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Saxon Math Intermediate 5 133 Adaptations Lesson 21

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2121 Teacher Notes:

• Introduce Hint #18 “Word Problem Cues, Part 2.”

• Review Hint #10 “Word Problem Cues, Part 1.”

• Review “Word Problem Keywords” on page 6 in the Student Reference Guide.

• Review reference chart “Word Problem Keywords.”

• Word Problems About Equal Groups

New ConceptNew Concept

• Formula for equal groups problems:

number in each group× number of groups total

Example

There are 4 classes of fifth graders with 30 students in each class. How many students are in the 4 classes?

30 students in each class× 4 classes 120 students in all 4 classes

4 30

?

Example

5 pens cost $2. How much would 10 pens cost?

1. Name the two things the problem is about. pens

____ $

2. Fill in what you know. pens

____ $ 5 __

2

3. Fill in what you are looking for. pens

____ $ 5 __

2 = 10 ___

?

4. Draw a loop around the numbers thatare diagonally opposite. The loop never

pens ____

$ 5 __

2 = 10 ___

?

includes the question mark.

5. Multiply the numbers inside the loop. 10 × 2 = 20Divide by the outside number. 20 ÷ 5 = $4

page 132

Math Language

Solve equal groups problems by using the loop method.

SM_H5_AD_L021_FF.indd 133SM_H5_AD_L021_FF.indd 133 11/1/07 10:32:03 AM11/1/07 10:32:03 AM


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Write an equation and find the answer.

a. On the shelf were 4 cartons of eggs. There were 12 eggs in each carton. How many eggs were in all four cartons?

4 12

t 12 eggs in each carton× 4 cartons eggs in all 4 cartons

12 × = t

t =

b. Thirty desks are arranged in 6 equal rows. How many desks are in each row?

6 n

30 desks in each row× rows 30 desks in all 6 rows

6n = missing factor divide

n =

c. Twenty-one books are stacked in piles with 7 books in each pile. How many piles are there?

7 g

25 7 books in each pile× g piles books in all 7 piles

7g = missing factor divide

g =

d. If 56 zebras were separated into 7 equal herds, then how many zebras would be in each herd?

7 n

56

zebras in each herd× 7 herds 56 zebras in all 7 herds

7g = missing factor divide

g =

e. Write an “equal groups” word problem for this equation.

6 0.75

tThen answer the question in your word problem.

6 × $0.75 = t t =

Pat bought pens for each.

did she spend? Pat spent $ .

Lesson Practice



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1. p students on each team 8p =

8 p

56

× teams

students in all

missing factor divide

p =

Use work area.

2. 32 ounces bottle

bowl t left

8 t

32

32 − = t

t = Use work area.

3. $487 earnedm more

cost

487 m

800

$487 + m =

m =

Use work area.

4. Draw an oblique line. Lines have arrows.

Use work area.

5.

6 7

42

) ____

) ____

× ×

Use work area.

Written PracticeWritten Practice page 136


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Written Practice,Written Practice, continued continued


6. 8 ) ____

7 2

8 ?

72

7. 6n = 42

6 n

42

n =

8. 9 ) ____

3 6

9 ?

36

9. 6n = 48

6 n

48

n =

10. 56 ÷ 7 =

7 ?

56

11. 70 ___ 10

=

10 ?

70

12. 24 ÷ 4 30 ÷ 6

13. Carry on your fingers.

367

× 8

14. $5.04× 7

two decimal places in answer

15. Write the “carry” number.

837

× 9

16. 6 × 8 × 10 = 17. 7 × 20 × 4 = 18. $40.00

– $00.00

19. r − 4568 = 6318

4568 6318

r

r =

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onWritten Practice,Written Practice, continued continued


20. 5003 − w = 876

876 w

5003

w =

21. 268+ m

687268 m

687

m =

22. sets of ten

$9.65$2.43

+ $1.45

24. number in each group missing factor divide

× number of groups

b

) ____

123

Twelve divided by is , so there are

items in each group.

25. …, 50, 60, 70, 80, 90, , ,

, …

26. Say the greater number (dividend) first.

10 ___ 2 words:

Use work area.

27. What number is the dividend?

60 ÷ 10 = 6

28. number in each group × number of groups

There were books in all 5

boxes.

Use work area.

23. 38296

+ 182

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29. Use fraction-decimal-percent pieces for help.

1 __ 2 = .

1 __ 2 =

Use work area.

30. See page 138.

a. island with greatest area: greatest

+ least island with least area:

b. islands with areas that have a difference of 250 square miles:

and

– 100 250 sq. mi

c. islands with combined areas equal to Attu’s area:

, , and

116134

+ 350

Use work area.

page 137


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2222 Teacher Notes:

• Refer students to “Tests for Divisibility” on page 20 in the Student Reference Guide.

• Review “Division” on page 8 in the Student Reference Guide.

• For additional practice, students may complete Targeted Practice 22.

• Division With and Without Remainders


• Division and multiplication are inverse operations.

Example

5 ) ____

1 6

Think: 5 times what is close to, but not more than, 16?

