SM H4 AD L111 FF - LearningTOPSlearningtops.yolasite.com/resources/H4_Lessons111-120_inv12.pdf · LESSON Name Saxon Math Intermediate 4 729 Adaptations Lesson 111 © 2008 Saxon 111111

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Saxon Math Intermediate 4 729 Adaptations Lesson 111

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• Estimating Perimeter, Area, and Volume

New ConceptNew Concept

• Use grids to estimate area:

A

FD

C

GE

B

1. Count the whole squares. (F)2. Count the mostly full squares. (E, B, G)3. Do not count squares that are mostly empty. (D, A, C)

Area = about 4 squares

• To estimate perimeter:

4 units

2+ units 3+ units

a little more than 3

a little more than 2

+ 4

Perimeter = a little more than 9

ActivityActivity 1 1 page 706

Estimating Perimeter and Area

• Use your textbook to complete this activity.

page 704


New Concept,New Concept, continued continued

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ActivityActivity 2 2 page 706

Estimating Volume

• Use your textbook to complete this activity.

Lesson PracticeEstimate the perimeter and area of each figure on these grids.

a. Each small square represents one square centimeter:

perimeter

area

b. Each small square represents one square inch:

perimeter

area

c. This problem is optional.


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1. a. min sec 1 __ = ? ____ 300

) _____

b. min sec ___ 60

– 60 ___ ? )

_____

a. b.

2. Trevor

Ann (2 × Trevor)

Lee (Ann + 5)

3. books per shelf

bookshelves

total books

4. a. 9 ___ 10

of 30 is of

___ = ? ___ 30

30 students

___ students

___ students

___ students

___ students

___ students

___ students

___ students

___ students

___ students

___ studentsdid not turn inhomework

110

turned inhomework

910

) _____

b. % did not turn in homework.

a. b.

Written PracticeWritten Practice page 707


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Written Practice,Written Practice, continued continued

8. Shade these to show that 6 __ 8

= 3 __ 4 .

Use work area.

9. Putt ’N’ Putt

Player 1 2 3 4 5 6 7 8 9 Total

Michelle 6 7 5 2 4 1 3 5 3 36

Mary 5 4 4 3 4 3 2 5 3 33

Michelle’s average

6. Write a fraction as your answer.

1 = ? __ 3

7.

= Use work area.

5. A

0.20 0.1 0.3

CB

a. point A (fraction):

b. point B (decimal number):

c. point C (fraction):

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onWritten Practice,Written Practice, continued continued

10. Time now:

Time until 4:20 p.m: hours, minutes

Use work area.

11. Finish this quadrilateral so that it has:

two parallel sides

one side that is perpendicular to the parallel sides

one side that is not perpendicular to the parallel sides

Type of quadrilateral?

12. Factors of 10: 1, 2, 5, 10

Factors of 15: 1, 3, 5, 15

Largest factor of both?

13. Factors of 8: , , ,

Factors of 12: , , , , ,

Largest factor of both?

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18. 1 9 ___ 10

− 1 2 ___ 10

19. 60× 800

20. 3 2× 2 3

+00000X

21. Convert to dollars.

× 9

16. 5 __ 8

+ 2 __ 8 = 17. 3 __

5 + 1 __

5 =

14. 4.3

.

+ .

15. 364.1

− .

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22. 103 = 23. short division

4x = 3500

)____

x =

24. short division

4824 _____ 8

=

25. long division

0 060 )

_________ 5 4 0

26. long division

0 R10 )

_________ 4 6 3

27. Estimate the perimeter and area of this figure. Each small square represents one square inch.

page 709


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28. Shade 25%.

4 cm

1 cm

Use work area.

29. Cylinder

A B C D

Tissues

30. volume = length × width × height

3 in.

2 in.

2 in.

My answer is r because it is the product of

l × w × h .

page 709

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112112 Teacher Notes:

• Introduce Hint 53 “Reducing Fractions (Manipulatives and Shortcuts).”

• Review “Fraction Families Equivalent Fractions” on page 18 in the Student Reference Guide.

• For additional practice, students may complete Fraction Activity J.

• For additional practice, students may complete Targeted Practice112.

• Reducing Fractions


• Divide the same number into the numerator (top number) and denominator (bottom number).

Example

Reduce 4 __ 6 .

Hint: ÷ 2

4 __ 6 = 4 ÷ 2 ______

6 ÷ 2 = 2 __

3

46

23

Lesson PracticeWrite the reduced form of each fraction:

Hint: ÷ 2 Hint: ÷ 2 Hint: ÷ 3

a. 2 __ 4 = b. 2 __

6 = c. 3 __

9 = d. 3 __

8 =

e. 2 ___ 10

= f. 4 ___ 10

= g. 9 ___ 12

= h. 9 ___ 10

=

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3.

