Word Problems About Comparing - District Home · Four hundred eighty-five is less than six hundred ninety. Use work area. 4. square numbers See page 5 in the Student Reference Guide

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Saxon Math Intermediate 4 199 Adaptations Lesson 31

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3131

• Word Problems About

Comparing

New ConceptNew Concept

• To compare two numbers Subtract.

Formula Problem Larger 43 apples− Smaller − 19 apples Difference 24 apples

• Watch for these words:

more fewer less than greater than

Lesson Practice a. How much greater? b. How many fewer? c. How many more?

43

−

greater

42 Mary

− Frank

fewer

95 Juanita

− Cesar

more

page 192

Always put the BIGGER number on top!

SM_H4_AD_L031_FF.Indd 199SM_H4_AD_L031_FF.Indd 199 11/2/07 10:45:24 AM11/2/07 10:45:24 AM


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1. 43 in the flock

− flew away

still in flock

2. 150

−

greater

3. 75 apples

−

fewer

4. It is morning. What time will it be 3 hours from now?

3

121110

9

87 6 5

4

21

time now:

Count forward 3 hours.

5. 412

expanded form:

words:

Use work area.

6.

Written PracticeWritten Practicepage 195



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onWritten Practice,Written Practice, continued continued

9.

20 30

50

+ + − −

Use work area.

7. 4 cm

2 cm

a. perimeter

b. area (area = length × width)

a.

b.

8. a. 2 × 5 =

b. 5 × 7 =

c. 2 × 7 =

d. 4 × 11 =

Use work area.

page 196

10. down 8 degrees

C

10

5

0

–5

–10



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Written Practice,Written Practice, continued continued

13. a. $1 = quarters

b. 1 quarter = of a dollar

c. 3 quarters = of a dollar

Use work area.

14. Three hundred nine is less than three hundred ninety.

Use work area.

15. 390

less

16. $4.22− $2.95

page 196

11. How much less?

75 100 125 150

A B

Find the pattern

B 110

A −

less

12. a. 5 × 8 =

b. 2 × 8 =

c. 5 × 9 =

Use work area.



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17. 909− 27

18. $422− $144

19. 703− 471

20. $4.86+ $2.95

21. 370− 209

22. 22+ n

37

n =

23. 76− c

28

c =

24. What multiplication fact is illustrated by this square?

× =

25. a. √__

9 =

× = 9

b. √___

25 =

× = 25

a.

b.

26. Which of these does not equal 9?

A 3 squared B √___

81

C √___

18 D √___

25 + √___

16

27. a. 1 × 1 =

b. 5 × 5 =

c. 8 × 8 =

d. 9 × 9 =

Use work area.

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28. Compare. Look at the hundreds.

Look at the tens.

Look at the ones.

a. 510 501

b. 722 976

c. 234 238

Use work area.

30. a. b.

r p

a l

c. d.

p o

l a

s

Use work area.

page 197

29. compatible numbers

318 is close to and 473

is close to .

+ =


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3232 Teacher Note:

• Refer students to the Multiplication Table on page 5 in the Student Reference Guide.

• Multiplication Facts:

9s, 10s, 11s, 12s


• In 9s multiplication facts:

The first digit of the product is one less than the factor.

The two digits of the product always add up to 9.

Magic of 9s

9 × 2 = 18 1 + 8 = 9

9 × 3 = 27 2 + 7 = 9

9 × 4 = 36 3 + 6 = 9

9 × 5 = 45 4 + 5 = 9

9 × 6 = 54 5 + 4 = 9

9 × 7 = 63 6 + 3 = 9

9 × 8 = 72 7 + 2 = 9

9 × 9 = 81 8 + 1 = 9

9 × 10 = 90 9 + 0 = 9

Lesson PracticeFind the product for each multiplication fact. Remember, the first digit is one less than the number multiplied, and the two digits add up to nine.

a. 9× 3

b. 5× 9

c. 8× 9

d. 6× 9

e. 9× 4

f. 7× 9

g. 9× 2

h. 9× 9

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Use the Multiplication Table on page 5 in the Student Reference Guide to find each product.

i. 10× 5

j. 10× 7

k. 10× 3

l. 10× 9

m. 11× 6

n. 11× 4

o. 11× 7

p. 11× 9

q. 12× 3

r. 12× 5

s. 12× 2

t. 12× 4

1. 215 in book

Kande has read

left to read

2. greater than 800.

even


3. Four hundred eighty-five is less than six hundred ninety.

Use work area.

4. square numbers See page 5 in the Student Reference Guide.

1, 4, 9, 16, , , , …

1 is the square of . 4 is the square of . To finish the

sequence, 5 × 5 = , 6 × 6 = , and 7 × 7 = .Use work area.