5 × 3 = 15

16 – 15 = 1 Subtract using Mental Math. 3 R15 )

____ 1 6

The remainder is 1.

• Multiply to check division.

3 × 5 = 15 Multiply the quotient times the divisor.

+ 1 ____ 16 Add the remainder.

• Divisibility tests tell whether division answers have remainders.

TESTS FOR DIVISIBILITY

A number is divisible by … 2 if the last digit is even.

5 if the last digit is 0 or 5.

10 if the last digit is 0.

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Divide. Write each answer with a remainder.

a. R5 )

____ 2 3 b.

R6 )

____ 5 0 c. 37 ÷ 8

R ) ____

d. R4 )

____ 2 3 e.

R7 )

____ 5 0 f. 40 ÷ 6

R ) ____

g. R10 )

____ 4 2 h.

R9 )

____ 5 0 i. 34 ÷ 9

R ) ____

j. Circle the division problem below that has a remainder. Use divisibility tests. Do not divide.

10 ) ____

6 0 5 ) ____

4 4 2 ) ____

1 8

k. Which of the numbers below can be divided by 2 without a remainder?

25 30 35


1. Draw two horizontal lines. Lines have arrows.

Use work area.

2. number of groups × number in each group 8g =

bags

gifts in each bag

gifts in all

missing factor divide

8 g

32

g =

Use work area.

Lesson Practice



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3. 26 miles total 9 miles ran m still to run

9 m

26

26 − = m

m =

Use work area.

4. Is 1000 a reasonable estimate for 384 + 618?

, because 384 is about and 618 is about

, which add up to a s of 1000.

Use work area.

5. Subtract using

Mental Math.

56 ÷ 10 =

6. 20 ÷ 3 = 7.

R7 )

____ 3 0

8. 3 × 7 × 10 =

9. Commutative Property of

Multiplication

2 × 3 × 4 × 5 =


$394

× 8


678

× 4

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$6.49

× 9


13. 63 ___ 7 =

7 ?

63

14. 56 ___ 8 =

8 ?

56 15. 42 ___

6 =

6 ?

42


$4.08

× 7


17. 3645× 6

18. 3904× 4

19. Property of Zero for

Multiplication

8 × 0 = 4n

= 4n

= n

n =

20. top missing Add.

c

– 462548

462 548

c

c =

21. $36.15

– $ .62

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22. 963+ a6000

963 a

6000

a =

23. Say the greater number (dividend) first.

4 ) ____

1 2

words:

Use work area.

24. odd× 2

product

2 ) ___

Is there a remainder?

, because when you multiply a number by 2, the product

is e . An even number divided by 2 does

have a remainder.

Use work area.

25. 50, 40, 30, 20, 10, , , , …

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26.

27. 46,208 46,028 28. How many fourths equal one half? Use fraction-decimal-percent pieces for help.


a. 1 __ 4

= .

b. 1 __ 4

= %

Use work area.

30. chairs in last row = remainder

10 ) ____

7 5

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2323 Teacher Note:

• Introduce Hint #20 “Comparing Fractions.”

• Recognizing Halves


• Many fractions equal one half.

12

24

36

48

510

• The numerator of each fraction is half the denominator.

2 __ 4 Two is half of four. 4 __

8 Four is half of eight.

3__6 Three is half of six. 5___

10 Five is half of ten.

• To compare fractions:

1. Cross multiply.

2. Compare the numbers on top.

Example

2 __ 3 > 4 __

9

18 12

Lesson Practice

a. Think of a counting number. Double it. Then write a fraction equal to 1 _ 2 using your number and its double.

counting number doubled fraction

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Lesson Practice, continued

b. Which of these fractions does not equal 1 _ 2 ?

A 7___14

B 8___15

C 9___18

D 21___42

c. Compare: 5 __ 8 5 ___

12

d. Compare: 12 ___ 24

6 ___ 12


1. $5.00 gave $ . cost m get back

3.48 m

5.00

$5.00 − = m

m =

Use work area.

2. $1.45 veggie wrap $ . fruit salad t together

1.45 0.95

t

$1.45 + = t

t =

Rounding $1.45 to and $0.95 to gives a sum of

, which is close to .

Use work area.



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3. Multiply the loop.

weeks days

1 __ 7 = d __

d

7 52

d

7 × = d

d =

Use work area.


3 d

24

Divide by the outside number.

kids $

24 ___ 24

= 1 __ d

× d = 24

d =

To find the missing

f , divide 24

by .

Use work area.

5. a. 1 _ 2 of 20 ounces

b. 1 _ 4 of 20 ounces

a.

b.

6. Cross multiply.

3 ___ 10

3 __ 6

7. Subtract using Mental Math.

40 ÷ 6 =

8. R3 )

____ 2 0 9. 60 = n × 10

10 n

60

) ____

n =

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$3.08

× 7


11. 2514× 3


697× 8

13. Say the greater number

(dividend) first.

7 ) ____

3 5

words:

Use work area.

14. 4 × 3 × 10 = 15. 12 × 2 × 10 =

16. bottom missing Subtract.