1 2 3 4 5cm

mm 10 20 30 40 50

a. millimeters

b. centimeters Use a decimal.

a.

b.

4. 5 __ 9 of 36 is

of 5 __

9 = ? ___

36

) _____

36 horses

___ horses

___ horses

___ horses

___ horses

___ horses

___ horses

___ horses

___ horses

___ horses

gray59

not gray49

1. a. boards ft of fence

10 ___ = ? ___ 50

) _____

b. $0.90

a.

b.

2. perimeter and area

3 cm

5 cm



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5. a. 15 ___ 2 )

_____

b. 15 ___ 3 )

_____

c. 15 ___ 4 )

_____

a.

b.

c.

6. more than 32 years old

less than 40 years old

prime number

7. a.

=

b. percent

a. b.

8. a. Draw all the lines of symmetry in this regular quadrilateral.

b. A regular quadrilateral has how many lines of symmetry?

c. Does a regular quadrilateral have rotational symmetry?

Use work area.

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9. Reduce. Hint: ÷ 3 Hint: ÷ 2

a. 3 __ 6 = b. 4 __

6 = c. 6 ___

12 =

a.

b.

c.

10. average

2336

34

) _____

11. $ 5 T-shirts

tax

Left out of $27?

12. 3 3 __ 9

+ 4 4 __ 9

13. 1 __ 7 + 2 __

7 + 3 __

7 = 14. 37.2

135.7 10.62 2.47+ 14.0

15. 11 ___ 12

– 10 ___ 12 = 16. 8 ___ 10

– 5 ___ 10 =

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17. 4 8× 3 6

+00000X

18. 7 2× 5 8

+00000X

19. $4.08

× 7

20. 25.42

+ .

21. 36.2− 4.27

22. long division

90 ÷ 20 =

23. 5 __ 8 – 5 __

8 = 24. short division

R7 )

____________ 2 5 4 9

25. short division

10 )

______________ $1 9 . 4 0

26. 400,000 and 500,000 halfway Add, then divide by 2.

27. A coin has 2 sides.

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28.

5 in.

2 in. 6 in.

a. geometric name

b. volume = length × width × height

c. True or False: All of the opposite faces of the box are parallel.

Use work area.

29. Act it out.

Turning a page in a book is like what geometric transformation?

30. Estimate the perimeter and area. each square = 1 square inch

To estimate the p , I

added the length of the sides in closest square inches.

To estimate the a , I counted

the whole and mostly full s .

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• Review Hint “42 Multiplication by Two Digits.”

• For additional practice, students may complete Targeted Practice 113.• Multiplying a Three-

Digit Number by a Two-Digit Number


• Carry on your fingers.

• Indent using X as a placeholder.

Lesson PracticeMultiply. Remember to write the dollar sign and decimal point in money problems.

a. 2 3 5× 2 4

+000000X

b. 4 3 0× 1 4

+000000X

c. $1. 2 5× 2 4

+000000X

d. 4 0 6× 3 2

+000000X

e. $6. 2 0× 3 1

+000000X

f. 5 6 2× 4 7

+000000X

page 715

1. 006380045600589

3000

Written PracticeWritten Practicepage 717


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2. perimeter and area

7 in.

7 in.

3. 2 m = cm

each side

4. 8 ft

12 ft

15 ft

10 ft

7 ft 2 ft a. perimeter

b. number of 1-foot square tiles to cover the floor

a. b.

5. 6843

6. Reduce. Hint: ÷ 5 Hint: ÷ 2

a. 4 __ 5 = b. 5 ___

10 = c. 4 ___

10 =

a. b. c.

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7. 374.251

words:

Use work area.

8. Shade these to show that 1 __ 2 = 4 __

8 .

Use work area.

9. 1 __ 4 = 0 __

8

1 __ 4 = 0 ___

12

1 __ 4 = 0 ___

20

Use work area.

10. dollars days

750 ____ = ? __ 1

) ____

11. Pikes Peak

estimated

less actual

12. short division

R6 )

____________ 4 8 3 7

13. short division

1372 _____ √___

16 )

____

14. long division

040 )

_________ 9 6 0

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15. long division

0 020 )

____________ 1 3 6 0

16. 30.07

– .

17. 46.0

– .

18. 37.15

.00

.00

.00

+ .

19. $3. 2 0× 4 6

+000000X

20. 3 0 7× 2 5

+000000X

21. 8 ___ 15

+ 6 ___ 15

= 22. 4 4 __ 5

– 1 3 __

5 _____

23. Estimate the perimeter and area.

each square = 1 square centimeter

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24. … 10,000, 20,000, 30,000, …

, ,

Use work area.