Lesson Practice, continued



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7. 6 + 6 + 6 + 6 + 6 + 6 + 6

× =

8. 3 nickels ¢

2 dimes ¢

Is the total even or odd?

10. centimeters

a. each side

b. perimeter

a.

b.

5. evening

3

121110

9

87 6 5

4

21

6. 729

expanded form:

words:

Use work area.

9. a. nearest ten 66

b. nearest dollar $6.60

c. nearest 25¢ $6.60

c.

b.

a.

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11. Perpendicular looks like this:

and

12. 62– w

38

w =

13. 14. Draw an array of Xs to show 5 × 5.

Use work area.

15. How much greater?

0 100 200

A B

Find the pattern.

B

A − greater

16. a. 9 × 6 =

b. 9 × 8 =

c. 9 × 4 =

d. 9 × 10 =

Use work area.

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17. a. 6 × 6 =

b. 4 × 4 =

c. 7 × 7 =

d. 10 × 10 =

Use work area.

18. a. 2 × 11 =

b. 8 × 11 =

c. 5 × 11 =

d. 3 × 11 =

Use work area.

19. a. What multiplication fact is shown here?

b. √___

25

a. × =

b.

20. √___

81

× = 81

21. $3.60− $1.37

22. 413− 380

23. 875− 218

24. 24 + 36 12 + 48

Use work area.

25. 8 × 8 =

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26. A 3 B 7 C 12 D 15

27. 4 × 6 = 24

6 × 4 = 24

Property of

Multiplication

Use work area.

28. batters

batters


620 East China Sea

121 Yellow Sea

difference

121 is close to .

620 – =

30. a. 11, 22, 33, 44, 55,

b. 12, 24, 36, 48, 60,

Use work area.

page 204


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3333 Teacher Notes:

• Introduce Hint #20 “Writing Numbers” and Hint #21 “Place Value (Digit Lines).”

• Review “Spelling Numbers” and “Place Value” on pages 12 and 13 in the Student Reference Guide.

• Review reference chart “Spelling Numbers.”

• Writing Numbers Through Hundred Thousands


• Place a comma after the word thousand:

4,507 four thousand, five hundred seven 34,507 thirty-four thousand, five hundred seven 234,507 two hundred thirty-four thousand, five hundred

seven

• Counting from the right, place a comma every three digits.

• Four-digit whole numbers are often written without a comma.

• Picture the numbers in groups of three.

Each group is a family (units family, thousands family). The comma tells us the family name. Each family has three members: ones, tens, and hundreds.

Example

Write 75,634 in expanded form.

70,000 + 5000 + 600 + 30 + 4

Example

Compare: 510,000 501,000

Start at the greatest place value, then compare place by place.

510,000 > 501,000

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Read the following numbers to your teacher:

a. 125 ,000 b. 435 ,000 c. 12 , 500

d. 25 , 375 e. 4 , 875 f. 250 , 625

Use words to write these numbers:

g. 2 , 750

h. 14 , 518

i. 500 ,000

Use digits to write each number.

j. twenty thousand ,

k. twelve thousand, three hundred fifty ,

l. one hundred twenty thousand, five hundred

,

Write in expanded form:

m. 5280 + + n. 2040 +

o. Which digit in 284,359 is in the ten-thousands place?

p. Compare: 760,000 670,000 Start at the greatest place value.

q. Arrange these dates in order from earliest to latest: Start at the greatest place value.

1969 1903 1957 1927

, , ,

Lesson Practice



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1. 272 K’Neesha

Marcos

more

2. 3425

expanded form:

words:

Use work area.

3. Draw 2 parallel lines (horizontal).

Cross with right-angle line (vertical).See page 16 in the Student Reference Guide.

Use work area.

4. 4 × 4 = 42

× = 49 √___

49 −

5.

a. perimeter

b. area (Area = length × width)

a.

b.

6. Put in commas. Circle groups.

2 5 0 0 0 0

words:

Use work area.

Written PracticeWritten Practice page 209



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7.

…, 230, 240, 250, 260, , , , , …

Use work area.

8. ten-thousands place

123,456

9. 9 × 4 √___

36

Use work area.

10. It is evening. What time will it be 2 hours and 25 minutes from now?

time now:

3

1211

10

9

87

65

4

21


Count forward 25 minutes.

11.

2000 2100 2200 2300

Find the pattern.

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12. a. 5 × 8 = b. 4 × 4 =

c. 8 × 8 = d. 12 × 12 =

a. b.

c. d.

13. a. 9 × 3 = b. 9 × 4 =

c. 9 × 5 = d. 9 × 10 =

b.a.

d.c.

