LESSON 111 Applications Using Name Division - Yolalearningtops.yolasite.com/resources/Crs1_Lessons111-120.pdfApplications Using Division (page 582) ... Round up.) ____ 2 8 vans d

Saxon Math Course 1 L111-441 Adaptations Lesson 111

L E S S O N

111 Name ©

200

7 H

arco

urt

Ach

ieve

Inc.

Applications Using

Division (page 582)

• When a division problem has a remainder, there are several ways to write the answer.

with a remainder as a mixed number as a decimal number

3 R 3 3 3 _ 4 3.75 4 )

___ 15 4 )

___ 15 4 )

______ 15.00

• Sometimes an answer with a remainder is not practical.

We may need to round the answer up or round the answer down.

Example: Fifteen children need a ride.Each car can transport 4 children. How many cars are needed?

Need 3 3 _ 4 cars.

( 3 _ 4 of a car is not a practical answer. ) We round 3 3 _ 4 cars up to 4 cars.

Example: Movie tickets cost $4.00. Jim has $15.00. How many tickets can he buy?

Jim can buy 3 3 _ 4 tickets.

( 3 _ 4 of a ticket is not a practical answer. ) We round 3 3 _ 4 tickets down to 3 tickets.

a. Ninety students were assigned to four classrooms as equally as possible. How many students were in each of the four classrooms?

4 ) ____

9 0 , , ,

b. Movie tickets cost $9.50. Aluna has $30.00. How many movie tickets can she buy? Round down.

) _________

$3 0. 0 0 tickets

c. Twenty-eight children need a ride to the fair. Each van can carry six children. How many vans are needed? Round up.

) ____

2 8 vans

d. Corrine folded an 8 1 _ 2 in. by 11 in. piece of paper in half. Then she folded the paper in half again as shown. After the two folds, what are the dimensions of the rectangle that is formed? How can you check your answer?

by Find half of each side.

I can check my answer by f

a piece of paper and measuring.

e. Kevin ordered four books at the book fair for summer reading. The books cost $6.95, $7.95, $6.45, and $8.85. Find the average (mean) price of the books.

Practice Set (page 584)

$6.95$7.95$6.45

$8.85


© 2

007

Har

cour

t A

chie

ve In

c.

1. ) ____

8 0 2. ) _____

$4 5

3. $15.60 4. 2 × 2 × 2 = 8 3 sugar cubes on each edge?

5. (5 × 103) + (4 × 101) + (3 × 100) 6. Get an in. and cm ruler.

12 in. is closest to how many centimeters?

7. • Use a piece of 1-in. grid paper. • Attach it to this worksheet. • Use the scale:

1 in. = 1 yd

8. Sum of angles in a triangle?

9. 10.

Written Practice (page 584)

, ,

Use work area.

Use work area. Use work area.


© 2

007

Har

cour

t A

chie

ve In

c.

11. 12. a. –6 + –12 =

b. –6 – –12 =

c. –12 + +6 =

d. –12 – +6 =

13. 6 1 __

4 ÷ 100 = 14. 0.3m = $4.41

15. 16. average of remaining scores

6.66.76.76.7

6.8

17. Which of the original s did

Andrea receive most frequently?

Answer:

18. area

19. verticesedges

_____

20.

Written Practice (continued) (page 585)


m =

Use work area.


© 2

007

Har

cour

t A

chie

ve In

c.

21. 3m + 1 = 100 22. ) _____

600 )

_____ 600

) _____

600 )

_____ 600

) _____

600 )

_____ 600

23. 3 shapes needed:

1 r

2 c

24. $0.89 $0.89

$0.89 $0.89

25. part

1 __________

1,000,000

part

whole 1

26.

In △ABC which angle corresponds to ∠D?

27. Which transformations would position △CDA

on △ABC? and

28. circumference

29. 10

___ 16

= 25

___ y 30. r =

50 mi ______

1 hr t = 5 hr

d = rt


∠

m =

Use work area.

Use work area.

d =y =

∙ ∙


L E S S O N

112 Name ©

200

7 H

arco

urt

Ach

ieve

Inc.

