SM H5 AD L081 FF - Weebly

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Saxon Math Intermediate 5 529 Adaptations Lesson 81

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8181 Teacher Notes:

• Introduce Hint #50 “Reducing Fractions (Manipulatives and Shortcuts).”

• Review “Tests for Divisibility” on page 20 and “Fraction Families Equivalent Fractions” on page 18 in the Student Reference Guide.

• Reducing Fractions, Part 1

New ConceptNew Concept

• To find equivalent fractions, multiply by a fraction name for 1.

1 __ 2 × 3 __

3 = 3 __

6

• To reduce fractions, divide by a fraction name for 1.

3 __ 6 ÷ 3 __

3 = 1 __

2 (3 ÷ 3 = 1)/

(6 ÷ 3 = 2)

• If both terms cannot be divided by the same number, the fraction cannot be reduced.

2 _ 5 cannot be reduced.

Lesson Practice

a. Reduce 8 __ 12 by dividing 8 __ 12 by 4 _ 4 . 8 ___ 12

÷ 4 __ 4 = 8 ÷ 4 _______

12 ÷ 4 = ___

b. Which of these fractions cannot be reduced? (Circle one.)

A 2 __ 8 B 3 __

8 C 4 __

8 D 6 __

8

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SM_H5_AD_L081_FF.indd 529SM_H5_AD_L081_FF.indd 529 11/2/07 3:37:26 PM11/2/07 3:37:26 PM


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Lesson Practice, continued

Add, subtract, or multiply as indicated. Remember to reduce the answers.

c. 3 __ 8

− 1 __ 8 = ___ ÷ ___ = __ d. 3 ___

10 + 3 ___

10 = ___ ÷ ___ = __

e. 2 __ 3

× 1 __ 2 = ___ ÷ ___ = ___ f. ___

30 ÷ ___ =

Rewrite each mixed number with a reduced fraction. (Keep the whole number. Reduce the fraction.)

g. 1 3 __ 9 h. 2 6 __

9 i. 2 5 ___

10

Find each sum or difference. Remember to reduce the answers.

j. 1 1 __ 4 + 2 1 __

4 = k. 1 1 __

8 + 5 5 __

8 = l. 5 5 ___

12 − 1 1 ___

12 =

Written PracticeWritten Practice page 530

1. highest

lowest

more

2. average 3. 1 ft = in.

( × ) + =

4. .

.



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onWritten Practice,Written Practice, continued continued

12. 3.4

+ .

13. 6.25

− .

14. Draw 32.

Use work area.

5. 2 __ 3 × ___ = ___

12

1 __ 4 × ___ = + ___ 12

Use work area.

6. prime numbers

,

7. 10 ___ 12

÷ 2 __ 2 =

8.

mm 10 20

1 __ 2 of length = width 9. a. 1 __

4 of 24 24 members

__ members

__ members

__ members

__ members

14

b. 1 __ 2 of answer to a.

c. 3 ___ 24

=

b.

a.

c.

10. rectangle in problem 8

Area = length × width

11. Q R S

?

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Written Practice,Written Practice, continued continued

15. 6 )

______________ $8 7 . 0 0

16.

R40 )

____________ 2 4 3 8

18. $10 − ($5.80 + 28¢) = 19. 5 3 __ 5 + 4 − 1 3 __

5 =

Convert.

21. 4 __ 3

× 1 __ 2 =

Reduce.

24. a. $ . collected from each

× customers

total

22. 10 ___ 7

× 7 ___ 10

=

Convert.

23. See page 532.

A translation B rotation

C reflection D slide

20. Reduce.

3 __ 6 ÷ 3 __

3 =

17. Divide 5280 by 9. Write the answer as a mixed number with a reduced fraction.

page 531

b. total

paid to company

profit

a.

b.



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25. number cube rolled once

a. probability of an even number =

b. different event with same probability: Probability of an number.

Use work area.

26.

0–3

7654321

Number of Books

Books Read Last Year N

umbe

r of

Stu

dent

s

4–7 8–11 12–15 16–19

a. How many students read 12 books or more?

b. How many students read 15 books or fewer?

b.a.

27. All s are r , but some r

are not s .

A SR B S

R C

RS

D R S

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28. fraction: 15% =

Reduce: ___ ÷ 5 __

5 = ___

29. 1 __ 2 × 1 __

2 1 __

2

Use work area.

30. See page 533.

283

261

I used c numbers that were multiples of 25.

+ + + =

Use work area.

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8282 Teacher Notes:

• Introduce Hint #51 “Finding the Greatest Common Factor.”

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

• For additional practice, students may complete Targeted Practice 82.

• Greatest Common Factor (GCF)


• To find the greatest common factor (GCF):

1. List the factors of the smaller number in order.2. Starting with the largest factor, cross out any factor

that does not divide evenly into the larger number.3. Circle the first number that divides evenly into the

larger number. This is the GCF.