14.

40 60

100

+

+

−

−

Use work area.

15. 20 + 20 + 20 + 20 + 20

×

16. $7.37− $2.68

17. 921− 58

18. 464+ 247

19. 329+ z

547

z =

20. $4.88+ $2.69

21. 555− c

222

c =

22. Which month?

5/27/98

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23.

1 inch

The diameter of a circle is equal

to radii.

26. 25,000 250,000

Start at the greatest place value.

Use work area.

28. 189 Kentucky176 Maryland

altogether

29. See page 1 in the Student Reference Guide.

12, 24, 36, 48, , ,

,

30. 10, 20, 30, , , , , ,

page 211

24. 48

12161428

+ 37

25. 587

146

21+ 15

27. Which number is not in the sequence?

1, 4, 9, 16, 25, 36, …

A 64 B 49

C 80 D 100


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3434 Teacher Notes:

• Review Hint #21 “Place Value (Digit Lines).”

• Review “Place Value” on page 13 in the Student Reference Guide.

• For additional practice, students may complete Targeted Practice 34.

• Writing Numbers Through Hundred Millions


• Use digit lines.

• Three digit lines will always follow a comma.

• Always put a comma after the words thousand and million.

hund

red

mill

ions

ten

mill

ions

mill

ions

hund

red

tho

usan

ds

ten

thou

sand

sth

ousa

nds

hund

red

ste

nson

es, ,

millions thousands units

Example

Use words to write:

12345678 12,345,678

Circle the families. 12 , 345 , 678

Write the families. Twelve million, three hundred forty-five thousand, six hundred seventy-eight

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Use words to write each number:

a. 121 , 340 , 000

b. 12 , 507 , 000

c. 5 , 075 , 000

Use digits to write each number:

d. twenty-five million , ,

e. twelve million, five hundred thousand

, ,

f. two hundred eighty million

, ,

g. Start at the greatest place value.

Compare: 34 million 43 million

h. Start at the greatest place value.

Arrange in order from least to greatest:

, ,

i. Start at the greatest place value.

Arrange in order from least to greatest: 12,3751,000,000

987,000

, ,

Lesson Practice



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1. 465

greater

2. 420 Marcie

Kareem

fewer

3. a. perimeter


Use work area.

4. 25,463

expanded form:

Use work area.

5.

4 cm

6. It is afternoon. What time will it be in 1 hour and 35 minutes?

Time now:

Count forward 1 hour:

Count forward 35 minutes:



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7.

10. a. 3 – 4

b. two million 200,000

Use work area.

8. 12 + 12 + 12 + 12 + 12

× =

9. 76

59

11. How much less?

200 210 220 230

A B

Find the pattern.

B

A –

less

12. a. 5 × 7 =

b. 6 × 6 =

c. 9 × 9 =

d. 10 × 10 =

Use work area.

13. a. 3 × 9 =

b. 9 × 7 =

c. 8 × 9 =

d. 9 × 1 =

Use work area.

14. a. 11 × 11 =

b. 6 × 12 =

c. 8 × 11 =

d. 10 × 12 =

Use work area.

page 216

15. a. Circle the families. 3,500,000

words:

b. seven hundred fifty thousand digit lines digits:

Use work area.



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16. 535– 268

17. 908– 43

18. $471– $346

19. c+ 329

715

c =

20. c– 127

398

c =

page 216

21. 12 in. = 1 ft

12 in.

d = 2r

22. Five squared is how much more than 5 + 5? 5 × 5

52

5 + 5 more

23. two odd

one even

fact family

+ + – –

Use work area.

24. × = 9

× = 16

√__

9

√___

16 +



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25. See page 15 in the Student Reference Guide.

Use work area.

26. thousands place

3,756,289

A 3 B 7 C 5 D 6

28. twelfth term

11, 22, 33, 44, , ,

, , ,

, , ,

29. eighth term

12, 24, 36, 48, , ,

,

27. In order from greatest to least:

, , ,

Use work area.

page 217

30. Caitlin needs bags because 25 + 25 + 25 + 25 = 100.

$2.49 per bag of 25

$ + $ + $ + $ = $

Use work area.


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3535

• Naming Mixed Numbersand Money


• Use the word “and” when naming mixed numbers.

two and one fourth

214

• To write money amounts using digits: There will always be two digits after the decimal point.