Multiplying and Dividing Integers (page 587)

• To multiply or divide two integers:

1. Multiply or divide as indicated.

2. Place a sign with the answer.

If the signs of the two numbers are the same, the answer is positive.

positive × positive = positive negative × negative = positive

If the signs of the two numbers are different, the answer is negative.

positive × negative = negative


a. (–5)(+4) =

b. (–5)(–4) =

c. (+5)(+4) =

d. (+5)(–4) =

e. +12

_____ –2

=

f. +12

_____ +2

=

g. –12

____ +2

=

h. –12

____ –2

=

Teacher Note:• Refer students to “Multiplying or

Dividing Two Signed Numbers” on page 26 in the Student Reference Guide.


© 2

007

Har

cour

t A

chie

ve In

c.

6. Use exponents.

20,510,000

1. Don’t leave any students behind.

200

3. a. (–2)(–6) = b. +6

___ –2

=

c. –6

___ –6

= d. (–2)(+6) =

4. a. –2 + –6 = b. –2 – –6 =

c. +2 + –6 = d. +2 – –6 =

5.

7. Round to the nearest cent.

$3.65 $3.65

8. ( 1 __ 2

) 2

+ 1 __

8 ÷

1 __

2 =

9. 10.


2. a. Use inches.

modelactual

___ =

___

b. each inch of the model = inches in actual

modelactual

1 in.

____ 1 in.

28 in.

______

Now convert to feet. a.

b.


( × ) + ( × ) + ( × )



© 2

007

Har

cour

t A

chie

ve In

c.

11. 12. 5 1 __

2 – m = 2

5 __

6

5

1 __

2 =

___

2 5 __

6 =

___

13. 6 ___

10 =

0.9 ___

n 14. 9x − 7 = 92

9x − 7 = 92

9x − 7 = 92

15. 0.05w = 8

16. a. bookspounds

3 ___

1 __

?

b. bookspounds

1 ___

___

?

17. v = lwh

18. mmm

1 ___

___

? 19. perimeter

20. area

21. A c has

square faces

that are the

s size.


m =

x =

Use work area.

w =

b. a.

n =


© 2

007

Har

cour

t A

chie

ve In

c.


24. H A V E 25.

26.

28. 40 number cards #1–40

multiples of 10: , , ,

One multiple of 10 is gone.

multiples of 10total cards

_____

29. area

30. 32 + 2 × 52 – 50 ÷ √___

25

32 + 2 × 52 – =

22. not a composite number

A 34 B 35 C 36 D 37

23. Round up to the nearest inch.

27. (–2, –3) and (6, –3)

a.

b.

( , )


L E S S O N

113 Name ©

200

7 H

arco

urt

Ach

ieve

Inc.

Adding and Subtracting Mixed Measures

Multiplying by Powers of Ten (page 592)

• To add or subtract mixed measures, units may need to be renamed.

• Regroup by borrowing and carrying. 5 17

Example: 6 ft 5 in.– 4 ft 8 in.

6 ft 5 in.– 4 ft 8 in.

1 ft 9 in.

• To multiply by powers of ten:

Move the decimal point to the right the same number of places as the exponent.

Examples: Write 1.2 × 103 in standard notation. 1.2 × 103 = 1.200 = 1200

Write 6.2 × 102 in standard notation. 6.2 × 102 = 6.20 = 620

• Sometimes powers of ten are written as words instead of numbers.

5.2 million means 5.2 × 1,000,000

• To write a number in standard notation:

1. If a fraction is given, change it to a decimal.

2. Write the power-of-ten word in number form and count the zeros.

3. Move the decimal point right the same number of places as zeros.

Example: Write 1 _ 2 million in standard notation.

1 __

2 = 0.5 0.5 × 1,000,000 = 500,000


a. 6 ft 5 in.+ 4 ft 8 in.

ft in.

b. 3 hr 15 min– 1 hr 40 min

hr min

Write the standard notation for each of the following numbers. Change fractions and mixed numbers to decimal numbers before multiplying.

c. 1.2 × 104 d. 1.5 million

, , ,

e. 2 1 __

2 billion (2.5) f.

1 __

4 million (0.25)

, , , ,

Teacher Note:• Refer students to “Multiplying by

Powers of Ten” on page 8 in the Student Reference Guide.


© 2

007

Har

cour

t A

chie

ve In

c.

1. $75.00 2. Use a meterstick to help.

A 0.5 m B 2 m

C 6 m D 36 m

3. Write the probability as a decimal.

rain+ not rain

100% total

4.