Example

Find the greatest common factor (GCF) of 8 and 20.

1. List the factors of 8. 1, 2, 4, 8

2. Eight does not divide evenly into 20.

Cross 8 out. 1, 2, 4, 8

3. Four divides evenly into 20.

Circle 4 and stop. 1, 2, 4 , 8

Four is the greatest common factor of 8 and 20.

Lesson PracticeFind the greatest common factor (GCF) of each pair of numbers:

a. 6 and 9

factors of 6: 1, 2, 3, 6

b. 6 and 12

factors of 6: , , ,

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c. 15 and 100

factors of 15: , , ,

d. 6 and 10

factors of 6: , , ,

e. 12 and 15 f. 7 and 10

, , , , , ,

Reduce each fraction by dividing the terms of the fraction by their GCF. (See problems a, b, and c.)

g. 6 __ 9 ÷ ___ = h. 6 ___

12 ÷ ___ = i. 15 ____

100 ÷ ___ =


1. 8 a.m. to 2 p.m. = hours

hours _______ dollars

0 ______ 34.50

= 1 __ ?

I used c numbers to check my answer. $34.50 is close

to .

÷ 6 = which is close to .



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2. Estimate the product.

396

507

3. …, 3452, 3552, 3652, ,…

4. The height of most cars is about:

A 4 to 5 feet B 8 to 10 feet

C 40 to 50 feet D 20 to 25 feet Measure yourself compared to a car.

5. .

.

6. octagon sides

each side = 12 in.

perimeter = in.

7. not prime

A 11 B 21

C 31 D 41

8. a. List the factors of the smaller number (20):

, , , , ,

Cross out those that are not factors of the larger number (30).

The biggest factor is the GCF. Circle it.

b. Divide both by the GCF. 20 ___ 30

÷ ___ = a.

b.

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9. 3 __ 4

of a foot

is of

__ = ? ___ 12

10. See page 537.

blue to gray


C reflection D flip

11. a. 1 __ 3 of 12 12

13

23

b. 2 __ 3 of 12

is of

__ = ? ___ 12

a.

b.

12. Reduce:

6 ___ 12

=

Divide both by the GCF.

13. 23 32

Use work area.

14. 5 __ 7 + 3 __

7 =

Convert.

15. 4 __ 4 − 2 __

2 =

Convert.

16. 2 __ 3 × ___ = 6 __

9

17. 976.5470.4436.7

+ 98.6

18. $40.00− $32.85

19. $8.47× 70

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20. R6 )

_______________ 4 3, 7 1 5

21. 2640 _____ 30

= 22. 367× 418

23. 3 1 __ 4 + 3 1 __

4 =

Simplify.

24. $18.64 ÷ 4 =

25. Find the probability that with one spin the spinner will not stop on A. Write the answer as a reduced fraction.

A

A

B

C

D

E

E

F

27. fraction: 22% =

Reduce: ÷ ___ =

26. All r are p , but

some p are not r .

A R P

B R P

C R

P

D

RP

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28. a. Soledad

Garret

needs

b. ft in.

1 __ 0 = 5 __ ?

Which child is exactly 5 feet tall?

c. average d. range e. median

Use work area.

29. Mt. Blackburn

Mt. McKinley (Mt. Blackburn + 1198)

Mt. Foraker (Mt. McKinley – 890)

Use work area.

30. 1976 I used c numbers.

1957 – =

Use work area.

Soledad

Hei

ght

(in in

ches

)

68

66

64

62

60

58

James

Heights of the Children

Garret

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Teacher Notes:

• Introduce Hint #52 “Faces on a Cube” and Hint #53 “Geometric Solids (Manipulatives).”

• Refer students to “Geometric Solids” on page 17 in the Student Reference Guide.

• Use geometric solids to illustrate concepts in this lesson.

• Properties of Geometric Solids


Geometric Solids

Shape Name

Cube

Pyramid

Rectangular prism

Cylinder

Sphere

Cone

• The flat surfaces of solids are called faces.

• Two faces meet at an edge.

• Three edges meet at a vertex.

edgeface

vertex

Example

AB C

D

E

FG

H

___ AB and

___ CD Parallel Segments remain the

same distance apart.___

CD and ___

CE Perpendicular Segments intersect at right angles.___

AG and ___

EH Skew Segments on different faces do not intersect.

page 539

Math Language

A plane figure is a flat shape.

8383L E S S O N

Math Language

Geometric solids are 3-dimensional shapes. They take up space.



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Name the geometric shape of each of these real-world objects.

a. brick b. soup can

c. ice cream cone d. shoebox

Use geometric solids for help.

e. The pyramid has how many triangular faces?

f. How many rectangular faces? g. Edges?

h. Vertices?