4035– s

3587

3587 s

4035

s =

17. top missing Add.

m– 1056

5694

1056 5694

m

m =

18. $70.00– $ 7.53

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19. $5.00

$ .00

$ .00

+ $ .

20. $6.25 + $0.85 + $4.00 + d = $20.00

$6.25

$ .

$ .

$20.00

$ .

d =

21.

7 9

63

× × ) ____

) ____

Use work area.

22. greatest to least

48, 16, 52

, ,

23. Draw two vertical lines side by side. Lines have arrows.

Use work area.

24. 212,500

words:

Use work area.

25.

7 9

16

+ + – –

Use work area.

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26. Which fraction below does not equal 1 _ 2 ?

A 10 ___ 20

B 20 ___ 40

C 40 ___ 80

D 80 ___ 40


3 __ 4 = .

28. value of nine quarters

9 × =

29.

3 12

p

There were customers in the diner. Each customer ordered

pancakes. In all, how many were ordered?

30. 8, 16, 24, 32, , , , , ,

page 148


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2424 Teacher Notes:

• Review “Properties of Operations” on page 22 in the Student Reference Guide.


page 149

Math Language

There are four operations of arithmetic:

addition

subtraction

multiplication

division

• Parentheses and the Associative Property


• Parentheses separate a problem into parts.

• Always work the part inside the parentheses first:

2 × (3 + 4) (2 × 3) + 4

2 × 7 6 + 4

14 10

• Associate Property of Addition: Any way we group the addends, the answer is the same.

(4 + 5) + 6 = 4 + (5 + 6)

• Associative Property of Multiplication: Any way we group the factors, the answer is the same.

(2 × 3) × 4

2 × (3 × 4)

• The Associate Property does not work for subtraction or division.

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a. 6 – (4 – 2) = b. (6 – 4) – 2 = c. (8 ÷ 4) ÷ 2 =

d. 8 ÷ (4 ÷ 2) = e. 12 ÷ (4 – 1) = f. (12 ÷ 4) – 1 =

g. Name the four operations of arithmetic: , ,

,

h. (8 ÷ 4) ÷ 2 8 ÷ (4 ÷ 2) Does the Associative Property apply?

i. (8 – 4) – 2 8 – (4 – 2) Does the Associative Property apply?

j. (8 × 4) × 2 8 × (4 × 2) Does the Associative Property apply?

Lesson Practice


1. one half of a dollar $0.50

one fourth of a dollar $ .

2. number in each group × number of

groups

25 × = t

25 4

t

t =

Use work area.



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3. carton

– e removed 9 remained

9 e

12

– e = 9

e = Use work area.

4. 956 seats s not occupied

occupied

498 s

956

956 – s = . I subtracted from

to get .

s = Use work area.

5.

5 10

50

× × ) _____

) _____

Use work area.

6. parentheses first

3 × (4 + 5) (3 × 4) + 5

3 × + 5

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7. 30 – (20 + 10) =

30 – =

8. (30 – 20) + 10 =

+ 10 =

9. Associative Property of Multiplication

4 × (6 × 5) (4 × 6) × 5

4 × × 5


60 ÷ 7 =

11. 50 ÷ 6 = 12. R10 )

____ 4 4


$50.36 × 4


14. 7408 × 4

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4637 × 9

16. w– $09.62

$14.08

9.62 14.08

w

w =

17. 4730– j

2712

2712 j

4730

j =

18. $30.00– $00.56

19. $3.54

$ .

$ .

20. $20.00

– $

21.

9 5

14

+ + – –

Use work area.

22. hundreds

256

23. $35 + $35 + $35 + $35 =

× =

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24. 10th term

3, 6, 9, 12, 15, …

25. Which is divisible by 5?

A 23 B 25 C 27 D 29


(8 + 4) + 2 8 + (4 + 2)

+ 2 8 +

29. a. half of 14

b. 1 __ 2 = 0 ___

14

a.

b.

26. Draw two vertical lines. Lines have arrows.

Use work area.

27.

7 8

56

× × ) _____

) _____

Use work area.

30. woke up 65°F

high temperature 83°F

Which equation shows the number of degrees the temperature increased?

A 65 + d = 83 B 83 + 65 = d

C d + 83 = 65 D 83 + d = 65

page 152


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• Listing the Factors of Whole Numbers


• To list the factors of whole numbers:

1. Always start with 1.

2. Always end with the number given.

3. Find all the other whole numbers that divide evenly into the given number.

Ask: Will 2 divide evenly?

Will 3 divide evenly? (etc.)

4. List the numbers in order.

Example

Factors of 20:

end withstart with

divide evenly into 20

1, 2, 4, 5, 10, 20

ActivityActivity

page 155

Grouping by Factors

Illustrate the factors of 12 by circling equal groups of dots and labeling each group.

groups of 1

groups of 2

2525 Teacher Notes:

• Introduce Hint #21 “Factors of Whole Numbers.”

• Refer students to “Factors” on page 8 in the Student Reference Guide.

• Review “Multiplication Table” on page 5 in the Student Reference Guide.

page 154

Math Language

The factors of a number are all the whole numbers that can divide it without leaving a remainder.