5. 4.5 × 106 6. a. (–12)(+3) =

b. (–12)(–3) =

c. –12

____ +3

=

d. –12

____ –3

=

7. a. –12 + –3 =

b. –12 – –3 =

c. +3 + –12 =

d. +3 – –12 =

9. 10.


8. 3 __

4 , 3

__ 5

, 4

__ 5

One way is to convert each f to a

d number, order the decimal n ,

and convert the d numbers back to

f in the new order.



Use work area.


© 2

007

Har

cour

t A

chie

ve In

c.

11. 12. 12 1

__ 4

in. =

___

– 3 5 __

8 in. =

___

13. 3 1 __

3 ft × 2

1 __

4 ft = 14. (3 cm)(3 cm)(3 cm) =

15. 0.6 m × 0.5 m = 16. 52 + 25 =

17. The area of the triangle is .

The area of the rectangle is .

I a the areas.

19. a. Which line is not a line of

symmetry? line

b. Does the figure have rotational

symmetry? , the figure will look

the same after turning °.


18. 2 ft 3 in.– 1 ft 9 in.

20.

Use work area.

Use work area.


© 2

007

Har

cour

t A

chie

ve In

c.

21. days$

3 ___

___

? 22. )

___ 70

) ___

70 ) ___

70

23. 900 million miles 24.

25.

27. 7, 8, 8, 8, 9, 9, 11, 12, 12, 16 28. mean

29. circumference

I can estimate by multiplying

the diameter by .

30. A = s2

s = 10 m


(0, 0), (0, 4), (4, 4)

a. area b. reflected across

the y-axis

26.

a.

b.

c.

A =

a.

b. (0, 0), ( , ), ( , )

∙ ∙


L E S S O N

114 Name ©

200

7 H

arco

urt

Ach

ieve

Inc.

Unit Multipliers (page 597)

• Unit multipliers reverse the positions of an equivalent fact.

3 feet = 1 yard 3 ft

____ 1 yd

and 1 yd

____ 3 ft

The units we change from are in the denominator.

The units we change to are in the numerator.

Cancel units just like canceling numbers.

Example: Convert 30 feet to yards using a unit mulitplier. (1 yd = 3 ft)

30 ft

_____ 1 ×

1 yd ____

3 ft = 10 yd

• The “multiply the loop; divide by the outside number” method may also be used to solve unit multiplier problems.

Example: Convert 30 feet to yards.ydft

1 __

3

? ___

30

(30 × 1) ÷ 3 = 10 yd


a. Write two unit multipliers for these equivalent measures:

1 gal = 4 qt

1 gal

_____ 4 qt

,

_________

b. Which unit multiplier from problem a would you use to convert 12 gallons to quarts?

4

________

c. Write two unit multipliers for these equivalent measures:

1 m = 100 cm

1 m _______

100 cm ,

_________

d. Which unit multiplier in problem c would you use to convert 200 cm to meters?

1

__________ 100

e. Use a unit multiplier to convert 12 quarts to gallons.

12 qt

_____ 1 ×

gal _______

qt =

f. Use a unit multiplier to convert 200 meters to centimeters.

200 m

______ 1 ×

cm _______

m =

g. Use a unit multiplier to convert 60 feet to yards. (1 yd = 3 ft)

60 ft

_____ 1 ×

yd _______

ft =

10

1


© 2

007

Har

cour

t A

chie

ve In

c.

1. tickets$

___ 6

? ___ 2.

minuteslaps

6 ___

? ___

3. 15

___ 25

played

___ 25

did not

4. 2 __

5 of 160 planted with alfalfa

___ 5

of 160 not planted with alfalfa

isof

___

___

5. ten-thousands place

94,763,581

6. a. 4 qt

_____ 1 gal

,

_______

b. to convert to quarts

_______

7. $36.43 $41.92 $26.70

8. 4 + 42 ÷ √__

4 – 4

__ 4

=

9. 3 1

__ 4 in. =

___

2 1 __

2 in. =

___

+ 4 5 __

8 in. =

___

10.


Use work area.

Use work area.


© 2

007

Har

cour

t A

chie

ve In

c.

11. 12.