25. a. equilateral equal sides

A B C D

b. Triangle B has one angle and two

angles.

c. Triangle B has two p segments.

The third segment intersects but is not p .

Use work area.

26. One full turn = 360º

Two full turns =

A 360º B 180º C 720º D 90º

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27.

a. Which of these letters has no lines of symmetry?

b. Which letter has rotational symmetry?

a. b.

28.

A

B

C

E

DF

r and t

29. perimeter

142 in.


5 cm 3 cm

3 cm

page 719

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114114 Teacher Note:

• Review “Mixed Numbers and Improper Fractions” on page 18 in the Student Reference Guide.

• For additional practice, students may complete Targeted Practice 114.

• Simplifying FractionAnswers


• Fix “top heavy” (improper) fractions. Change to mixed numbers.

Example

5 3 __ 5 /0

+ 6 4 __

5 ______

11 7 __ 5 /0 11 7 __

5 / = 11 + 1 2 __

5 / = 12 2 __

5

• Reduce fractions when possible.

Example

3 __ 4 – 1 __ 4 = 2 __

4 2 ÷ 2 _____

4 ÷ 2 = 1 __

2

Lesson PracticeSimplify the answer to each sum or difference.

Fix or reduce.

a. 4 __ 5 + 4 __

5 = 8 __

5 = b. 5 __

6 – 1 __

6 = = c. 3 2 __

3

+ 1 2 __ 3

=

d. 5 1 __ 4

+ 6 3 __ 4

e. 7 7 __ 8

– 1 1 __ 8

f. 5 3 __ 5

+ 1 3 __ 5

= = =

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1. 70 copies× $0.06 each

$0.25 tax$ . $ .

$5.00 paid

$ . $ . change

My answer is r because I broke the problem into

steps and Tessa ended up with c .

2.

6 cm

a. area b. perimetera.

b.


3. a. Walker

Dembe (2 × Walker)

Chris (Dembe + $6)

b. Walker Dembe Chris )

____

Totala.

b.


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4. Number of Bagels 12 24 36 48 60

Number of Dozens 1 2 3 4 5

a. Rule: To find the number of b , multiply the number of

dozens by .

b. How many bagels in 12 dozen?

a.

b.

6. I used compatible n .

1800 ÷ 9 = , so the exact quotient should be close

to .

Use work area.

5.

quarters

rolls

40 ___ 1 = ? __ 2

$0.25

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7. Reduce.

Hint: ÷ 2

a. 2 ___ 12

=

Hint: ÷ 2

b. 6 __ 8 =

Hint: ÷ 3

c. 3 __ 9 =

a.

b.

c.

8. 1 __ 3 × 2 __

2 =

3 __ 6 + __ = ___

9. black

red (not last)

green (one ahead of black)

first:

second:

last:

Use work area.

10. Act it out. 11. 50% of $40 12. 4.62

.00

+ .

Use work area.

13. 14.62 – (6.3 – 2.37) =

6.3 14.62

Written Practice,Written Practice, continued continued page 723

14. 3 __ 5 + 4 __

5 =

Fix the top heavy (improper) fraction.

15. 16+ 3 3 __

4


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16. 1 2 __ 3

+ 3 1 __ 3

=

Fix.

17. 2 __ 5 + 3 __

5 =

Fix.

18. 7 4 __ 5

+ 7 1 __ 5

=

Fix.

19. 6 2 __ 3

+ 3 2 __ 3

=

Fix.

20. 3 7 2× 3 9

+000000X

21. 1 4 2× 4 7

+000000X

22. 360 × √___

36 =

360

×

24. short division

8y = 4832

y =

25. short division

2840 _____ 23

26. long division

0 R30 )

_________ 9 6 3

23. Estimate the area.

each square = 1 square centimeter

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27. Which arrow could be pointing to 427,063?

A B C D

500,000300,000 400,000

28. perimeter

141 in.

29. What is the geometric shape of a volleyball?

page 724

30. Distributive Property

5(20 + 6)

(5 × ) + ( × ) =

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• Review “Fraction Families Equivalent Fractions” on page 18 in the Student Reference Guide.


• Renaming Fractions


• Rename fractions using the loop method.

2__3

= ?___15 15 × 2 = 30 2__

3= 10___

15 30 ÷ 3 = 10

Lesson PracticeComplete each equivalent fraction:

a. 1__4

= ___12 b. 2__

3= ___

12 c. 5__6

= ___12

d. 3 __ 5 = ___ 10 e. 2 __

3 = __ 9 f. 3 __

4 = __ 8

page 725


1. $ people

__ 3 = ? ___

12 )

____ 2.

5 ft

4 ft2 ft

3 ft

3 ft

7 ft

a. perimeter

b. area

a.

b.