New Concept,New Concept, continued continued

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groups of 3

groups of 4

groups of 6

groups of 12

Lesson PracticeList the factors of each number:

a. 4 1 , , 4 b. 3 1 ,

c. 6 1 , , , d. 5 ,

e. 8 , , , f. 11 ,

g. 9 , ,

h. 12 , , , , ,

i. 1 j. 14 , , ,

k. 2 , l. 15 , , ,

m. Two is not a factor of which of these numbers?

A 236 B 632 C 362 D 263

n. Five is not a factor of which of these numbers?

A 105 B 150 C 510 D 501

o. Which of these numbers is not a factor of 40?

A 2 B 5 C 6 D 10



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9 × = t

t =

Use work area.

2. $10.00 paid

$ . cost m got back

6.75 m

10

$10 − = m

m =

My answer is r because $6.75 + = $10.

Use work area.


cartons $

1 __ = 4 __ c

4 × = c

c =

Use work area.

4. factors of 13:

,




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5. factors of 10:

1 , , 10

factors of 30:

1 , , , ,

, , , 30

, , ,


4 (6 10)

(4 6) 10

4 × × 10

7. Which property of multiplication is illustrated in problem 6?

Property


6 × (7 + 8) =

9. (6 × 7) + 8 = 10.

10 12

120 ) _____

) _____

× ×

Use work area.

11. 9n 54

9 n

54

n =


55 ÷ 8 =


1234× 5

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14. two decimal places in answer

$5.67× 8

Use work area.

15. 987× 6

16. w − $13.55 = $5

13.55 5

w

w =

17. 2001 − r = 1002

r 1002

2001

r =

18. 4387

+

19. 3715

+

20. $6.75 + $8 + $1.36 + p = $20

$6.75

$ .

$ .

$20.00

$ .

p =

21. 1 _ 2 of a dollar $0.50

1 _ 4 of a dollar $ .

1 __ 10 of a dollar $ .

22. 894,201

words:

Use work area.

page 157

23. Which number is the divisor?

7

6 ) ____

4 2

24. 10th term

5, 10, 15, 20,…



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25. whole number

× 2

Answer odd or even?

26. Two is not a factor of which of these numbers?

See “Tests for Divisibility” on page 20 of the

Student Reference Guide.

A 456 B 465 C 654 D 564

27. Which property of addition is illustrated below?

(6 + 7) + 8 = 6 + (7 + 8)

Property

28.

× × =


1 ___ 10

= .

30. Number of Yards 1 2 3 4

Number of Feet 3 6 9 12

a. To find the number of feet, m the number of yards

times .

b. 20

feet = 20 yards

Use work area.

page 158


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2626

• Division Algorithm


• Use short division when divisors are one-digit.

• After multiplying and subtracting, any number “left over”goes in front of the next digit.

• Place a digit above each digit.

• Use zero as a placeholder.

• Any final number “left over” becomes the remainder(must be less than the divisor).

Example

234 ÷ 5 =

0 4 6 R 45 )

______ 2 3 34

• Factor missing Divide.

5n = 365 n = 365 ÷ 5

n = 73 0 7 35 )

______ 3 6 15

5 n

365

page 159

Teacher Notes:

• Introduce Hint #22 “ShortDivision.”

• Review “Division” on page 8 in the Student Reference Guide.



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Divide, using short division with one-digit divisors.

a. $4 )

__________ $5 . 5 6 b.

0 R9 )

_________ 3 7 5 c.

$3 )

__________ $4 . 6 5 d. 5 )

_________ 6 4 5

e. $0

7 ) __________

$3 . 6 4 f. 0 R7 )

_________ 3 6 5 g.

0 R10 )

_________ 5 4 6 h.

$4 )

__________ $4 . 5 6

i. Show how to check this division answer. 1 2 R 36 )

____ 7 5

Find each missing factor. Check each answer using a calculator.

j. 3x = 51 ) ___

k. 4y = 92 ) ___

x = y =

l. 6z = 252 ) ___

z =

I divided to find the missing f .

Lesson Practice


1. $5.00 paid

$ . cost m get back

2.98 m

5.00

$5 – $ = m

m = $

Use work area.


3 12

t

3 × = t

t = Use work area.



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3. s before 3 new after

3 s

28

s + 3 =

s =

I subtracted 3 from

and got .

Use work area.

4. a. smallest

even

b. half of that

c. 1 __ 2 =

a.

b.

c.

5. factors of 8: factors of 16:

1 , , , 8 1 , , , , 16

, , ,

6. short division

5 ) _________

3 7 5

7. short division

R4 )

_________ 3 6 5

8. 6m = 234

) ___

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9. short division

$ 0 .6 )

__________ $4 . 3 2

10. short division

3 ) _________

1 2 3

11. short division

6 ) _________

5 7 6


$7.48

×



609

×

14. Associative Property of

Multiplication

7 × 8 × 10 =

15. Property of Zero for

Multiplication

7 × 8 × 0 =

16. 9374 – m = 4938

m 4938

9374

m =

17. $10.00

$1010.00

18. l 427+ 85 2010

2010

l =

19. $12.43

$12.43

$12.43

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20. 3 × 40 3 × 4 × 10

Since 4 × 10 = , the quantities are the s .