13. fraction answer

3.25 ÷ 2 __

3

14. 3m – 10 = 80

=

=

15. 3 __

2 =

18 ___

m 16. a. (–5)(–20) =

b. (–5)(+20) =

c. –20

____ +5

=

d. –20

____ –5

=

17. mihr

55

___ ? __

6

Will she reach Los Angeles?

18. area

19. perimeter 20. a. –5 + –20 =

b. –20 – –5 =

c. –5 – –5 =

d. +5 – –20 =


Use work area.

Use work area.

m =

Use work area.m =

Use work area.


© 2

007

Har

cour

t A

chie

ve In

c.

21. ∠1 = half of a right angle 22.

23. Write two different prime numbers.

,

Find their LCM.

24. 1.5 × 106

25.

27. • Draw the center at (1, 1).• One point on the circle is (1, –3).

• a. radius • b. A = πr2

28. 95 highest 35 range

lowest


29. 4 ft 3 in.– 2 ft 9 in.

26. galqt

1 ___

? __

8

30. Rule: To find A, I must s s.

a.

b.

Use work area.b. a.

∠

s A

1 1

2 4

3 9

4 16


L E S S O N

115 Name ©

200

7 H

arco

urt

Ach

ieve

Inc.

Writing Percents as Fractions,

Part 2 (page 602)

• To write a percent as a fraction:

Remove the percent sign, write the number with a denominator of 100, and reduce the fraction.

Example: 50% = 50

____ 100

= 1 __

2

If the percent includes a fraction, divide by 100.

Example: Convert 3 1 __

3 % to a fraction. 3

1 __

3 ÷

100 ____

1

1

10

___ 3 ×

1 ____

100 =

1 ___

30

10


a. Convert 66 2 __

3 % to a fraction.

66 2 __

3 ÷

100 ____

1

200

____ 3 ×

_____ =

b. Convert 6 2

__ 3

% to a fraction.

6 2

__ 3 ÷

100 ____

1

_____ ×

_____ =

c. Convert 12 1 __

2 % to a reduced fraction.

12 1 __

2 ÷

100 ____

1

_____ ×

_____ =

d. Write 14 2

__ 7

% as a reduced fraction.

14 2 __

7 ÷

100 ____

1

_____ ×

_____ =

e. Write 83 1 __

3 % as a reduced fraction.

88 1 __

3 ÷

_____

_____ ×

_____ =

Teacher Note:• Review “Fraction Decimal

Percent” on page 13 in the Student Reference Guide.


© 2

007

Har

cour

t A

chie

ve In

c.

1. $12.60 $12.60

$12.60 $12.60

2. 16 2

__ 3

÷ 100

____ 1

3. 4. ms

331

____ ? _______

5. (5 × 104) + (6 × 102) 6. diameter

7. 3 2 __

3 2

2 __

3

_____ ×

_____ =

Now round.

8. Multiply the probabilities.

+ 3 red+ 3 white+ 3 total

3 _____ ×

2 _____ =

9. 10.




© 2

007

Har

cour

t A

chie

ve In

c.

11. 7x – 3 = 39

=

=

12. x __

7 =

35 ___

5

13. a. (–3)(–15) =

b. –15

____ +3

=

c. –15

____ –3

=

d. (+3)(–15) =

14. –6 + –7 + +5 – –8 =

15. 0.12 ÷ (12 ÷ 0.4) = 16. Round to the hundredths place.

) ______

0000

17. × = 10,000 18. area

19. perimeter

20. volume


x = x =

Use work area.


© 2

007

Har

cour

t A

chie

ve In

c.

21. J 31 J 31 F 28 A 31 M 31 S 30 A 30 O 31 M 31 N 30 J 30 D 31

22. containersounces

7 ___

10 ___

?

23. 4 1 __

2 million 24. 58,697,284

25. 26. 9 lb 7 oz 2 months later 7 lb 9 oz birth

27. (0, 0), (5, 0), (6, 3), (1, 3)

area

30. Gilbert can divide 323.4 miles by gallons to calculate the miles per g .


28. greatest weight

A 6.24 lb

B 6.4 lb

C 6.345 lb

29. 2 gal 2 qt 1 pt+ 2 gal 2 qt 1 pt

Use work area.


L E S S O N

116 Name ©

200

7 H

arco

urt

Ach

ieve

Inc.

Compound Interest (page 606)

• Principal is the money you deposit in a bank.