Use the rectangular solid to answer problems i–k.

i. Name a pair of parallel line segments.

j. Perpendicular line segments: K

H I

JN

OL

M

k. Pair of skew line segments:

l. Which figure has faces that are perpendicular to its base?

A B C D

m. Which figure has six congruent faces?

A B C D

Lesson Practice



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1. time Alycia left:

Count hours forward.

Count 1 _ 2 hour forward.

2. Subtract the largest value coins first.

47¢

− 25¢ 1 quarter dimes?

nickels?

pennies?

3. twenty-three million, two hundred eighty-seven thousand, four hundred twenty

digits: , ,

Use work area.

5. prime numbers

, , ,

6. a. List the factors of the smaller number (4).

, ,

Cross out those that are not factors of the larger number (8). The biggest factor is the GCF. Circle it.

b. Divide both by the GCF. 4 __ 8 ÷ __ =

Use work area.

Written PracticeWritten Practicepage 543

4. a. 1 __ 3 of 24

b. 2 __ 3 of 24

2413

23 is __

of 00 ___

00 = ? ___

24

a.

b.



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7. a. Shape?

b. How many faces?

a. b.

8. Shape of the earth?

A circle B cylinder

C sphere D plane

9. 1 7 ___ 10

decimal number

.

10. distance across a circle

A center B circumference

C radius D diameter

11. 3.62

+ .

12. 3.704

– .

13. 162 + √___

16

+

14. $6.25

15. 6w = $14.58

w =

16. 1 __ 3 × __ = 00 ___

12

3 __ 4 × __ = 00 ___

12

=

Convert.

Use work area.

17. Reduce.

6 __ 8 =

Divide both by the

GCF.

18. Write the numerator as your answer.

3 __ 4 × __ = 00 ___

12

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19. 4 1 __ 6

+ 2 1 __ 6

=

Reduce.

20. 3 3 __ 4

+ 1 1 __ 4

=

Convert.

21. 5

− 1 1 __ 4

=

22. 0.1 0.01

0.1

0.01

Use work area.

23. 3 × 1 __ 2 =

1 __ 2 + 1 __

2 + 1 __

2

Convert.

24. Age

Adults $10.00

$8.50

$6.50

Age 9–12

Under 9

Price a. $4.50 Madison (12)

$ . Douglas (8)

$ . Mom

+ $ . Dad

b. $6.50

before 5 p.m.

after 5 p.m.

before 5 p.m.

saved

b.a.

25. Which “takes up space?”

A B C D

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26. Estimate the area.

14 ft 2 in.

10 ft 3 in.

14 ft 2 in. ft

10 ft 3 in. ft

27. a. Which expense consumes about one third of the budget?

b. About what fraction of the budget does food consume?

Entertainment

Rent

Food

Car

Utilities

b.a.

28. perimeter

2.4 cm

Rhombus

29. Which transformation?


C reflection D flip

30. See page 545.

a. range of the temperatures

b. September October warmer or cooler?

c. November October warmer or cooler? Use work area.

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8484 Teacher Notes:

• Review Hint #37 “Average.”

• Refer students to “Statistics” on page 20 in the Student Reference Guide.

• Review “Average” on page 9 in the Student Reference Guide.

• Mean, Median, Mode,and Range


Statistics

Median: the middle number of a set of numbers arranged in order

Median middle

1, 3, 4, 4 , 5, 6, 6median = 4

Mode: the number that appears the most often in a set of numbers

Mode most

3, 5, 8, 2, 5, 7, 6, 1mode = 5

Range: the difference between the least and the greatest numbers in a set of numbers

Range span

3, 5, 8, 2, 5, 7, 7, 6, 1

8 – 1 = 7range = 7

Lesson PracticePut the numbers into numerical order first.

a. 3, 7, 9, 9, 4 Mean: Median:

3, , , , 9 Mode: Range:

b. 16, 2, 5, 7, 11, 13 Mean: Median:

, , , , , Mode: Range:

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c. 3, 10, 2, 10, 10, 1, 3, 10

, , , , , , ,

Mean: Median: Mode: Range:

d. Name Andrei Raj Althea Mary Bedros Ann Yolanda

Age 13 10 10 11 11 10 11

, , , , , ,

Mean: Median: Mode: Range:


1.

3 ) _____________

$2 4 5 7

2. Shade 1 __ 3 .

% shaded

Use work area.

3. one kilogram = grams 4. Estimate the product.

732

480




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5. At which of these times do the hands of a clock form an acute angle?

A 3:00 B 6:15 C 9:00 D 12:10

3

121110

9

87 6 5

4

21

3

121110

9

87 6 5

4

21

3

121110

9

87 6 5

4

21

3

121110

9

87 6 5

4

21

6. least to greatest 0.1

0.1, 0.01, 1.0, 1.01 0.01

1.0

1.01

, , ,

8. a. 1 __ 4 of 80 = 80

14

34

b. 3 __ 4 of 80 =

is __ of

80 ___ 80

= ? ___ 80

b.a.