$0.04 = 4¢40¢ = $0.40

• To write money amounts using words: Use “and” in place of the decimal point. $30.76 thirty dollars and seventy-six cents

Lesson PracticeWhat mixed numbers are pictured here?

a. = b. =

Shade these circles to show the mixed numbers:

c. 1 1 __ 4 d. 2 3 __

4

page 218

Math Language

A mixed number is a whole number and a fraction:

3 1 __ 2



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Use words to write each mixed number:

e. 12 3 __ 4 f. 2 7 ___

10

g. 6 9____100

Write each amount with a cent sign instead of a dollar sign:

h. $0.17 i. $0.05

Write each amount with a dollar sign instead of a cent sign:

j. 8¢ k. 30¢

l. Write the value of two quarters, two dimes, and one nickel with a dollar sign. Then use a cent sign to write this amount again.

$ . ¢

Use words to write:

m. $20.05 _______________________________________

n. Show how to write the dollars line on a check for $12.25.

100


1. 72 in 1998

in 1968

more




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8. The square root of 81 is how much less than seven squared?

7 × 7 =

______ × ______ = 81

72

√___

81

9. It is evening. What time will it be 2 hours and 20 minutes from now?

time now:



Use work area.

2. 300 yd

100 yd

+ + + =

The distance around the block is the .Use work area.

Written Practice,Written Practice, continued continued page 222

6. Find the pattern. 7. See page 15 in the Student Reference Guide.

A B C D

3. 97 first

second

third

in all

4. mixed number

5. four dollars and sixty-five cents



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10. 2 3 ___ 10

words:

Use work area.

11. Find the difference. B

A −

difference

Find the pattern.

300 400 500 600

A B

12. $1.43

words:

Use work area.

13. a. 6 × 9 =

b. 4 × 9 =

c. 3 × 9 =

d. 10 × 9 =

Use work area.

14. a. 6 × 6 =

b. 7 × 7 =

c. 8 × 8 =

d. 11 × 11 =

Use work area.

15. × = 25

× = 16

√___

25

√___

16 −




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19. $5.32+ $3.44

20. c+ 294

870

c =

21. 423− 245

22. 670− z

352

z =

23. Write two hundred fifty million. Use digit lines.

, ,

24.

…, 3400, 3500, 3600, 3700, ,

, , …

Use work area.

25. a. 7 7

b. $6. 82

Use work area.


16. Shade 2 __ 3 .

Use work area.

17. $6.05− $2.53

18. 489+ z

766

z =



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26. If 7 + = 10, then which of the following equals 7 − ?

A 3 B 4 C 7 D 10

27. a. thirty thousand 13,000

b. 74¢ $0.74

Use work area.

28. greatest to least Start at the greatest place value.

, ,

Use work area.

29. twelfth term

a. 11, 22, 33, 44, , ,

, , , ,

,

b. 12, 24, 36, 48, , ,

, , , ,

,

a.

b.

30. Name a real-world example of:

a. parallel linesParallel looks like railroad tracks.

b. perpendicular linesPerpendicular looks like this:

a.

b.

page 224


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3636

• Fractions of a Dollar


• Coins can be shown as fractions of a dollar.• One penny is one hundredth of a dollar. 100 pennies = 1 dollar

3 pennies = 3 ____ 100

of a dollar

$0.03 = 3 ____ 100

of a dollar

• One fourth is also called “one quarter.” 4 quarters = 1 dollar

1 quarter = 1 __ 4 of a dollar

$0.25 = 1 __ 4 of a dollar

• One dime is one tenth of a dollar. 10 dimes = 1 dollar

3 dimes = 3 ___ 10

of a dollar

$0.30 = 3 ___ 10

of a dollar

• One nickel is one twentieth of a dollar. 20 nickels = 1 dollar

7 nickels = 7 ___ 20

of a dollar

$0.35 = 7 ___ 20

of a dollar

Lesson Practice

a. three quarters

__ $ .

b. three nickels

__ $ .

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c. fifty pennies.

__ $ .

d. 1___10

of a dollar 1__4 of a dollar e. 1__

2 of a dollar $0.25

¢ ¢ ¢ ¢

f. List all of the different ways to pair two coins.Act it out.

nickel, quarter quarter,

nickel, quarter,

nickel, half dollar dime,


1. 70 in. Dad

Quinh

shorter

2. $36.49 into the store

spent

left the store

3. 11 at school

homework25 total

4. mixed number




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5. Which letter below has NO right angles?

T H E N

6. 2,700,000 Circle the families.

words:

Use work area.

7. eighty−two thousand, five hundred digit lines

,

Use work area.

8. It is morning. What time will it be 4 hours and 20 minutes from now?

time now:

3

121110

9

87 6 5

4

21



9. 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4

×

10. a. nearest ten: 176

b. nearest dollar: $17.60

a.

b.

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11. How much less? Find the pattern.

500 600 700

X Y Y

X –

less

12. a. 2 × 8 =

b. 5 × 6 =

c. 4 × 5 =

d. 5 × 8 =

Use work area.