• Interest is the money your money earns. Interest is figured as a percentage.

• Compound interest is a percentage of the principal and accumulated interest (interest earning interest).

• Simple interest is a percentage of the principal only.

Example: Find compound and simple interest on $100.00 earning 6% interest over 2 years.

Compound Interest Simple Interest

principal $100.00 principal $100.00 1st yr interest (6% of $100.00) 6.00 1st yr interest 6.00 total after one year $106.00 2nd yr interest + 6.00 2nd yr interest (6% of $106.00) 6.36 total after two years $112.00 total after two years $112.36

• To use a calculator to figure compound interest:

1. First, enter a decimal number that equals the whole amount plus the percent of interest. (If the interest is 6%, enter 1.06—since 100% principal plus 6% interest equals 106% or 1.06. If the interest is 10%, enter 1.1.)

2. Then put this number into the calculator’s memory using the “Min” or “M ” key.

3. Enter the amount of the principal.

4. Enter “×”, “MR”, and “=” to get the first-year interest. Continue entering “×”, “MR”, and “=” for the number of years.


a. Mrs. Vasquez deposited $2000 in an account that earns 10% compound interest. After the third year, $2662 was in Mrs. Vasquez’s account. If the account continues to grow 10% annually, how much money will be in the account 1. after the tenth year and 2. after the twentieth year? Round answers to the nearest cent.Use a calculator.

1. Enter 1.1. [whole amount (100%) plus 10%]

2. Enter “M ”.

3. Enter “2662”. [principal]

4. Enter “×”, “MR”, and “=”. [4th year total]

Continue entering “×”, “MR”, and “=” 6 more times. [10th year total]


1. after 10 years

2. after 20 years

Teacher Notes:• Refer students to “Simple Interest”

on page 23 in the Student Reference Guide.

• Check classroom calculators before teaching the method described in this lesson.

• The final Practice Set problem is optional.


© 2

007

Har

cour

t A

chie

ve In

c.


1. area

2. ft$

___

___ ?

3. a. isof

6 ___ =

___

b.

___ 15

= ? ____

100

4. Write the probability as a percent.

correct choicestotal choices

_____

5. buy lunch

isof

2 __

5

___

30

bring lunch

isof

___

___ 30

6. 1.2 × 109 7. c = pw

p = $1.25

________ 1 pound

w = 5 pounds

Practice Set (continued) (page 608)

b. Nelson deposited $2000 in an account that pays 4% interest per year. If he does not withdraw any money from the account, how much will be in the account 1. after three years, 2. after 10 years, and 3. after 20 years?Use a calculator.

1. Enter 1.04. [whole amount (100%) plus 4%]

2. Enter “M ”.

3. Enter “2000”. [principal]

4. Enter “×”, “MR”, and “=”. [1st year total]

Continue entering “×”, “MR”, and “=” 2 more times. [3rd year total]



1. after 3 years 2. after 10 years 3. after 20 years

c. How much more money will be in Mrs. Vasquez’s account than in Nelson’s account?

1. after 3 years 2. after 10 years 3. after 20 years

buybring

___

c =

a. b.


© 2

007

Har

cour

t A

chie

ve In

c.

8. least to greatest

9.9 9.95 9.925 9.09

9.

10. 11. 9x + 17 = 80

9x + 17 = 80

9x + 17 = 80

12. x __

3 =

1.6 ___

1.2 13. –6 + –4 – +3 – –8 = 14. decimal answer

6 + 3 3 __

4 + 4.6

15. 210 yd ∙ ft

_______ yd

= 16. ) _____

210 ) _____

210 ) _____

210 ) _____

210 ) _____

210 ) _____

210 ) _____

648

17. oz$

32

___

___ ?

18. area

19.


a.

b.

, , , Use work area.

Use work area. x =

x =

∙ per


© 2

007

Har

cour

t A

chie

ve In

c.

21. 0.6y = 54 22. a. (−8)(−2) =

b. (+8)(−2) =

c. +8

___ −2

=

d. −8

___ −2

=

20. volume of cube

volume of pyramid = 1 __

3 (volume of cube)

23. List the number of students in each room.

, , , ,

, , , ,

How many have exactly 30?

) _____

306

24. a. The sum of the angles in a triangle is 180°.

b. Complete the triangle. Label the angle measures.