9. 1 __ 2 × __ = 3 __ 6 10. Reduce.

4 __ 6 =




The biggest factor is the GCF. Circle it.

b. Divide both by the GCF. 8 ___ 12

÷ __ =

b.a.

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14.

R30 )

_________ 6 7 2

15. 5 × 68¢ = 16. $3.40 ÷ 5 = 17. 10 − 3 1 __ 3 =

20. In rectangle MNOP, which segment is parallel to

–––– MN ?

A ––––

MP B –––

PO C –––

NO D ––––

MO

M N

P O

21. Which appears to be a right angle?

O

A

BC

D

A ∠AOB B ∠BOC

C ∠BOD D ∠AOD

18. 3 __ 4

× 5 __ 4 = 19. Opposite faces are p .

Adjacent faces are p .

Use work area.

11. Mixed number and decimal

.

12. 9.9

0.0

0.0

+ .0

13. $10.00

– $ .

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22. a. $3.10 eggs

$0.00 juice

$0.00 juice

+ $0.00 cereal

Milk . . . . . . . Milk . . . . . . . Milk . . . . . . . Milk . . . . . . . Apple juice . . Apple juice . . Eggs . . . . . . Cereal . . . . .

TOTAL

1.941.941.941.941.381.383.103.98

17.60 b. average (mean)

c. median

d. mode

e. range

a. e.c. d.b.

23. Draw the next figure in the pattern, and then

count the dots.

Use work area.

24. perimeter in inches

34

1411

25. fraction: 90% =

Reduce: ÷ __ =

decimal: .

.

26. See page 2 in the Student Reference Guide.

212ºF water boils

____________ water freezes

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27. It takes the moon about 29 1 _ 2 days to complete one cycle. Estimate the number of

cycles the moon completes in 365 days. Explain.

I used c numbers.

365 is about and 29 1 _ 2 is about .

÷ =

Use work area.

28. Draw a translation of the triangle shifted down 2 units.

x

y54321

1 2 3 4 50Use work area.

29. See page 552. Write the names of the lakes on the graph.

800

700

600

500

400

300

200

Dep

th (i

n fe

et)

Maximum Depth of Lakes

Use work area.

30. area 16 feet

12 feet

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8585 Teacher Notes:

• Introduce Hint #54 “Measuring Liquids and Capacities of Containers.”

• Refer students to “Liquids” on page 1 in the Student Reference Guide.

• Review “Equivalence Table for Units” on page 1 in the Student Reference Guide.

• Display reference chart “Liquids.”

• Units of Capacity


• Capacity is the amount of liquid a container can hold.

Equivalency Table for Units of Liquid Measure

U.S. Customary System Metric System

16 oz 1 pt2 pt 1 qt4 qt 1 gal

1000 mL 1 L

A liter is about 2 ounces more than a quart.

Lesson Practice

a. One fourth of a dollar is a quarter. What is one fourth of a gallon?

b. How many pints equal 1 gallon?

c. How many milliliters equal 2 liters? L ______ mL

1 __ 0 = 22 ____

??

d. A cup is one half of a pint. A cup is how many ounces?

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1. Shade all but 2 __ 5 .

___ 5 = percent

2. prime number 4

1

0

A prime number can’t end in an even number.

3. length in centimeters and in millimeters

1 2 3cm

mm 10 20 30

.

4. 1 minute = seconds

heartbeats ____________________ seconds

20 ___ 15

= ? __ 0

5. perpendicular to –––

AB

A –––

BC B –––

CD C –––

DA D –––

DC

BC

D

A



Circle the GCF.

b. Divide both by the GCF.

6 __ 9 ÷ ___ =

b.a.



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7. a. 1 __ 5 of 60 60

15

25

b. 2 __ 5 of 60

is ____ of

0 __ 0

= ?? ______ 6060

b.a.

8. Find –––

AC . Label the figure.

CBA

?


0.

0.01

1.0

0.1, 0, 0.01, 1.0

, , ,

10. qt

____ pt

1 __ 0 = 4 __

?

11. L ______ mL

1 __ 0 = 33 ____

?? 12. Divide 100 by 6.

Write the answer as a mixed number.

Reduce.

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13. $17.56

$ .

+ $ .

14. 4.324

– .

15. 396× 405

16. $1.25

17.

R9 )

____________ 3 6 0 5

18. $2.50 ÷ 10 = 19. Reduce.

15 ___ 20

=


20. 3 − 2 2 __ 3 − 1 = 21. 3 __

5 × __ = 0000 ___

10

1 __ 2 × __ = 0000 ___

10

= Convert.

Use work area.

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22. 0000 .

0000 .

23. Count the 1 _ 4 s.

24. a. 1 ft = in.