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3. ( × ) − 8 =

4. 2 __ 3 of 306

) ____

123

306 words

___ words

___ words

___ words

memorized23

left to memorize13

is of

2 __ 3 = ? ____

100

5.

1 2 3 4cm

mm 10 20 30 40

a. centimeters

b. millimeters

a.

b.

6. 356,420

words:

Use work area.

7. 356,420

A B C D

500,000300,000 400,000

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8. Complete each equivalent fraction:

a. 1 __ 2 = ? __

6

b. 1 __ 3 = ? __

6

c. 1 __ 2

= ? __ 6

a.

b.

c.

9. Write the reduced form of each fraction:

Hint: ÷ 2 Hint: ÷ 3

a. 2 __ 6 = b. 6 __

9 = c. 9 ___

16 = a.

b.

c.

10. a. overtime = all workers

(Reduce the fraction.)

b. percent

a.

b.

11. different three-digit

numbers

Use work area.

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12. $10 10th

11th

12th

13th

14th

15th

13. 2 1 __ 2 mi

+

=

Fix.

14. 9.36 − (4.37 − 3.8) =

4.37

9.36

Use work area.

15. 24.32 − (8.61 + 12.5) =

8.61

24.32

Use work area.

16. 5 5 __

8 ___

0

+ 3 3 __ 8 _____ 0

=

Fix.

17.

6 3 ___ 10

____

0

+ 1 2 ___

10 ______ 0

=

Reduce.

18.

8 2 __ 3 ___

0

− 5 1 __ 3 _____ 0

19.

4 3 __ 4 ___

0

− 2 1 __

4 _____ 0

=

Reduce.

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20. 1 2 5× 1 6

+000000X

21. $1. 5 0× 6

+000000X

22. short division

6m = 3642

m =

23. short division

$125 ÷ 5 =

24. long division

0 R40 )

_________ 6 4 5

25. 3m = 62

=

m =

m =

26. n = 16

3n =

n =

27. average

1821

21

) ____

28. Dion’s temperature

normal temperature

above

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29. Estimate the perimeter and area.

each square = 1 square mile

30. 1

2

4

36

8

7

5

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116116

• Common Denominators


• To rename fractions so that they have a common denominator:

1. Look down the multiplication table column for each denominator.

2. Find the smallest number both columns share. 3. Rename (loop method).

Example

2 __ 3 and 3 __

4

1. Go down the 3s column and the 4s column.

2. Find that they both share a 12.

3. Rename:

2 __ 3 = ? ___

12 12 × 2 = 24 2 __

3 = 8 ___

12

24 ÷ 3 = 8

3 __ 4 = ? ___

12 12 × 3 = 36 3 __

4 = 9 ___

12

36 ÷ 4 = 9

Lesson Practice a. Rename 1 __

2 and 1 __

5 so that they have a common denominator of 10.

1 __ 2 = ___ 10 1 __

5 = ___

10

b. Rename 1 __ 2 and 5 __

6 so that they have a common denominator of 12.

1 __ 2 = ___

12 5 __

6 = ___ 12

page 729

Math Language

Common denominators are equal.

Common denominators

3 __ 8 5 __

8

Different denominators

3 __ 8 5 __

9


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Lesson Practice, continued

Rename each pair of fractions using their least common denominator.

c. 1__2

= __6 d. 1__

3= __

2 __ 3 = __ 6 1 __

4 = __

e. 1__2

= __ f. 2__3

= __

3 __ 5 = __ 2 __

5 = __


1. 1 __ 4

of 24 24 seashells

___ seashells

___ seashells

___ seashells

___ seashells

gave14

kept34

is of

3 __ 4 = ? ___ 24

) _____

2. twice the perimeter

2 mi

1 mi

3. oranges$

2____0.42

= __?

)_____


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4. a. 3 __ 4

of 64 = 64 cards

___ cards

___ cards

___ cards

___ cards

rookie players34

not rookie players14

is of

3 __ 4 = ? ___ 64

) ____

b. % showed rookie players

Use work area.

5. 7.2, 7 7 ___ 10

, 7 3 ___ 10

, 7.5

87

, , , greatest least

6. Reduce each fraction first.

A 3 __ 6

=

B 5 ___ 10

=

C 10 ___ 21

=

D 50 ____ 100

=

7. Complete each equivalent fraction:

a. 1 __ 2 = ___

12

b. 1 __ 3 = ___ 12

c. 1 __ 4 = ___ 12

Use work area.


a. 5 ___ 10

=

b. 8 ___ 15

=

c. 6 ___ 12

=

Use work area.