13. a. 3 × 3 =

b. 5 × 5 =

c. 9 × 9 =

d. 10 × 10 =

Use work area.

14. a. 9 × 7 =

b. 9 × 4 =

c. 9 × 8 =

d. 9 × 12 =

Use work area.

15. × = 36

× = 49

√___

36

√___

49 +

16. $7.32– $3.45

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17. $4.89+ $2.57

18. 464– 238

19. 548+ 999

20. 487+ z

721

z =

21. 250– c

122

c =

22. c– 338

238

c =

23. 87– b

54

b =

24. ten−thousands place

8,367,254

25. Which does not equal one half of a dollar?

A 2 quarters B 0.50¢

C $0.50 D 50¢

26. 5 in.

4 in.

area = length × width

A 9 in. B 18 in.

C 20 sq. in. D 18 sq. in.

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27. a. –12 –21

b. 1 __ 4 of a dollar $0.25

¢ ¢

a.

b.

28. tenth term

a. 12, 24, 36, 48, 60, , ,

, ,

b. 11, 22, 33, 44, 55, , ,

, ,

a.

b.

29.

List all of the different ways to pair two bills. Act it out.

$1, $5,

$1, $5,

$1, $10, Use work area.

30. 397

296

Louisiana

Oregon

combined

397 rounds to and 296 rounds to .

+ = Use work area.

page 232


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3737

• Reading Fractions and Mixed Numbers from a Number Line


• To name mixed numbers on a number line:

1. Count from the whole number to the arrow to find the numerator (top number).

2. Count the segments between whole numbers to find the denominator (bottom number).

3. Don’t forget the whole number.

Example

5 6 7

1. Two segments between 5 and arrow The numerator is 2.2. Three segments between 5 and 6 The denominator is 3.3. The whole number is 5.

The answer is 5 2 __ 3 .

Lesson PracticeName each fraction or mixed number marked by the arrows below:

0 1 2 3

a. b.

0 1 2 3

c.

a.

b.

c.

d.

e.

0 1 2 3

d. e.

page 233

Teacher Note:

• For additional practice, students may complete Targeted Practice 37.



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f. Label 25 3 __ 4 , 26 1 __

2 , and 27 1 __

4 .

25 26 27


1. Pearl River

San Juan River

longer

2. Sabine

+ longer430 Wisconsin

3. four hundred seventy-five thousand, three hundred forty-two digit lines

Circle the digit in the ten-thousands place.

,

4. area = length × width

is a reasonable answer

because the tiles will be placed

across and down.

× =




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5. mixed number

10 11 12

7. 8. 12 3___10

words:

Use work area.

9. 7026

expanded form:

words:

Use work area.

6. 5 cm

3 cm

perimeter Add all sides.

10. It is early morning. What time will it be 2 hours and 35 minutes from now?

3

121110

9

87 6 5

4

21

time now:



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11. three quarters How many quarters in a dollar?

a. fraction

b. value

a.

b.

12.

× =

13. a. 9 × 6 =

b. 9 × 5 =

c. 9 × 0 =

Use work area.

14. a. 10 × 10 =

b. 7 × 7 =

c. 8 × 8 =

Use work area.

15. a. 5 × 7 =

b. 6 × 5 =

c. 2 × 8 =

Use work area.

16. × = 81

× = 49

√___

81

√___

49 +

17. $6.63– $3.55

18. $4.99+ $2.88

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19. a– 247

321

a =

20. z+ 296

531

z =

21. 523– z

145

z =

22. 2846486432

+ 344

23. a.

…, 450, 460, 470, 480, ,

, , …

b. Count by .

Use work area.

24.

1 ft

1 ft = in.

d = 2r

25. a. 1 __ 4 of a dollar 1 __

2 of a dollar

¢ ¢

b. 101,010 110,000

b.a.

26. One yard does not equal which of the following?

See page 2 in the Student Reference Guide.

A 36 in. B 3 ft

C 1 m D 2 ft + 12 in.

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27. In order from smallest to largest:

, , ,

Use work area.

28. Twice the weight of a cheetah would be 130 + = ,

which is close to 170.

29. 23

30. 47° July 34° minimum

cooler

Written PracticeWritten Practice,, continued continued page 237


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3838 Teacher Note:

• Refer students to Multiplication Table on page 5 in the Student Reference Guide.

• Multiplication Facts (Memory Group)


• This is the memory group:

3 × 4 = 12 4 × 7 = 28

3 × 6 = 18 4 × 8 = 32

3 × 7 = 21 6 × 7 = 42

3 × 8 = 24 6 × 8 = 48

4 × 6 = 24 7 × 8 = 56

Lesson Practice a. Complete Power Up F.

