinder. How do you use

the circumference of the base of the

cylinder to help you find the surface area of

the cylinder?


MentalMath

35



Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________

Order from least to greatest.

6. –10, 8, 9, 0, –5, –3

7.1

2, ,

1

3,

1

4 2

3,

5

6

8. 4.6, 42

3, –4.4, –4

1

2, 0

9. 8.3, 8, 0.8, 8.2% , 8%

10. 14%, -.125, 0, .15, -1, .5

Compare. Write <, >, or =.

1. 472

3 47.75

2. –72.01 –721

25

3. 51

3 5.27

4. –0.76 –0.67

5. – 16 –4

1. 214 + 12 + (-28)

2. 0.81 + 16.99

3.17

5 –

2

5

4. 5% of what number is 20?

5. What is the prime factorization of 18?


7. Find the area of a square with sides of 1.2 meters.

8. Simplify: 62 ! (-2) + 14

9. Round 4,132 to the nearest hundred.

10. Mark owes Julie $13.75. How much change will he

receive from a $20 bill?


35Visual

Multi-Step




What Do You Say?The surface area of a cylinder is determined by finding

the sum of the areas of the cylinder's surfaces: two

circles and one rectangle.

SA = 2(area of circular base) + area of rectangle

The circumference of the base of the cylinder can be used

to determine the area of the rectangle.

Area of rectangular surface = circumference of the base

of the cylinder x the height of the cylinder.

Mental Math1. 198

2. 17.8

3. 3

4. 400

5. 2 ! 32

6. 8

7. 1.44 m2

8. 58

9. 4,100

10. $6.25

Keeping Skills Sharp1. <

2. >

3. >

4. <

5. =

6. –10, –5, –3, 0, 8, 9

7.1

4, , ,

1

3,

1

2 2

3 5

6

8. –41

2, –4.4, 0, 4.6, 4

2

3

9. 8%, 8.2%,0.8, 8, 8.3

10. –1, –.125, 0, 14%, .15, .5

Answer:

Answer: m = b ! 200

m = 6 ! 200

m = 1,200

Answer: 22 = 2n + 8

14 = 2n

7 = n

Answer: 72 = 49

+ 1 = 50

! 2 = 100

100 is the starting answer. To check fill in the

numbers; start with 100.

100 ÷ 2 = 50

50 – 1 = 49

49 = 7

Answer: 9 feet

39











Answer Key




Visual

Multi-Step



What Do You Say?

What is the probability of

spinning a multiple of 8?

12

2

16

810

6

14

4

Sasha and Gabriella went on a fishing

trip. They started out heading east of

the dock. They went 3 miles before

Sasha decided to turn north. They went

5 miles north and turned the engine off.

They drifted south for 2 miles.

Gabriella then realized that she needed

to get back to the dock quickly. They

decide to go directly to the dock with

no turning. How far is it from the point

they are now to the dock? (Round to

the nearest tenth of a mile.)

If this figure is folded along the

dotted lines, what solid shape would

be formed?

Write an equation represented by the problem

and solve:

There are 18 sea gulls circling the boat. Half

of them fly away. If 2 return how many are

left circling the boat?

Draw a Diagram

There are 30 pennies in a row. A nickel

replaces the second penny and every second

penny after it. Then a dime replaces the third

coin and every third coin after it. Next, a

quarter replaces the fourth coin and every

fourth coin after it. Finally, a fifty-cent piece

replaces the fifth coin and every fifth coin

after it. What is the value of the thirty coins in

a row?

For which of these situations would you need

to find the volume of a cylinder?

1. How much milk will the cylinder hold?

2. How much paper would it take to cover the

cylinder?

Explain your choice by telling how the

situation relates to finding the volume of the

cylinder.


MentalMath

36


1. Estimate: 18.32 – 4.689

2.1

2 • 14(6 + 7)

3. 10 ÷ 5

6

4. (2.97)0

5. 22 + 31 + 52

6. 8.1 ÷ 0.09

7. 0.625 = ? %

8.1

16

9. 25% of $80

10. 13

8 =

?

8

1. 3,840 – 69 =

2. 56.24 – 33.06 =

3. Solve for n: 26

50 100 =

n

4. 93 is 75% of what number?



7. Find the area of a circle with a radius of 3.5 feet.

8. Simplify: 63 ÷ 7 + 3 ! 5

9. Round 905 to the nearest ten.

10. -32.7 ! (-2.8) + (-27.63) ÷ 0.9 =


Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________


36Visual

Multi-Step




What Do You Say?

Mental Math1. 13 to 14

2. 91

3. 12

4. 1

5. 32

6. 90

7. 62.5

8.1

4

9. $20

10. 11


2. 23.18

3. 52

4. 124

5. 3 ! 17

6. 108

7. approximately 38.5 ft2

8. 24

9. 910

10. 60.86

Answer:

Answer: 4.2 miles

Answer: square pyramid

Answer:1

2 ! 18 + 2 = n

11 = n

1 1

5

1 1 1 1

10 25 50 10

1 1

25

1 1 1 1

10 50 25

1 1

5

1 1 1 1

50 25 10

1 1

50

1 1 1 1

10 5 25

1 1

50

1 1 1 1

10 25 505

50¢ $3.00

25¢ 1.50

10¢ .60

5¢ .20

1¢ .08

$5.38

Situation 1 requires a volume formula. Situation 2

requires a surface area formula. Volume relates to

filling an object. Surface area relates to covering or

wrapping an object.

28











Answer Key


Patterns, Relationships, and Functions

Quarter 1Number Line and

Rational Numbers

3.01

3.05

Equations/

Inequalities

3.02

3.03

3.04

Quarter 2 Quarter 3 Quarter 4

Data, Probability, and Statistics

Quarter 2Statistics

4.03

4.04

4.05

4.06

Quarter 1Histograms

4.01

4.02

Quarter 3 Quarter 4Probability

4.07

4.08

4.09

4.10

Sample Mathematics Pacing Guide - Grade 7

Number Sense, Numeration, and Computation

Quarter 1Number Line and

Rational Numbers

1.01

1.02

1.08

Integers

1.03

1.04

1.08

Quarter 2Proportions

1.05

1.08

Quarter 3Percent Applications

1.06

1.08

Quarter 4Pythagorean Theorem

1.07

1.08

Spatial Sense, Measurement, and Geometry

Quarter 1 Quarter 2Lines/Angles/

Transformations

2.01

2.02

2.03

Proportions

2.11

Quarter 3Solid Geometry

2.05

2.06

Surface Area and

Volume

2.07

2.08

2.09

2.10

Quarter 4Pythagorean Theorem

2.04

Problems of the Week 28 -...

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