21. 8 × 90 = 8 × 9 × n

n =

22. ) ___

) ___

8 9

72

× ×

Use work area.

23. missing factor Divide.

8s = 64 ) ___

24. 3 _ 4 of a dollar $0.75

$0.75 3 __ 10 of a dollar

25. What number is halfway between 400 and 600?

600400

26. This equation shows that 7 is a factor of 91. Which other factor of 91 is shown by this equation?

1 37 )

____ 9 1

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27. 347

28. 1 6 R 34 )

____ 7 5

Check: 4 × =

+

Correct or not?

Todd’s answer correct because

the product plus the does not equal the dividend.

Use work area.

29. Which of these numbers is not a factor of 15?

A 1 B 2 C 3 D 5

30. 3n = 24

bought three packages of .

If she had 24 in all, how many were in each pack?

missing factor Divide.

n =

Use work area.

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2727

• Reading Scales


• Number lines can be horizontal, vertical, or curved.

• They can count by any number.

• To find points on number lines, split the difference:

1. Subtract the two numbers on both sides of the pointto find the difference.

2. Count the parts between the numbers.

3. Divide the difference by the number of parts.

4. Now count by that number.

Example

200 600

400

1. Subtract two adjacent numbers: 600– 400

200

2. Count the parts between the numbers: 4

3. Divide 200 by 4: 5 04 )

_____ 2 0 0

4. Now count by 50s: 400, 450, 500, 550

page 165

Teacher Notes:

• Introduce Hint #23 “Splitting the Difference.”

• Refer students to “Temperature” on page 2 in the Student Reference Guide.

• Display reference chart “Fahrenheit and Celsius Temperature Scales,” from Intervention Masters.



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• The number line on a thermometer is a scale for measuring temperature.

Water boils.

Celsius Scale Fahrenheit Scale

room temperature

Water freezes.

100

20

0

212

32

68

FC

Lesson Practice a. Finish labeling this number line b. On the Celsius scale, what is five temperature from 0 to 100 degrees less than the freezing using tens: point of water?

1000

c. Points A and B on this number line indicate two numbers. Write the two numbers, using a comparison symbol to show which is greater and which is less.

50 1000

A B

50– 0

5 ) ___

00

A B



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1. 408 mi Day 1 347 mi Day 2 419 mi Day 3 t altogether

408 + + = t

t =

Use work area.


ft in.

1 __ = 5 __ t

5 × = t

t =

Use work area.

3. f total

purchased7 remained 27 7

f

f – = 7

f =

Use work area.


$ cups 0.15 ____ 1 = m __

× $0.15 = m

m =

Use work area.

5. 1 _ 2 of Mahmood’s age = Colvin’s age

1 _ 2 of =

6. short division

864 ÷ 5 =

7. short division

$2.72 ÷ 4 =

8. short division

608 ÷ 9 =


378 ÷ (18 ÷ 3) =




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10. Split the difference.

100

90

80

70

60

F

80– 70

5 ) ___

00

– 13

15. 3864287672

+ m5350

5350

m =

16. Finish labeling this number line from0 to 50 using tens:

500

Use work area.

12. 3874× 6

13. 9063× 8


200 400

60

400200

) ___

page 168

11. $52.60× 7



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17. The number 78 is between which of these pairs of numbers?

A 60 and 70 B 70 and 80

C 80 and 90 D 0 and 10

18. factors of 30

1 , , , ,

, , , 30

Use work area.

19. 405

22. Subtract to find the rule.

…, 160, 170, 180, ,

, ,…

Use work area.


40 6020 80

60 40

) ___

20. In Khadija’s class, there is one more boy than there are girls. Which could not be the number of students in Khadija’s class?

Which number does not have a

remainder when divided by 2?

A 25 B 27 C 28 D 29

21. On the Celsius scale, what temperature is ten degrees below the freezing point of water?

See “Temperature” on page 2 of

the Student Reference Guide.

23. hundreds

537

24. 327,040

words:

Use work area.

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26. Show three ways to write “24 divided by 3.”

÷ _____ ) _____

Use work area.

27. 1 4 R 27 )

_____ 1 0 0

Check: 14 × =

+

Correct or not?

Madeline’s answer is because the p

plus the r equals the dividend.

Use work area.


12 ÷ ( 6 ÷ 2 ) (12 ÷ 6) ÷ 2

12 ÷ ÷ 2

Does the Associative Property apply

to division? Use work area.


3 ___ 10

= .

30. a. To find the number of centimeters, d the number of

m by .

b. ) _________

1 0 0

a. Use work area.

b.

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2828 Teacher Notes:

• Introduce Hint #24 “Reading Clocks” and Hint #25 “Elapsed Time.”

• Refer students to “Time” on page 2 in the Student Reference Guide.


• Measuring Time and Elapsed Time


• A half hour, or 30 minutes, later or earlier is a line directly across the clock from where the minute hand is pointing.

• Twelve hours later or earlier is the same time as now—only the a.m. or p.m. changes.