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9. $ clips

0.42 ____ 6 = ? __

1 $ erasers 0.64 ____

8 = ? __ 1

cost per clip ¢ cost per eraser ¢

Total: (10 × clip) + (20 × eraser) = $

Use work area.

10. 1st 14

2nd 16

3rd 18

4th

5th

6th

7th

8th

9th

10th

11. a. 1 __ 4 = ___ 12

2 __ 3 = ___ 12

b. 1 __ 3 = __

3 __ 4 = __

Use work area.

12.

1

5

3

Probability = 0 Cannot happen

Probability = 1 Certain to happen

13. 47.14 − (3.63 + 36.3) =

3.63

47.14

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14. 50.1 + (6.4 − 1.46) =

6.4 50.1

17. 5 3 __ 5

+ 1 2 __ 5

=

Fix.

18. 5 __ 6

+ 1 __ 6

=

Fix.

19. 12 3 __ 4

− 3 1 __ 4

=

Reduce.

20. 6 1 __ 5

1 1 __ 5 –

21. 3 4 0× 1 5

+000000X

22. 3 0 7× 2 6

+000000X

23. 2500× 70

24. short division

3550 _____ 5

=

25. long division

432 ÷ 30 =

26. short division

R

9 ) ____________

5 7 8 4

15. 3 __ 4

+ 3 __ 4 + 3 __

4 =

Fix.

16. 4 1 __ 6

+ 1 1 __ 6

=

Reduce.

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27. Look at flight schedules on page 733.

a. If Karen wants to arrive in Los Angeles in the morning, how much will she pay for airfare?

b. If Karen chooses the lower priced round trip, when is her return flight scheduled to land back in Chicago?

c. Plane arrives in Los Angeles at 8:21 p.m., which is 10:21 p.m. in Chicago.

Use your student clock to find elapsed hours from 6:11 p.m. to 10:21 p.m.

A 2 hours B 4 hours C 6 hours D 8 hours

c.a. b.

28. Estimate the area.

each square = 1 square inch

29. Look at the pentagon in problem 28.

a. Does it have reflective symmetry?

b. Does it have rotational symmetry?

Use work area.

30. See page 734.

a. A would move one rectangle on top of the other.

b. total area:

Use work area.

page 733

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• Review Hint #12 “Estimating or Rounding.”

• Review “Place Value” on page 24 in the Student Reference Guide.• Rounding Whole Numbers

Through Hundred Millions


Whole-Number Place Values

hund

red

tril

lions

ten

trill

ions

trill

ions

hund

red

bill

ions

ten

bill

ions

bill

ions

hund

red

mill

ions

ten

mill

ions

mill

ions

hund

red

tho

usan

ds

ten

thou

sand

sth

ousa

nds

hund

red

ste

nson

esd

ecim

al p

oint

, , , , .

• To round numbers through hundred millions:

1. Underline the place value that you will be rounding to.

2. Circle the digit to its right.

3. Ask: Is the circled number 5 or more? (5, 6, 7, 8, 9)

Yes Add 1 to the underlined number.

No The underlined number stays the same.

4. Replace the circled number (and any numbers after it) with zero.

Example

3 8 ,274 40,000 12, 8 76,250 13,000,000

4 2 7,063 400,000 4 2 7,063,000 400,000,000

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Round each number to the nearest ten thousand:

a. 1 9 ,362 ___ ___, ___ ___ ___ b. 31,289 ___ ___, ___ ___ ___

Round each number to the nearest hundred thousand:

c. 868,367 ___ ___ ___, ___ ___ ___ d. 517,867 ___ ___ ___, ___ ___ ___

e. Round 2,156,324 to the nearest million. ___, ___ ___ ___, ___ ___ ___

f. Round 28,376,000 to the nearest ten million. ___ ___, ___ ___ ___, ___ ___ ___

g. Round 412,500,000 to the nearest hundred million.

___ ___ ___, ___ ___ ___, ___ ___ ___

Lesson Practice


1. 45

45 ÷ 4 = .

Each group has

students, except for the one group

that has an extra student because

of the remainder.

2. 12 cm

8 cm

a. area

b. perimeter

a.

b.


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3. 5 __ 6 of 90

) ____

123 is of

__ = ? ___ 90

90 questions

___ questions

___ questions

___ questions

___ questions

___ questions

___ questions

correct56

not correct16

4. What shape?

a. roll of paper towels

b. baseball

a.

b.


a. 3 __ 6 =

b. 5 ___ 15

=

c. 8 ___ 12

=

a.

b.

c.

6. Rename 3 __ 4 and 5 __

6 using their least

common denominator.

3 __ 4 = ___

5 __ 6 = ___

Use work area.

7. ten-millions place

328,496,175


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8. How many miles is it from Winder to Atlanta?

Winder

AtlantaAthens

23 mi?