Genaro (5 × ) + in.

Roberta (Genaro − 4 in.) in.

b. Stan (Roberta + 6 in.) in.

b. ft in.a. ft in.

25. Double the previous number.

4, , , , …

26. The probability of “heads” is what fraction?

of 50 =

27. 90, 85, 80, 90, 95, 90, 100 Put the numbers in order.

, , , , , ,

a. range

b. The mode is because it is the score that occurs often.

c. The median is because it is the score.

a. b. Use work area. c. Use work area.

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28. Maya

Justin (Maya + 3)

Coretta (Justin + 2)

Use work area.

29.

, , , , , . . .

a. Draw the next term of the sequence.

b. Which transformation describes the change from term to term in this sequence?

A translation B rotation C reflection D flip

a. Use work area. b.

30. 154

147

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8686

• Multiplying Fractions and Whole Numbers


• To multiply a fraction and a whole number:

1. Convert the whole number to a fraction. (Write the whole number over 1.)

2. Multiply the fractions.3. Simplify the answer.

Example

What number is 2 __ 3 of 4?

2 __ 3 of 4

2 __ 3 × 4 __ 1 = 8 __ 3 = 2 2 __

3

Lesson PracticeMultiply. Simplify answers when possible. Reverse the order of factors to check your answer.

a. 1 __ 3 × 4 b. 3 __

5 × 2 c. 2 __

3 × 2 d. What number is 1 __

5 of 4?

1 __ 3 × 00 ___ 00 = 3 __ 5 × 00 ___ 00 = 2 __

3 × 00 ___ 00 = 1 __

5 × 00 ___ 00 =

e. What number is 1 __ 6 of 5? f. What number is 2 __

3 of 5?

1 __ 6 × 00 ___ 00 = 2 __

3 × 00 ___ 00 =

page 559

Teacher Note:

• For addtional practice, students may complete Targeted Practice 86.



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g. Shade to show 1 _ 3 of 4.

1. Draw two horizontal parallel segments.

Make the lower segment longer.

Connect the ends.

Use work area.

2. Estimate the difference.

6970

3047

3. The sum of six and four is ten. 4. LmL

1 __ = 2 __ ?


5. fraction, decimal, and percent shaded

.

6. a. 1 __ 3 of 120

b. 2 __ 3 of 120

is of

___ = ? ____ 120

12013

23

a.

b.



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7. Which segment names a diameter of this circle?

A ___

RS B –––

RT

C –––

OS D –––

OT

R

S

TO

8. least to greatest Compare each to 1 _ 2 .

9 ___ 18

, 8 __ 7 , 7 ___ 16

, 6 __ 6 , 5 __ 8

, , , ,

9.

2 3 4

10. 2 __ 3 × 00 ___ 00 =

Convert.

11. 3 __ 4 of ___ =

Convert.

12. 3 − 2 3 __ 5 − 1 1 __

5 =

13. 4.7

.

+ .

14. 301.4− 143.5

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15. 4760× 890

17. Cancel matching final zeros.

40 ) ____________

3 4 8 0

18. $42.36 ÷ 6 = 19. 222 =



Circle the GCF.


60 ____ 100

÷ __ =

a.

b.

21. 3 __ 4 = ___ 12

2 __ 3 = ___ 12

Use work area.


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16. 4 )

_________ 3 4 8



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23. a. Shape?

b. How many vertices?

a.

b.

24. a. 12 goal

Steven

more

Number of Books Read

Class Book Club

Willis

Stu

den

t StevenYuko KentBeth

0 4 8 12 b. books pages 1 ____

180 = ___

?

c. median

a. b. c.

25. What is the probability of rolling a number under 5? Reduce.

1 2

3

26. 1 quart = 1 __ 4 gallon

1 quart = percent of a gallon

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27. 1 quart 1 liter

See page 1 in the Student Reference Guide.

Use work area.

28. 1 1 __ 2 morning

+ 2 1 __ 2 evening

one day

Use work area.

29.

, , , ...

a. Draw the next term.

b. Which transformation describes the change from term to term?

A translation B rotation C reflection D slide

a. Use work area.

b.

30. A 10° change on the Celsius scale is an 18° change on the Fahrenheit scale.

212

685032

F

100

2030405060708090

100

C

Label the blank tick marks.

Use work area.

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8787

• Using Manipulativesand Sketches to DivideFractions


• When dividing fractions, you can:

Use fraction manipulatives. Make sketches.

Lesson Practice

a. How many one sixths are in one half?

b. How many one twelfths are in one third?

Find each quotient. Try answering the problems mentally.

c. 2 __ 3 ÷ 2 __

3 = d. 1 ÷ 1 __

4 =

How many fourths are in one?

e. 2 __ 3 ÷ 1 __

3 = f. 1 ÷ 1 __

2 =

How many thirds are in two thirds?

page 565



1. 10 ft

a. perimeter

b. Area = length × width

a. b.