• Twenty-four hours later or earlier is exactly the same time as now, only the day before or after.

• Elapsed time is the amount of time between a starting time and an ending time.

Example

You started your homework at 4:00 p.m. and finished at 5:15 p.m. How long did it take?

4:00 p.m. 5:00 p.m. = 1 hour5:00 p.m. 5:15 p.m. = 15 minutes

1 hour and 15 minutes

Lesson Practice

a. Four centuries is how many years? number in each group × number of groups

b. According to the calendar on page 172, what is the date of the third Thursday in June 2014?

, month day year

page 171

Math Language

Use a.m. for the 12 hours before noon.

Use p.m. for the 12 hours after noon.

Midnight is 12:00 a.m.

Noon is 12:00 p.m.



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c. A leap year has how many days?

d. What is the name for 1 __ 10 of a century? 10 ) _____

e. Write the time that is 2 minutes after eight in the evening.

f. Write the time that is a quarter to nine in the morning.

g. Write the time that is 20 minutes after noon.

h. Write the time that is 30 minutes after midnight.

i. Write the time that is a quarter after nine in the morning.

j. If it is morning, what time is shown

by the clock? 3

121110

9

87 6 5

4

21

k. 2 hours later? Count forward 2 hours:

2 hours earlier? Count backward 2 hours:

l. The movie started at 3:15 p.m. and ended at 5:00 p.m. How long was the movie?

3:15 p.m. 4:15 p.m. = hours

4:15 p.m. 5:00 p.m. = minutes

hours and minutes




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1. m had $600 rent

remaining 600 1267

m m − $600 = $

m = $

Use work area.

2. $1873 had

$ more t total

1873 200

t $1873 + $ = t

t = $

Use work area.

3. cards in each pile

piles

cards in all

4c = missing factor Divide.

c = ) _____

I divided by and got .

Use work area.

5. factors of 18: 1 , , , , , 18

factors of 24: 1 , , , , , , , 24

, , ,

4. 1 _ 2 of a decade years




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528 ÷ (28 ÷ 7) =

9. 6w = 696

) ____

6 w

696

w =

11. half past noon 12. 1 _ 2 of a dollar $0.50

5 __ 10 of a dollar $0.

13.

SFTWTMS321

10987654171615141312112423222120191831302928272625

MAY 2042

May 10, 2042 is what day of the week?

14. largest 567

even

10. It is evening. What time is shown by this clock?

3

121110

9

87 6 5

4

21What time will it be in three hours?

time now:

Count forward 3 hours.

Use work area.

6. short division

543 ____ 3 =

7. short division

$6.00 _____ 8 =

page 175



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15. 43872965

+ 4943

16. $63.75

.....$ .00

17. 4010– f

563

563 f

4010

f =

18. 3408× 7

19. $3.56× 8

20. 487× 9

21. Use your student clock.

What time is 5 minutes before 9 in the morning?

22.

2 10

20

× × ) _____

) _____

Use work area.

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23. 2 2 R 29 )

_____ 2 0 0

Check: 22 × =

+

Use work area.

24. …, 400, 500, 600, 700, ,

, , …

Use work area.

25. Split the difference. 00600040 )

____

40 6020 80

27. How many centuries equal a millennium?

100 years in a century× c centuries 1000 years in a millennium

28. How many fourths equal one whole? Use fraction-decimal-percent pieces for help.

29. a. one hour = minutes

b. half of an hour = minutes

c. 1 __ 2 =

Use work area.

30. See page 176.

A n + 29 = 50 B n = 29 + 48

C 29 + n = 48 D n + 48 = 29

26.

× =

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2929 Teacher Notes:

• Introduce Hint #26 “Multiplying by 10, 100, or 1000.”

• Review “ Multiplication Table” on page 5 in the Student Reference Guide.


• Multiplying by Multiplesof 10 and 100


• To multiply a whole number by 10, attach a zero.

25 × 10 = 250

• To multiply a whole number by 100, attach two zeros.

25 × 100 = 2500

• When multiplying by multiples of 10, use offset multiplication:

1. Write the multiple of 10 as the bottom number.

2. Let the zero “hang out” (offset to the right).

3. Copy the zero into the answer.

4. Multiply.

zero “hangs out” Copy the zero. Multiply.

to the right

250× 30

250× 30

0

250× 30

750• When multiplying a money amount by a multiple of 10, put

two decimal places in the answer.

$3.755× 10

$37.50

$2.4000× 200

$480.00

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Lesson Practice

Use offset multiplication.

a. 34 × 20 340 × 20

b. 50 × 48 480 × 50

c. 34 × 200

×

d. 500 × 36

×

e. 55 × 30

×

f. $1.25 × 30

×

g. 55 × 300

×

h. $1.25 × 300

×

i. 60 × 45

×

j. $2.35 × 40

×

k. 400 × 37

×

l. $1.43 × 200

×



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1. missing factor Divide.

3c =

c = ) _____

Use work area.

2. 00$841 had00$ 75 tax00 m after

75 m

841

$841 – $ = m

m = $Use work area.


10 × = t

t =

Use work area.

4. 1845

one century

5. factors of 60:

1 , , , , , ,

, , , , , 60

Use work area.