Find each product.

b. 11× 11

c. 12× 12

d. 12× 9

e. 12× 6

f. 12× 8

g. 12× 7

h. 12× 5

i. 12× 11

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1. 405 harbor

river

more

2. five hundred seventy-five thousand, five hundred forty-two digit lines.

,

3. 2503

expanded form:

words:

Use work area.

4.

a. perimeter


a.

b.




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5.

7 8 9 10

6. Which street is parallel to Broad St.?

MAIN ST.

BROAD ST.

ELM

ST.

9. It is morning. How long is it until 12:30 p.m?

time now: 3

121110

9

87 6 5

4

21

Count forward hours: 7:25 − 12:25

Count forward minutes: 12:25 − 12:30

7.

page 240

8. a. nearest ten 624

b. nearest dollar $6.24

c. nearest 25 cents $6.24

a.

b.

c.



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10. fifty-cent coin

a. fraction

b. value

b.

a.

11. 2 11 ____ 100

words:

Use work area.

12. 6 squared

× =

15. a. 6 × 7 =

b. 6 × 8 =

c. 7 × 8 =

a.

b.

c.

16. 1 ___ 10

of a dollar 1 __ 2 of a dollar

¢ ¢

page 241

13. a. 3 × 4 =

b. 3 × 6 =

c. 3 × 8 =

a.

b.

c.

14. a. 4 × 6 =

b. 4 × 7 =

c. 4 × 8 =

a.

b.

c.



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17. $7.23− $2.54

18. $5.42

+

19. 943− 276

20. top missing Add.

z

− 581222

z =

21. c+ 843

960

c =

22. 100 cm

23. 28 + 36 + 78 + √___

49 =

283678

+

24. × = 144

× = 121

√____

144 − √____

121

– =

25. Which of the following is not 1 ___ 10

of a dollar?

A dime B 0.10¢

C $0.10 D 10¢

26. Which digit in 457,326,180 is in the hundred-thousands place?


A 1 B 6

C 4 D 3

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27. a. A angle has s corners.

b. An angle is than a right angle.

c. An angle is than a right angle.

Use work area.

28. 12, 24, 36, 48, …

a. rule: Count by

b. Complete the sequence. Circle the eleventh term.

12, 24, 36, 48, , , , , , ,

Use work area.


$14.99$18.95

$14.99 rounds to and $18.95 rounds to .

+ =

Use work area.

30. How much for six?

Cost $11 $22 $33

Number of Tickets 1 2 3 4

$44

5 6

page 242


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3939 Teacher Notes:

• Introduce Hint #22 “Reading Inch Rulers.”

• Use a tape measure to illustrate concepts in this lesson.• Reading an Inch Scale

to the Nearest Fourth


• The long marks on this ruler are inch marks.

321 4inch

inchmark

inchmark

inchmark

12

inchmark

12

• The marks halfway between the inch marks are 1 __ 2 -inch

marks.

• Each inch is divided into fourths.

321 4inch

The short tick marks are 1 __ 4 -inch marks.

One quarter inch = 1 __ 4 inch

2 __ 4 = 1 __

2 (Think: Two quarters equal half of a dollar.)

ActivityActivity page 244

Make a Ruler and Measure

Use an inch ruler to measure the segments below.

a.

b.

c.

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a. Shade these circles to show that 2 __ 4 equals 1 __

2 .

Name each point marked by an arrow on this inch scale. Remember to write the whole number.

321 4inch

b c d e

b. c. d. e.

f. Measure the length and width of this paper.

length: width:

g. Find the distance from A to C.

A B C

h. If Pam stacks two of these blocks together, what are all the possible combined heights she could make?

Act it out.

1inch

2inches

inches

121

, ,

Lesson Practice



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1. 35 mother

Trinity

older

This is l − s = d

problem because it c two numbers.

2. four hundred sixty-eight thousand, five hundred two digit lines

,

3. 3905

expanded form:

words:

Use work area.

4. 243 J’Maresh

Leilani

total

Odd or even?

5. 100 1 ____ 100

words:

Use work area.




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6. Negative nineteen is greater than negative ninety.

Use work area.

7. Use a dollar sign and a decimal point to write the value of two dollars, one quarter, two dimes, and three nickels.

$ 2.00 $ . $ . $ .

8. It is morning. School begins at 8:15 a.m.

time now: 3

121110

9

87 6 5

4

21

early or late?

how many minutes? Use work area.

9. nine dimes

a. fraction

b. value

b.

a.

10. One kilometer is how many meters? See page 1 in the Student Reference Guide.

11. 12. Find the length to the nearest quarter inch.