23 mi+ ? 73 mi

9. Use your student clock.

Time shown:

3

121110

9

87 6

54

21

Count forward three quarters of an

hour:

10. See page 738.

minimum temperature:

maximum temperature: Use work area.

11. 4.36

.

+ .

12. 8.54 – (4.2 – 2.17) =

4.2

.

8.54

.

13. 5 __ 9 + 5 __

9 =

Fix.

14. 3 2 __ 3

+ 1 2 __ 3

=Fix.

15. 4 5 __ 8 + 1 = 16. 7 2 __

3

+ 1 2 __ 3

= Fix.

17. 4 4 __ 9

+ 1 1 __ 9

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18. 11 ___ 12

+ 1 ___ 12

=

Fix

19. 5 7 0× 6 4

+000000X

20. 3 8 2× 3 1

+000000X

21. 5 4× 1 8

+00000X

22. short division

3731 _____ 7 =

23. short division

0 0 R9 )

____________ 5 4 3 2

24. long division

0 0 R60 )

_________ 5 4 8

25. 1×1, 2×2, 3×3…

1, 4, 9, 16, 25, , ,

× =

Use work area.

27. a. What word does not name this shape?

A quadrilateral B parallelogram

C rhombus D trapezoid

b. 2 a angles and 2 o angles

c. 2 pairs of p sides

a.

page 738

26. 20,851,820


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28. 6 cm = mm

perimeter = mm

each side = mm

Use work area.

30. 900

800

700

600

500

400

Ele

vatio

n(a

bov

e se

a le

vel i

n fe

et)

Milligan,OH

Danbury, CT

Pahala,HI

Elevations of U.S. Cities

Holly Springs, MS

City and State

a. Cities with an elevation difference of 250 feet:

850

– 250

and

b. is the fewest feet above sea level.

Use work area.

29. a. top layer

× total

b. vertices of cube

vertices of pyramid

more

a. b.

page 739

L E S S O N

Name


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• Introduce Hint #54 “Long Division, Part 2.”

• For additional practice, students may complete Targeted Practice 118.• Dividing by Two-Digit

Numbers


Use long division:

1. Divide2. Multiply3. Subtract4. Bring down

Use zero as a placeholder.

If the ones digit is 4 or less, round down before guessing:

0 0

32 ) _____

1 2 8

Think: 30 ) _____

1 2 0 3 goes into 12 four times.

4 or less 0 0 432 )

_____ 1 2 8

1 2 8 0

If the ones digit is 5 or more, round up before guessing:

0 0

36 ) _____

1 2 8

Think: 40 ) _____

1 2 0 4 goes into 12 three times.

5 or more 0 0 3 R 2036 )

_____ 1 2 8

1 0 8 2 0

When you multiply, if the answer is greater than the dividend, try a smaller number.

0 0

43 ) _____

2 4 6 Think: 40 ) _____

2 4 0 0 0 643 )

_____ 2 4 6

2 5 8 too large, so try

5 as the answer

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Lesson PracticeDivide. Use long division.

a. 0 0 R32 )

_________ 1 2 8 b.

0 R21 )

_____ 9 0 c.

0 R25 )

_____ 6 8

d. 0 0 R42 )

_________ 2 5 0 e.

0 R41 )

_________ 8 8 0 f.

0 R11 )

_________ 5 5 5


1. a. On which day was the temperature

the highest?

b. What was the high temperature

70°F

60°F

50°FTem

per

atur

e High Temperatures for the Week

S T T SW FMDay of the Week on Tuesday?

c. Wednesday

Monday

up

Use work area.

2.

24 m

15 m

a. perimeter

b. area

a.

b.


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3. See the circled numbers in the multiplication table on page 5 in the Student Reference Guide.

Average of 1, 4, 9, 16, 25 11

Average of , , , ,

4. Jan. Apr. July Oct.

Feb. May Aug. Nov.

Mar. June Sept. Dec.

5. Reduce the fraction.

6. Name each shape.

a. b. c.

See “Geometric Solids” on page 17 in the Student Reference Guide.

a.

b.

c.


a. 6 __ 8 =

b. 4 __ 9 =

c. 4 ___ 16

=

a.

b.

c.

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8. Rename 2 __ 3 and 3 __

4 using their least

common denominators.

2 __ 3 = 25 ___

25

3 __ 4 = 25 ___

25

Use work area.

9. 27,386,415

words:

Use work area.

10.

600400 500

W

W =

11. Draw two parallel segments that are one inch long and one inch apart.

Make a quadrilateral by drawing two more parallel segments.

Type of quadrilateral:

Use work area.

page 744

12. 4 4 __ 5

+ 3 3 __ 5

= Fix.