25. probability of “sector 3” × 60 =

A 60 times B 40 times

C 20 times D 10 times

26. area

each side

perimeter of triangle

27. 11 1

__ 9

÷ 100

____ 1

29. 3 lb 08 oz 2 lb 12 oz

30. no lines of symmetry

A B C


Use work area.

28. List in order. , , , ,

mean median

range

equilateral isosceles scalene

y =

a.

Use work area.


L E S S O N

117 Name ©

200

7 H

arco

urt

Ach

ieve

Inc.

Finding a Whole When aFraction is Known (page 612)

• To illustrate finding a whole when a fraction is known:

1. Draw a picture showing parts (denominator).

2. Mark off parts required (numerator).

3. Divide; then label each part.

4. Count total of parts.

Example: 3 _ 8 of the people in the town voted. If 120 of thepeople voted, how many people lived in the town?

120 ÷ 3 = 40

8 × 40 = 320

• To find a whole when a fraction is known without an illustration:Set up as an “is/of” loop problem (as taught on Lesson Worksheet 22).

Example: 120 is 3 __

8 of what number?

isof

3 __

8

120 ____

?

isof

3 __

8

120 ____

?

40

8 ∙ 120

_______ 3

= 320

1

Cancel.


a. Eight is 1 __

5 of what number? b. Eight is

2 __

5 of what number?

isof

1 __

5

8 ___

?

isof

___

____ ?

c. Nine is 3

__ 4

of what number? d. Sixty is 3

__ 8

of what number?

isof

___

____ ? is

of

___

____

?

e. Three fifths of the students in the class were girls. If there were 18 girls in the class how many students

were in the class?

18 is 3

__ 5

isof

___

____ ?

Teacher Notes:• Refer students to “Finding the

Whole When a Fraction or Percent is Known” on page 15 in the Student Reference Guide.

• Review Hint #35, “Fraction of a Group, Part 2.”


© 2

007

Har

cour

t A

chie

ve In

c.

1. 120 is 3 __

5

isof

____ 120

____ ?

2. ) ______

1 3 0

3. 11:15 a.m. 2:15 p.m. = hr

2:15 p.m. 2:45 p.m. = min How many half hours?

$1.25× $1.25

4. area of square

each side

area of circle

5.

____ = ____

100

7. one hundred five thousandths

8. Round to the nearest cent.

) ______

$7.00

9. least to greatest Change to decimals.

81% 4

__ 5

0.815

10. 6x – 12 = 60

=

=

6. (3, 6), (5, 0), (0, 0) area


, , ,

, , x =


© 2

007

Har

cour

t A

chie

ve In

c.

11. 9 ___

15 =

m ___

25 12. 6 is

2 __

5

isof

___ 6

___ ?

13. ( 5 – 1 2

__ 3 ) – 1

1 __

2 = 14. 2

2 __

5 ÷ 1

1 __

2

15. 0.625× 252.4

16. –5 + –5 + –5 =

17. ) ___

36 )

___ 36

) ___

36 )

___ 36

18. $12.50 $12.50

$12.50 $12.50

19. area

20. 6 × 105


m =

∙


© 2

007

Har

cour

t A

chie

ve In

c.

21. a. –20

____ –4

= b. –36

____ 6 =

c. (–3)(8) = d. (–4)(–9) =

22. volume

23. Complete the triangle.

24. mean 89

median 87

mode 92

25. a. Write as a decimal.

100% + 6.5% = %

b. $1000 at 6.5% compound interest after 3 yearsUse a calculator.

1. Enter interest.

2. Enter “M ”.

3. Enter principal.

4. Enter “×”, “MR”, and

“=” for each year.

27.

Rotate and translate to form a

A square B parallelogram C octagon

28.

h

29. √____

100 + 32 × 5 – √___

81 ÷ 3 = 30. a. most lines of symmetry?

b. rotational symmetry?

A B C

26. spun twice

greater than one

_______________ total sections

_____


Use work area.

a triangle

b. a.

a. .

b.


L E S S O N

118 Name ©

200

7 H

arco

urt

Ach

ieve

Inc.

Estimating Area (page 617)

• Estimate the area of a figure using a grid.