2. In which of these numbers does the

1 mean 1 __ 10 ?

A 12.34 B 21.43

C 34.12 D 43.21

3. least to greatest Find the least and greatest numbers. Then

compare the other two.

1, 0, 1 __ 2 , 0.3

1 _ 2 = 0.5

, , ,

4. qt

oz 1 ___ 32

= __ ?

5. a. A quarter is what fraction of a dollar?

b. one dollar = quarters

c. quarters

dollars

__ = ? __ 3

a. b. c.


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6. fraction, decimal, and percent shaded

.


7. If a = 3, then 2a + 5 equals which of the following?

A 10 B 11 C 16 D 28

8. Find BC.

1 __ 4 of 84 mm is mm.

BA C?

9. 1 __ 2 = ___

6

1 __ 3 = ___

6

Use work area.


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onWritten Practice,Written Practice, continued continued page 569

11. 3 __ 5 of 4 12. 1 __

2 ÷ 1 ___

12 =

How many 1 __ 12 s are in 1 _ 2 ?

Use fraction manipulatives.

13. 3 7 __ 8 − 1 1 __

8 =

Reduce.


, , , , ,

Cross out those that are not factors of the larger number (50). Circle the GCF.


20 ___ 50

÷ __ =

a. b.



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14. Cancel matching zeros.

2250 ÷ 50 =

15. 5 )

_________ 2 2 5

16. 5365428

3997659

7073+ 342

17. 4 )

__________ $8 . 2 0

18. 202 − √____

100

20

−

19. $12.750× 80

20. Divide 100 by 8.

Write the answer as a mixed number.

Reduce.

21. How many 1 _ 8 s are in 1 _ 4 ?

Use fraction manipulatives.


23. a. Marysville to Red Bluff

Marysville to Sacramento

more than

Red Bluff

Chico

Marysville

Sacramento

41

49

40

b. Sacramento to Chico

halfway to Marysville

still to go a. b.

page 569



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24. eggs5 2 10

cereal

a. How many students ate cereal for breakfast?

b. How many students ate eggs for breakfast?

c. How many students ate both cereal and eggs for breakfast?

d. Altogether, how many students ate eggs or cereal or both?

e. How many of the 20 students ate neither eggs nor cereal for

breakfast? Use work area.

25. 57˚ highest

lowest

8˚ greater

26. started eight hours before midnight

started

5:32 drove

stopped

page 570



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27. studied

1 3 __ 4 read

total

28. 3 1 __ 4 dozen made

− dozen eaten

dozen left

29. Use compatible numbers.

186

184

Use work area.

30. Use the data on page 571 to make a line graph.

0

2

4

6

8

10

12

Tem

per

atur

e

Time

6:00 am 9:00 am noon 3:00 pm 6:00 pm

Mt. Wilson Temperatures

Use work area.

page 570


L E S S O N


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• Transformations


Transformations

Name Movement

Translationsliding a figure in one direction without turning the figure

Reflectionreflecting a figure as in a mirror or “flipping” a figure over a certain line

Rotation turning a figure about a certain point

x

y

translationx

y

reflection x

y

rotation

• Rotations can be described by their direction and by their degree.

clockwise same direction as clock hands

counterclockwise opposite direction as clock hands

full turn 360º

half turn 180º

quarter turn 90º

turn clockwise14 turn counterclockwise1

4

8888 page 572

Name



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ActivityActivity page 574

Describing Transformations

• This activity is optional.

Lesson Practice a. Sketch an uppercase letter R after a b. Sketch an uppercase letter R after a reflection in its vertical segment. 180º counterclockwise rotation.

Name the transformations that could be used to position triangle A on triangle B.

c. y

x

A B

d. y

x

AB

r r

e.

AB

x

y f. y

x

A

B

r , r ,

t r ,

t

New Concept,New Concept, continued continued



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1. Lilah lives 1 _ 4 mile from school. How far does she travel each day going to school

and back?

Home School

mi14

2. According to this calendar, what is the date of the first Friday in April 2070?

MARCH 2070

310172431

S

29

162330

18

152229

7142128

6132027

5121926

4111825

FTWTMS

,

3. .

– .

.

4. a. one dollar = dimes

b. dimes ______ dollars

1 __ 1 = ? __ 5

a.

b.

5. 2 __ 3 of 150

is __ of

1 __ 1 = ? ____ 150

6. gallon

quart

quart

quart

quart12 gallon



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7. Which part of a bicycle wheel is most like a radius?

hub

rim

spoke

tire

A rim

B spoke

C hub

D tire

8. 5 __ 6

1 __ 3 = 0 __

6

= Reduce. Use work area.

9.

a. fraction shaded Reduce.

b. percent shaded

b.

a.

11. 3 __ 5

+ 3 __ 5 + 3 __

5 3 × 3 __ 5

Use work area.