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13. a. 4 × 3 =

b. 8 × 3 =

c. 8 × 4 =

d. 4 × 12 =

Use work area.

14. a. 6 × 3 =

b. 6 × 4 =

c. 7 × 6 =

d. 6 × 12 =

Use work area.

15. a. 7 × 3 =

b. 7 × 4 =

c. 8 × 6 =

d. 8 × 12 =

Use work area.

16. × = 64

× = 36

√___

64

√___

36 −

17. $4.86+

18. $4.86− $2.47

22. 463+ q

527

q =

page 247

23. 8 squared

× =

24. … , 470, 480, 490, 500,

, ,

, …

Use work area.

19. 293

+

20. 893− 678

21. 463− y

411

y =



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25. Draw a triangle that has three acute angles.


Use work area.

26. Which of these does not equal 9 + 9?

A 2 × 9 B 9 × 2

C 3 × 6 D nine squared

27. In order from most expensive to least expensive:

Use work area.

29. What are the perimeters?

6 in. 4 in.

6 in. 2 in.

4 in. 2 in.

28. Anastacia’s estimate

reasonable because

350 – 200 = ,

which close to 140.

Use work area.

30. How many inches in 20 feet?

feet × 12 = inches

page 248


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4040 Teacher Notes:

• Introduce Hint #24 “Measuring Liquids and Capacities of Containers.”

• Refer students to “Liquids” and “Equivalence Table for Units” on page 1 in the Student Reference Guide.

• Display reference chart “Liquids.”

• Capacity


Abbreviations forU.S. Liquid Measures

fluid ounce fl oz

cup c

pint pt

quart qt

gallon gal

1 cupHalf&

Half

Milk

1 cup1 oz1 mL 1 pint 1 quart 1 liter 1 gallon2 litersgallon12

ActivityActivity page 251

Measuring Capacity

a. How many cups of liquid equal a pint?

b. How many pints of liquid equal a quart?

c. How many quarts of liquid equal a half gallon?

d. How many half gallons of liquid equal a gallon?

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e. How many quarters equal a dollar?

f. How many quarts of liquid equal a gallon?

g. U.S. Liquid Measure

8 fl oz 1 c

c 1 pt

pt 1 qt

qt 1 gal

h. Compare: 1 quart 1 liter

i. Compare: 1__2 gallon 2 liters

j. How many liters will it take to fill a gallon container?

k. A full 2-liter bottle of liquid contains how many milliliters of liquid?

Lesson Practice

a. Complete this table. b. How many quarts in 12 gallons?

Gallons 1 2 3 4 5 6 7 8

Quarts 4 8

c. one pint = 2 cups

one cup = 8 ounces

How many ounces is one pint?

2 × =

d. About how many milliliters would it take to fill a 3 1__2 -liter container?

1000 + 1000 + 1000 + 500 =

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1. 112 big

small

fewer

2. 36 in. one yard 12 in. one piece

other piece

3. 47 Mrs. Green

husband

son

in all

5. thousands place 27,384,509

6. $3.00 $ . $ . $ .

words:

Use work area.


7. 1 gal = qt See page 1 in the Student Reference Guide.

8.

4. 7,500,000 Circle the families.

expanded form:

words:

Use work area.



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12. What type of angle is formed by the hands of the clock in problem 11?

A acute B right

C obtuse D straight

9. 10. 1 gal = 3.78 L

Use this information to compare:

1 gallon 3 liters

Use work area.

11. It is evening. How long until 12:00?

time now:

Count forward minutes:

3

121110

9

87 6 5

4

21

10:10 11:00

Count forward hours:

11:00 12:00

13. a. −29 −32

b. $0.75 3 __ 4 of a dollar

¢ ¢

Use work area.

14. 2 cm

15. a. 6 × 6 = b. 7 × 7 = c. 8 × 8 = d. 12 × 12 =

Use work area.

16. a. 7 × 9 = b. 6 × 9 = c. 9 × 9 = d. 9 × 12 =

Use work area.

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17. a. 7 × 8 = b. 6 × 7 = c. 8 × 4 = d. 12 × 7 =

Use work area.

18. $4.98+ $ .

19. m− $6.70

$3.30

m =

20. 416− z

179

z =

24. 10 1 ___ 10

words:

Use work area.

25. two quarters

a. fraction b. value

a.

b.

21. 536+ z

721

z =

22. √__

1

√__

4

√__

9 +

23. Draw an array of Xs to show 3 × 7.

Use work area.

26. A rectangle has an area of 24 square inches. Which of these could be the length and width of the rectangle? Circle one.

Area = length × width

A 6 in. by 6 in. B 12 in. by 12 in.

C 8 in. by 4 in. D 8 in. by 3 in.