1. Shade the squares that have most of their area within the circle.

2. Put a dot in the squares that have about half of their area in the circle.

3. Add the shaded squares plus half of the dotted squares.

Example:

24 shaded squares 8 dotted squares

24 + 1 __

2 (8) = 28 squares

Example: Each square on the grid represents one acre.


Estimate the area of the paw print shown below.

37 whole squares+ 35 (10 half squares)

42 acres

whole squares

half squares

total units2


© 2

007

Har

cour

t A

chie

ve In

c.

1. How many students get 8 cards?

7 ) ___

52

2. Use a cm ruler to measure a pencil.

A 1.8 cm

B 18 cm

C 180 cm

3. 6 million is 3 ___

10

isof

___

___ ?

4. The symbol ≠ means “is not equal to.” Which statement is true?

A 3

__ 4 ≠

9 ___

12 B

3 __

4 ≠

9 ___

16 C

3 __

4 ≠ 0.75

5. $14.49 $14.49

$14.49 $14.49

6. truckscars

___

7. mean

172427

28

8. least to greatest

6.1, √___

36 , 6 1

__ 4

9. 9 is 3 ___

10

isof

___

___

10. Buz can divide the c by π to

calculate the d .


Use work area.

, ,


© 2

007

Har

cour

t A

chie

ve In

c.

11. 12 is 3

__ 4

isof

___

___

12. 2 2

__ 3 + ( 5

1 __

3 – 2

1 __

2 ) =

13. 6 2 __

3 ÷ 4

1 __

6 14. decimal answer

4 1 __

4 + 3.2

15. 1 – (0.1)2 = 16. √_____

441 (try 20)

17. 2.2 lb ∙ oz _______

1 lb = 18.

19. perimeter 20. A square has how many total lines of symmetry?


a.

b.


© 2

007

Har

cour

t A

chie

ve In

c.

21. Round first.

4.11 ft ft

22. f ___

12 =

12 ___

16

23. rule: M x by

to get y.

missing number:

25. –5 + +2 – +3 – –4 + –1 =

27. 7 1 __

2 ÷

100 ____

1

29. 1st draw 2nd draw


5°

x y

2 10

3 15

5 25

? 40

28. –3°F

30. a. area of QRST

b. Circle the best unit for the area.

A square B square C square inches feet miles

24. 1.25 × 104

26. $4000

2 1

__ 2

% (0.025) interest

2 years

Use a calculator.

1. Enter interest.2. Enter “M ”.3. Enter principal.4. Enter “×”, “MR”, and

“=” for each year.

b. Use work area.

f =

Use work area.

a.


L E S S O N

119 Name ©

200

7 H

arco

urt

Ach

ieve

Inc.

Finding a Whole When a Percent is Known (page 621)

• To find a whole when a percent is known:

1. Change the percent to a reduced fraction.

2. Set up as an “is/of” loop problem.

Example: Thirty percent of what number is 120?

3 ___

10 is 120

isof

3 ___

10

120 ____

?

10 ∙ 120 _________

3 = 400

Example: Sixteen is 25% of what number?

16 is 1 __

4

isof

1

__ 4

16 ___

?

4 ∙ 16 ______

1 = 64


a. Twenty percent of what number is 120? b. Fifty percent of what number is 30?

20% = 1 __

5 50% =

isof

1

__ 5

120

____ ?

isof

___ 30

___ ?

c. Twenty-five percent of what number is 12? d. Twenty is 10% of what number?

25% = 10% =

isof

___ 12

___ ?

isof

___

___ ?

e. Twelve is 100% of what number? f. Fifteen is 15% of what number?

100% = 15% =

isof

___

___ ?

isof

___

___ ?

g. 15% × n = 12

percent of what number is ? Answer:

isof

___

___ ?

Teacher Notes:• Review “Finding the Whole When

a Fraction or Percent is Known” on page 15 in the Student Reference Guide.

• Students using the “is/of” method are not required to translate word problems into equations.

40

1

Cancel.


© 2

007

Har

cour

t A

chie

ve In

c.


1. 12 ) _____

555 2. lowest not counted

9.75 9.8 9.9 9.4 9.9 9.95

3. 6 is 10%

10% =

isof

___

___ ?

4. 8 is 2

__ 3

isof

___

___

5. (1 × 105) + (8 × 104) + (6 × 103) 6. inchfeet

1

__ 8

___

7. 8. 8 1 __

3 ÷

___

9.