10. Find ST.

R TS ?

1 _ 3 of 84 mm is mm.

12. In this drawing, which angle appears to be obtuse?

A

BC

D A ∠ABC B ∠ABD

C ∠BDC D ∠DAB

page 577



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13. 1 __ 8 × 3 =

Convert.

14. 3 __ 8 ÷ 1 __ 8 =

How many 1 _ 8 s are in 3 _ 8 ?

Use fraction pieces.

16. 1 __ 4 + 1 __ 4 =

Reduce.

17. 7 __ 8 – 1 __

8 =

Reduce.

18. 5 – 1 3 ___ 10

=

19. $6.57

$8.43

+ $ .

20. 421.05

– 421.05

21. 302 =

15. a. How many 1 _ 4 s are in 1?

b. 1 __ 6 × ___ =

Reduce.

a.

b.

22. School Schedule

Subject Time

Reading 8:00–8:50

Math 8:50–9:40

Recess 9:40–10:10

Language 10:10–10:50

Science 10:50–11:30

Lunch 11:30–12:30

a. reading

language

total

b. lunch ends:

Count hours forward.

Counts minutes forward.

a. b.

page 578



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23. 6070× 340

24. 9 )

__________ $7 . 6 5

25. area 30 ft.

30 ft.

26. 1 __ 2

, 1, 1 1 __ 2 , 2, 2 1 __

2 , 3, ,

, , …

Use work area.

28. a. See page 16 in the Student Reference Guide.

P T

A P T

B

TP

C

PT

D

b. ; No p is a t , and no

t is a p .Use work area.

29. area of shaded portion

1 in.

1 in.

in.12

in.34

27. probability of black

W W W

B B B B BBBBBB

R R

Reduce.

page 579

30. anniversary 1983

first flight (anniversary − 200)

bicycle invented (first flight + 56)


L E S S O N

Name


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8989 Teacher Note:

• Use geosolids to introduce this concept.

• Analyzing Prisms


• A prism is a three-dimensional solid with two congruent bases.

Triangular prism6 vertices9 edges

Rectangular prism8 vertices12 edges

Trapezoidal prism8 vertices12 edges

Pentagonal prism10 vertices15 edges

Hexagonal prism12 vertices18 edges

Octagonal prism16 vertices24 edges

Lesson PracticeName each type of prism in a–c.

a. b. c.

d. Look at the prism in problem a.

How many perpendicular rectangular faces?

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e. Look at the prism in problem b.

How many pairs of parallel faces?

f. Look at the prism in problem c.

How many edges?

g. Is this figure a prism?

, because it does not have two p

c bases.


1. Thomas Jefferson wrote the Declaration of Independence.

1776 wrote

25 later

became president

2. Greater than or less than a year?

a. $ days

__ 1 =

10,000 _______

?

b. Greater than or less than a year?

b.

a.

3. Which is divisible by both 4 and 5? Look down the 4s and 5s columns of the Multiplication Table.

A 15 B 16 C 20 D 25




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1.5 3 __ 2

1.

0.

1.1

0.5, 3 __ 2 , 1, 0, 1.1

, , , ,

5. a. one gallon = half gallons

b. half gallons

gallons

1 __ 1 = ? __

3

a.

b.

6. one million, three hundred fifty-four thousand, seven hundred sixty

, ,

7. 5 __ 6

1 __ 2 = __ 6

= Reduce.

Use work area.

8.

a. fraction shaded (Reduce.)

b. percent shaded

a.

b.

9.

a. Shape?

b. How many edges?a.

b.

page 583



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12. 2 __ 5

+ 2 __ 5 + 2 __

5 =

Convert.

13. 1 1 __ 4 + 1 1 __

4 =

Simplify.

14. 3 5 __ 6 − 1 1 __

6 =

Simplify.

15. 42.6

.

.

+ .

16. $10 − (57¢ + $2.48) = 17. 42 × 5 × 36 =

18. $6.15 × 10 = 19. 40 )

____________ 2 7 6 0

page 583

10. length in centimeters and in millimeters

10 20 30 40mm

1 2 3 4cm

.

11. 2 __ 5 of ___ =

Convert.



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20. 4w = 276

w =

21. 1 __ 2 ÷ 1 ___ 10 =

How many 1 __ 10 s are in 1 _ 2 ?


22. 1 __ 2 × 6 __

8 =

Simplify.

23. Divide 371 by 10. Write the answer with a remainder.

24. Fill in the chart starting with Monty.

Age

Monty

Noah

Jenny

Dad

a. How old is Jenny?

b. How old is Jenny’s dad?

a.

b.

25. √___

25 − √__

9

− =

26. 32 + 42

+ =

page 584



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27. A dime is tossed and then a quarter is tossed.

List the possible outcomes.