13. 5 1 __ 6

+ 1 2 __ 6

= Reduce.


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14. 7 3 __ 4

+ 1 __ 4

=

Fix.

15. long division

0 R13 )

_____ 5 0

16. long division

0 0 R72 )

_________ 2 9 7

17. 5 3 __ 8

+ 5 1 __ 8

=

Reduce.

18. 4 1 __ 6

+ 2 1 __ 6

=

Reduce.

19. 7 2 0× 3 6

+000000X

20. 1 4 7× 5 4

+000000X

21. short division

R8 )

____________ 5 7 6 6

22. long division

021 )

_________ 4 4 1

23. 4.75

.

+ .

24. 18.4 − (4.32 − 2.6) =

4.32 18.4

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25. 18, 9 76,457 26. 297,576,320

27. 75, 80, 85, 90, 90, 95, 95, 95, 100

a. median:

range:

b. mode:

Use work area.

28. 5 11 ____ 100

5.67 5.02 5 83 ____ 100

, , , least greatest

Use work area.

29. long division

0 R13 )

_____ 5 7

Use work area.

30. Rename.

2 __ 3 = 0 ___ 15

3 __ 5 = 0 ___ 15

Use work area.

page 745

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119119

• Adding and Subtracting Fractions with Different Denominators


1. Find a common denominator.2. Rename (loop method).3. Add or subtract the renamed fractions.

Example

1 __ 4 = __ 8

+ 3 __ 8 = __ 8

1 __ 4 = 2 __

8

+ 3 __ 8 = 3 __

8

5 __ 8

Lesson PracticeFind each sum or difference.

a. 1 __ 2 = __ 6

+ 2 __ 6 = __ 6

b. 1 __ 3 = __ 9

+ 1 __ 9 = __ 9

c. 1 __ 8 = 00 ___ 00

+ 1 __ 2 = 00 ___

d. 3 __ 8 = 00 ___ 00

− 1 __ 4 = 00 ___

e. 2 __ 3 = 00 ___ 00

− 2 __ 9 = 00 ___

f. 7 __ 8 = 00 ___ 00

− 1 __ 2 = 00 ___

page 746

Teacher Note:



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1. 15 ft.

12 ft.

2. a. perimeter

b. equilateral, isosceles, or scalene?

2.2 cm

1.9 cm1.2 cm

a.

b.

3. 3 __ 8 of 32

) ____

123

32 pencils

___ pencils

___ pencils

___ pencils

___ pencils

___ pencils

___ pencils

___ pencils

___ pencils

erasers58

no erasers38

is of

3 __ 8 = ? ___

32

4. a. dozen pencils

1 __ = ? __

) _____

b. 50% of one dozen pencils

a. b.


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5. Rounding both factors up would make the estimate too b .

Rounding both factors down would make the estimate too s .

I used c numbers. 70 × 80 = .

Use work area.

6. volume in cubic centimeters

top layer

×

total

7. DVD

DVD

CD

CD

tax

total

I added the price of 2

and 2

plus tax.

8. miles hours

285 ____ = ? __

) _____

9. Not equivalent to 1 __ 2 ?

Reduce each fraction first.

A 4 __ 8 = B 11 ___

22 =

C 15 ___ 30

= D 12 ___ 25

=

page 748


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10. Reduce.

a. 8 ___ 10

= b. 6 ___ 15

= c. 8 ___ 16

=

a.

b.

c.

11. Add commas.

1 2 3 4 1 5 7 2 0

words:

Use work area.

12. 8.3

.

.

+ .

13. 17.42 − (6.7 − 1.23) =

6.7 17.42

14. 3 3 __ 8

+ 3 3 __ 8

=

Reduce.

15. 1 __ 4 = 00 ___ 00

+ 1 __ 8 = 00 ___

16. 1 __ 2 = 00 ___ 00

+ 1 __ 6 = 00 ___

=

Reduce.

17. 5 5 __ 6

− 1 1 __ 6

=

Reduce.

page 748


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18. 1 __ 4 = 00 ___ 00

− 1 __ 8 = 00 ___

19. 1 __ 2 = 00 ___ 00

+ 1 __ 6 = 00 ___

=

Reduce.

20. 8 7× 1 6

+00000X

21. 3 4 0× 4 9

+000000X

22. 504× 30

23. short division

$35.40 ÷ 6 =

24. short division

5784 _____ 4

=

25. short division

R7 )

____________ 2 3 8 5

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26. long division

0 30 )

_________ 4 5 0

27. long division

0 R32 )

_________ 4 5 0

28. long division

0 15 )

_________ 4 5 0


hearts _________ full deck

___ 52

= 00 ___ 00

30. Shade 30%.

5 cm

2 cm

Use work area.

page 749

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120120

• Adding and Subtracting

Mixed Numbers with

Different Denominators


• To add or subtract mixed numbers with different denominators:

1. Copy the problem vertically.2. Rename the fractions so that they have common

denominators.3. Add or subtract the fraction side.4. Add or subtract the whole numbers.5. Reduce the fraction side.