___ = ____

100 10. 12 is 20%

20% =

isof

___

___

a.

b.

,

a.


© 2

007

Har

cour

t A

chie

ve In

c.


11. 9 is 3 ___

10

isof

___

___

12. (−5) − (+6) + (–7) =

13. (–15)(–6) =

14. Reduce.

60

___ 84

=

15. 2 1 __

2 =

___

– 1 2

__ 3 =

___

16. 17.

18. volume

19.

20. cube, pyramid, or cone?

21. 3m – 5 = 25

3m – 5 = 25

3m – 5 = 25

m =


© 2

007

Har

cour

t A

chie

ve In

c.


22. rule: M x by to get y.

missing number:

x 3 4 6 ?

y 12 16 24 32

23. tonspounds

1 ___

___

?

24. Which is not a quadrilateral? See the Student Reference Guide.

A parallelogram B pentagon C trapezoid

25.

area of square area of circle

26. (–3, –2), (0, 0), (x, 4)

Draw a line through the points.

28. Flip a coin 3 times.

probability of heads all 3 times:

1st 2nd 3rd

___ ×

___ ×

___ =

29. area

27. Flip a coin 3 times.

probability of heads on third flip

headstotal faces

_____

30. 4, 7, 6, 4, 5, 3, 2, 6, 7, 9, 7, 4, 10, 7, 9

List in order: , , , , , ,

, , , , , , , ,

x =

a.

b.


L E S S O N

120 Name ©

200

7 H

arco

urt

Ach

ieve

Inc.

Volume of a Cylinder (page 626)

• To calculate the volume of a cylinder:

1. Find the area of a circular end of the cylinder.

area = π r2

2. Multiply that area by the height of the cylinder.

volume = π r2 ∙ height


a. A large can of soup has a diameter of about 8 cm

and a height of about 12 cm. The volume of the can

is about how many cubic centimeters?

Round your answer to the nearest hundred

cubic centimeters.

Teacher Note:• Review “Geometric Solids” on page

30 in the Student Reference Guide.


1. ) _____

750 )

_____ 750

) _____

750 )

_____ 750

) _____

750

2. Use a centimeter ruler.

A 0.5 mm B 5 mm

C 50 mm D 500 mm

∙ ∙


© 2

007

Har

cour

t A

chie

ve In

c.

3. partsgrams

3 ___

8 __

?

4. 3 ___

24 =

8 __

w

5. (7 × 103) + (4 × 100) 6. two hundred five million, fifty-six thousand

7. a. (17 + 23 + 25 + ) ÷ 4 = 25

b. range

8. a. –6 – –4 =

b. –10 + –15 =

c. (–10)(–10) =

9. 16 2 __

3 ÷

___

10. 24 is 4 __

5

isof

___ 24

___ ?

11. 1 1 __

3 =

00 ___

00

3 3 __

4 =

00 ___

00

+ 1 1 __

6 =

00 ___

00

12. 5 __

6 ×

___

1 ×

___

3 =


w =

a.

b.

a.

b.

c.

© 2

007

Har

cour

t A

chie

ve In

c.

13. 5.625.62

+ 5.62

14. 0.08 ÷ (1 ÷ 0.4) =

15. (–2) + (–2) + (–2) = 16. √_____

2500 + √___

25 =

17. $oz

___ 16

?

____ 1 18. circumference

19. area

each side

perimeter

20. volume

21. 18 is 60%

60% =

isof

____ 18

____

22. 1st 2nd 3rd

___ ×

___ ×

___ =


per



© 2

007

Har

cour

t A

chie

ve In

c.

23.

___ 4

of 20 24. a. (–8) – (+7) =

b. (–8) – (–7) =

25. +3 + –5 – –7 – +9 + +11 + –7 =

27. 2nd 3rd

___ ×

___ =

28. volume = π r2 ∙ height

.

29. 1 cm3 = 1 mL

Round to the nearest ten milliliters.

30.


26. (0, 0), (–8, 0), (–8, –8) area

y

x

a.

b.

Documents

LESSON 111 Applications Using Name Division - Yolalearningtops.yolasite.com/resources/Crs1_Lessons111-120.pdfApplications Using Division (page 582) ... Round up.) ____ 2 8 vans d