7. Associative Property of Multiplication, then

offset

37 × 6 × 10 =

8. Offset.

46× 50


6. Offset.

37× 60



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9. Offset.

$0.73× 60

10. parentheses first, then offset

50 × (1000 − 200) =

11. 356

12. Use your student clock.

30 minutes before noon

13. 1 _ 2 of a dollar $0.50

3 _ 4 of a dollar $ .

3 __ 10 of a dollar $ .

14. Offset.

38

×

15. 944,000

words:

Use work area.

16. 46372843

+ 6464

17. 4618– 2728

18. $60.00– $07.63

page 180



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19. short division

364 ÷ 10 =

20. 7w = 364

7 w

364

) _____

w =

21. short division

7 ) _________

3 6 4

Use work area.

23. According to this calendar, what is the date of the third Sunday in May 1957?

SFTWTMS4321

1110987651817161514131225242322212019

313029282726

MAY 1957 , month date year

Use work area.

24. The number 356 is between which pair of numbers?

A 340 and 350 B 350 and 360 C 360 and 370 D 370 and 380

25. …, 600, 700, 800, , , , …

Use work area.

page 181

22. ( × 2 ) + 1 =

whole number odd or even?



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26. a. See “Tests for Divisibility” on page 20 of the Student Reference Guide.

A 205 B 502 C 250 D 202

b. is e , so 2 is a factor, and since it ends

in 0, is a factor.Use work area.

27. 4 3 R 17 )

_____ 3 0 0

Check: 43 × =

+

correct or not?


a. 12 – (6 – 2) (12 – 6) – 2

12 – – 2

b. Does the Associative Property apply to subtraction?

Use work area.


5 ___ 10

= .

30. a. greatest to least

, , ,

b. Two stores with a cost difference of $1.30

and

Use work area.

page 181


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3030 Teacher Notes:

• Introduce Hint #27 “Naming Fractions/Identifying Fractional Parts.”

• Review “Fraction-Decimal-Percent Equivalents” on page 19 of the Student Reference Guide.

• Review reference chart “Fraction-Decimal-Percent Equivalents.”

• Interpreting Pictures of Fractions, Decimals, and Percents


• Name how many parts are shaded out of a total number of parts.

25 is not shaded.

35 is shaded.

14 is shaded.

34 is not shaded.

• Just as one cent is one hundredth of a whole dollar ($0.01), one percent is one hundredth of a whole (0.01).

of a dollar is 50¢ or $0.50.

12

of a whole is 50% or $0.50 0.5.

12


14

of a whole is 25% or $0.25.

14


110

of a whole is 10% or $0.10 0.1.

110

Lesson PracticeUse fraction-decimal-percent pieces for help.

a. What fraction of the triangle is shaded?

b. What percent of the triangle is shaded?

c. What decimal part of the triangle is shaded? .

page 183



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d. What two fractions name the shaded part of this circle?

,

e. What percent of the circle is shaded?

f. What decimal part of the circle is shaded? .

g. What fraction of this rectangle is shaded?

h. What percent of the rectangle is shaded?

i. What decimal part of the rectangle is shaded? .

Name the percent of a dollar represented by the number of coins stated and write the value as a decimal number.

Number of quarters

Percent of a dollar

Value

4 quarters j.

3 quarters k.

2 quarters l.

1 quarter m.

Number of

dimesPercent of

a dollarValue

10 dimes n.

09 dimes o.

08 dimes p.

07 dimes q.

06 dimes r.

05 dimes s.

04 dimes t.

03 dimes u.

02 dimes v.

01 dime w.




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1. 100 points on a quiz

division pointss other points

36 s

100

100 − = s

s = Use work area.

2. common year0031 days January

d left

31 d

365

−31 = d

d = Use work area.

3. Multiply the loop. Divide by the outside number.

quarts

______ cups 1 __ 1 = q ___

28

q = 28

q =

Use work area.


$ _______ stamps

0.45 ____ 1 = m __ m

× $0.45 = m

m =

Use work area.

5. Draw two vertical lines that stay the same distance apart.

Use work area.




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6. factors of 25:

, ,

factors of 50:

, , , , ,

, ,

7. a. fraction shaded?

b. fraction not shaded?

a.

b.

9. quarter to 8 in the morning 10. top missing Add.

w

− $19.46$28.93

19.46 28.93

w

w =

11. 3010− 1342

12. 28547591

+ 26

13. 7640× 30

14. $9.080× 60

8. denominator

2 __ 3

page 186



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15. short division

6 ) __________

$7 . 4 4

16. 362 ÷ 10 = 17. short division

R4 )

_________ 8 9 8

18. $42.37

$00.00

$00.00

+ $00.00

20. Commutative Property of

Multiplication, then offset

6 × 30 × 12 =

23. Which of these numbers is between 360 and 370?

A 356 B 367

C 373 D 381

24. …, 250, 260, 270, 280, ,

, , …


(48 × 6) − 9 =

21. Don’t count February.

February 1 September 1

22. 605

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40

30

C

40˚c

30˚c

) _____

27. two quarters

a. decimal part of a dollar:

.

b. percent of a dollar:

Use work area.