Use work area.

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27. Two quarters equal half of a dollar.

8 2 __ 4 = 8

Use work area.

28.

24 ft.

24 ft.

12 ft.12 ft.

+ + + =

The perimeter is so the gardener should buy the roll.

Use work area.


$0.66 $ $0.66 $ $12.00 + $12.00

The tax on each pair of gloves is about . The total cost is a little

more than $12 + $12 + + = .

Use work area.

30. How many different three-digit numbers can you make with 6, 2, and 0?

Label even or odd.

page 255


Saxon Math Intermediate 4 259 Adaptations Investigation 4A/B

Name ©

200

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I N V E S T I G A T I O N 4A/B4A/B

page 256

Focus onFocus on• Tenths and Hundredths

• Relating Decimals and Fractions

• The value of coins can be shown as a fraction of a dollar.

• We use decimal numbers when we write money amounts.

1___10

$0.10 1___20

$0.05 1____100

$0.01 1__4

$0.25

• The numbers after the decimal point show parts of a dollar.

.1s

place place places 1

101

100s

decimal point

ActivityActivity 1 1 page 256

Tenths and Hundredths

Show these amounts with your money manipulatives.

1. $345.23 2. $0.42 3. $5.20 4. $3.02

Write the amount shown in your textbook.

5. 6. 7.

Teacher Note:

• Student will need Lesson Activity 23 to complete Activity 2.

SM_H4_AD_Inv4A-B_FF.Indd 259SM_H4_AD_Inv4A-B_FF.Indd 259 11/2/07 10:44:38 AM11/2/07 10:44:38 AM

I N V E S T I G A T I O N continued4A/B

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Use money manipulatives to compare.

8.

9. $0.40 $0.07

Write the amounts shown in your textbook in order from greatest to least for problems 10 and 11.

10. $1.10 , ,

11. $1.20 , ,

Use bills and coins to show these decimal numbers:

12. 3.42 three and forty-two hundredths

13. 0.24 twenty-four hundredths

14. 12.03 twelve and three hundredths

15. 1.3 one and three tenths

• The square is divided into 10 equal parts.

110 0.1 (Both say one tenth.)

• One part is shaded.


I N V E S T I G A T I O N continued4A/B©

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Use the pictures in your textbook for problems 16-19.

16. decimal:

fraction:

17. decimal:

fraction:

18. decimal:

fraction:

19. decimal:

fraction:

• The square is divided into 100 equal parts.

• One part is shaded.

1100 0.01 (Both say one hundredth.)



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Use the pictures in your textbook for problems 20-23.

20. decimal: 21. decimal:

fraction: fraction:

22. decimal: 23. decimal:

fraction: fraction:

• Look at problems 19 and 22. Half of each square is shaded.

1 __ 2 = 5 ___

10 = 50 ____

100 and 1 __

2 = 0.5 = 0.50

24. Which of the following numbers does not equal one half?

A 5 ___ 10

B 5 C 50 ____ 100

D 0.05

Complete each comparison.

25.

0.1 0.10

26.

0.2 0.02

27. The pictures above show the decimal numbers 0.1, 0.2, 0.02.

Arrange the numbers in order from least to greatest.


I N V E S T I G A T I O N continued4A/B©

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Activity 2Activity 2 page 260

Using Unit Squares to Relate Fractions and Decimal Numbers

• Use your textbook to complete this activity.

• Fractions and decimals are two ways to describe parts of a whole.

• Decimals use place value to show the part of the whole.

0 . 2 5 whole number . tenth hundredth

one decimal place two decimal places three decimal places

0.1 = 1 ___ 10

0.12 = 12 ____ 100

0.123 = 123 _____ 1000

Read each number aloud. Remember to say tenths, hundredths, or thousandths.

33. a. 75 ____ 100

b. 0.75

34. a. 7 ____ 100

b. 0.07

35. a. 3 ___ 10

b. 0.3

36. a. 2 ___ 10

b. 0.2



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• To name 12.25:

wholenumber fraction

.

1. Name this part.2. Say or write “and.”3. Then name this part.

12 25

Read each number aloud. Then use words to write each number.

37. a. 10.75

b. 12.5

38. a. 6.42

b. 10.1

Use digits to write each of these decimal numbers:

39. one and three tenths _____

40. two and twenty-five hundredths _____

41. three and twelve hundredths _____

42. four and five tenths _____

ActivityActivity 3 3 page 262

Using Decimal Numbers on Stopwatch Displays

• This activity is optional.


Documents

Word Problems About Comparing - District Home · Four hundred eighty-five is less than six hundred ninety. Use work area. 4. square numbers See page 5 in the Student Reference Guide