Example

4 1 __ 6 = 4 1 __

6

+ 2 1 __ 2 = 2 3 __

6

6 4 __ 6 = 6 2 __

3

Lesson Practice

Add. Reduce when possible.

a. 3 1 __ 2 = 3 00 ___

00

+ 1 1 __ 4 = 1 1 __

4

b. 4 3 __ 4 = 00 ___

00

+1 1 __ 8 = 00 ___

c. 4 1 __ 5 = 00 ___

00

+ 1 3 ___ 10

= 00 ___ =

d. 6 1 __ 6 = 00 ___

00

+ 1 1 __ 3 = 00 ___

=

page 750


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Lesson Practice, continued

Subtract. Reduce when possible.

e. 3 7 __ 8 = 3 7 __

8

– 1 1 __ 4

= 1 00 ___

f. 2 3 __ 5 = 00 ___

00

– 2 1 ___ 10

= 00 ___

=

g. 6 7 ___ 12

= 00 ___ 00

– 1 1 __ 6

= 00 ___

h. 4 3 __ 4 = 00 ___

00

– 1 1 __ 2 = 00 ___


1. gallons

quarts

1 __ = 11 ___ ?

2. 1 __ 4 of 60 )

____ 60 people

___ people

___ people

___ people

___ people

play trumpet14

do notplay trumpet

34

is of

__ 4 = ? ___

60

3. 10 mm

a. area

b. perimetera.

b.


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4. a. Esteban b. average

Trevin (Esteban − 8) 61 in. ) ____

+ Chelsea (Trevin − 5)

a. b.

5. parallel line segments

A B

CD

and

Use work area.

6. 47 mi 24 miAltoona Mayville Watson

?

I used c numbers. 45 + 25 = , which

is close to .

Use work area.

page 752


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3

1

5

4

2

6

8. $2 9 8,900

9. See “Solids” on page 17 in the Student Reference Guide.

a. name:

vertices

edges

faces

b. name:

vertices

edges

faces

Use work area.

page 752


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10. Reduce.

a. 9 ___ 15

=

b. 10 ___ 12

=

c. 12 ___ 16

=

a.

b.

c.

11. one hundred nineteen million, two hundred forty-seven thousand, nine hundred eighty-four

, ,

Use work area.

12. 14.94 − (8.6 − 4.7) =

8.6

14.94

13. 6.8 − (1.37 + 2.2) =

1.37

6.8

14. 3 2 __ 5

+ 1 4 __ 5

=

Fix.

15. 5 __ 8 = 5 __

8

+ 1 __ 4 = __

8

16. 1 1 __ 3 = 00 ___

00

+ 1 1 __ 6 = 1 1 __

6

=

Reduce.

17. 5 9 ___ 10

= 5 9 ___ 10

– 1 1 __ 5 = 00 ___ 00

18. 5 __ 8 = 5 __

8

– 1 __ 4 = 00 ___ 00

page 753


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19. 1 __ 3 = 1 __

1

– 1 __ 6 = 1 __

1

20. 217× 38

+

21. 173× 60

22. 90× 500

23. short division

R7 )

____________ 2 9 4 2

24. long division

0 R10 )

_________ 4 5 3

Use work area.

25. long division

0 R11 )

_________ 4 5 3

Use work area.

26. Evaluate m + n. m = 3 2 __ 5

n = 2 1 ___ 10

Reduce.


3 ft 2 ft

2 ft

28. A B C?121 in.

123 in.

29. 493,782 30. 1 __ 2 %

1 __ 4 %

page 753

Saxon Math Intermediate 4 791 Adaptations Investigation 12

I N V E S T I G A T I O N©

200

8 S

axon

page 754

Focus onFocus on• Solving Balanced

Equations

• An equation states that two quantities are equal.

• A balanced scale is one way to picture an equation.

The combined weight on one side equals the combined weight on the other side.

Example

333N4

N 3 10

3

43

3

N

3

N 7

X 33

33

X

2X 12

3

3

X

33

33

X

X 6

ActivityActivity page 755

Solving Equations

• Use your textbook and Lesson Activity 49 to complete this activity.

1212Name

Documents

SM H4 AD L111 FF - LearningTOPSlearningtops.yolasite.com/resources/H4_Lessons111-120_inv12.pdf · LESSON Name Saxon Math Intermediate 4 729 Adaptations Lesson 111 © 2008 Saxon 111111