28. 100 ÷ 7 = 14 R 2

Check: 14 × =

+

correct or not?

29. 100 ÷ 4 100 ÷ 5

The more parts a number is divided into, the s the parts

will be, so 100 ÷ 5 is than 100 ÷ 4.

30. 2n = 20

At snacktime, each child in the class ate pieces of fruit. If 20

pieces of were eaten altogether, how many children

were in the ? n =

26. 1803

one decade

page 188


Saxon Math Intermediate 5 193 Adaptations Investigation 3

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page 189

Focus onFocus on• Fraction: Thirds, Fifths,

and Eighths

• To find a fraction of a number, divide by the denominator (bottom number).

1 _ 3 of a number Divide by 3.

1 _ 5 of a number Divide by 5.

1 __ 10 of a number Divide by 10.

Example

1 _ 3 of 24 83 )

____ 2 4

The survey has 120 questions.

1 _ 3 of 120 were true/false.

1 _ 5 of 120 were fill-in-the-blank.

1 _ 8 of 120 were short answer.

The rest of the 120 were multiple choice.

Stephanie answered 1 _ 2 of 120 in the first hour.

1. How many questions did Stephanie answer in 2 ) ________

1 2 0

the first hour?

Teacher Notes:

• Review Hint #15 “Fraction Manipulatives,” Hint #16 “Fraction of a Group, Part 1,” and Hint #17 “Percent.”

• Review “Fraction-Decimal-Percent Equivalents” on page 19 of the Student Reference Guide.

33Name

SM_H5_AD_Inv03_FF.indd 193SM_H5_AD_Inv03_FF.indd 193 11/1/07 10:29:47 AM11/1/07 10:29:47 AM


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I N V E S T I G A T I O N continued

2. How many questions were true/false? ) _____

1 2 0

3. How many questions were fill-in-the-blank? 5 ) ____

21

4. How many questions were short answer? ) ____

21

5. How many questions were multiple choice?

true/false 120 questions

fill-in-the-blank total

short answer multiple choice

total

6. Did the multiple-choice questions make up more than or less

than 1 _ 3 of the questions on the survey?

multiple choice 1 __ 3

7. Together, did the true/false and fill-in-the-blank questions make up more than or less than half of the survey?

true/false total half of 120

fill-in-the-blank

total

3



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8. Together, did the true/false and short-answer questions make up more than or less than half of the survey?

true/false total half of 120

short-answer

total

ActivityActivity page 190

Using Fraction Manipulatives

Use fraction pieces.

9. How many eighths equal one half?

10. How many tenths equal one fifth?

11. How many eighths equal a fourth?

12. Is two fifths more or less than one half?

13. Two fifths of a whole is what decimal part of a whole?

14. Three fifths of a whole is what decimal part of a whole?

15. Four eighths of a whole is what decimal part of a whole?

16. Can you make a half using only thirds?

17. Can you make a half using only fifths?

3



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18. If you had fraction pieces for sevenths, could you make a half using only sevenths? Why or why not?

, because the denominator is an number.

Half of an number is not a whole number of

fraction pieces.

19. Sarah has one half, one quarter, and one eighth. How much

more does she need to have a whole?

20. What single fraction piece equals 2 _ 8 ?

21. If you had a half made from eighths, could you take away three eighths? Why or why not?

because 1 _ 2 is the same as 4 _ 8 , and 3 _ 8 is

than 4 _ 8 .

22. What fraction is 1 _ 2 of 1 _ 2 ?




Use fraction pieces to illustrate these addition and subtractions. Write a complete equation for each.

26. 1 __ 5 + 2 __ 5 1 _ 5 + 2 _ 5 = 00 __

00

3



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27. 3 __ 8 + 5 __

8 3 _ 8 + 00 __

00 = 00 __

00

28. 2 __ 3 − 1 __

3 2 _ 3 − 00 __

00 = 00 __

00

29. 5 __ 8 − 2 __

8 5 _ 8 − 00 __

00 = 00 __

00

Compare. Use fraction pieces for help.

30. 1 __ 8 + 1 __ 5 1 __

2

31. 1 __ 8 + 1 __

8 1 __

2

32. 1 __ 3 + 1 __

3 1 __

2

33. 1 __ 3 + 1 __

3 + 1 __ 5 + 1 __ 8 1

34. Arrange in order from least to greatest:

1 __ 2 , 1 __

8 , 1 __

5 , 1 __

3 , 1 ___

10 , 1 __

4

First compare 1 _ 2 with 1 __ 10 .

, , , , ,

least greatest

35. Arrange in order from least to greatest.

0.3, 0.125, 0.10, 0.50, 0.25, 0.20

, , ,

, ,

3



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Refer to your manipulatives or “Fraction-Decimal-Percent Equivalents” on page 19 of the Student Reference Guide.

36. One third of a whole is what percent of a whole?

37. Three fifths of a whole is what percent of a whole?

38. Four eighths of a whole is what percent of a whole?

Compare.

39. 2 __ 3 50% 40. 2 __

5 50%

3


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