Dime Quarter

heads tails

Use work area.

28. a. A pint is what fraction of a quart?

b. What fraction of a gallon is a quart?

c. What fraction of a gallon is a pint?

d. The answers to a–c show that one half of one fourth equals what fraction?

Use work area.

29. See page 585.

and Use work area.

30.

Act it out.

triangular faces

rectangular faces Use work area.

page 584


L E S S O N

Name


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9090 Teacher Notes:

• Review Hint #50 “Reducing Fractions (Manipulatives and Shortcuts)” and Hint #51 “Finding the Greatest Common Factor.”

• Review “Factors” on page 8, “Tests for Divisibility” on page 20, and “Fraction Families Equivalent Fractions” on page 18 in the Student Reference Guide.

• For additional practice, students may complete Targeted Practice 90.

• Reducing Fractions,Part 2


• To reduce a fraction to lowest terms:

1. Find the GCF of the numerator and denominator.2. Divide both by the GCF.

Example

Reduce 8 ___ 12

factors of 8: 1, 2, 4 GCF

8 ___ 12

= 8 ÷ 4 _______ 12 ÷ 4 = 2 __ 3

• To write a percent as a reduced fraction:

1. Write the percent as a fraction.2. Cancel matching zeros.3. Reduce the fraction.

Example

Write 40% as a reduced fraction.

1. 40% = 40 ____ 100

2. 40 ____ 100

= 4 ÷ 2 _______ 10 ÷ 2

= 2 __ 5

Lesson PracticeReduce each fraction to lowest terms.Find the GCF first.

a. 4 ___ 12

= b. 6 ___ 18

= c. 16 ___ 24

=

page 586



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d. 4 ___ 16

= e. 12 ___ 16

= f. Cancel matching zeros.

60____100

=

Solve. Reduce each answer to lowest terms.

g. 7 ___ 16

+ 1 ___ 16

=

h. 3__4

× 4__5

= i. 19 ___ 24

− 1 ___ 24

=

Write each percent as a reduced fraction.

j. 25% = k. 60% = l. 90% =


1. See page 589. 2. Convert.

1 __ 2 = 00 ___

10

3 __ 5 = 00 ___

10

3. a. one gallon = quarts

b. gal

___ qt

1 __ 0 = 6 __

?

a.

b.

4. .

. 0



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5. decimal, reduced fraction, and percent shaded

.

6. How many vertices?

7. Which segment is parallel to –––

AB ?

x

y

D A

C B

A –––

BC B –––

CD

C –––

BD D –––

DA

8. Classify triangle BCD by angles.

x

y

D A

C B

9. What transformation would move triangle DAB to triangle BCD?

x

y

D A

C B

r

10. 5 __ 6 + 5 __

6 =

Convert and reduce.

11. 5 __ 6 × 2 =

Convert and reduce.

page 589



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12. 2 __ 5 ÷ 1 ___

10 =

How many 1 __ 10 s are in 2 _ 5 ?


13. 1 ___ 12

+ 7 ___ 12

=

Reduce.

14. Borrow and rename.

6 2 __ 3 − 4 − 1 __

3 =

15. 2 __ 3 × 3 __

4 =

Reduce.

16. 26.4

+ .00

17. 8.36

− .00

18. 402 = 19. √___

36 + √___

64

+

20. 480 ÷ 10 =

21. 5n = 240

n =

22. 1 ÷ 1 __ 3 =

How many 1 _ 3 s are in 1?

23. 3 __ 4 × 3 =

Convert.

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24. 3 __ 5 × __ = 60 ____

100

25.

Magazine report

TV report

Book report

Museum report

Extra Credit

35 points

50 points

75 points

100 points

a. book report 2 magazine reports TV report

points earned

b. 400 total earned

needs

a. b.

26. probability of orange

O O O O O OW W W W W

R R RB B

Reduce.

27. area = 25 in.2

a. each side

b. perimeter

a. b.

page 590



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28. , , , ...

3 sides, sides, sides, sides

This is a pattern of regular p .

The number of sides is i by .

Use work area.

29. a. factors of 16: , , , ,

b. Is the number of factors odd or even?

c. What is the median of the factors?

d. What is √___

16 ?

Use work area.

30. $24,575

$23,460

I used c numbers.

$24,575 is about .

$23,460 is about .

– =

Use work area.

page 591


Saxon Math Intermediate 5 589 Adaptations Investigation 9

Name I N V E S T I G A T I O N©

200

8 S

axon

page 592

Focus onFocus on• Performing Probability

Experiments

• A typical dot cube has six faces.

• Each time a dot cube is rolled there are 6 possible outcomes.

Each outcome is equally likely.

The probability of each outcome is 1_6 .

• The total of the possible outcomes must add up to one.

1__6

+ 1__6

+ 1__6

+ 1__6

+ 1__6

+ 1__6

= 6__6

= 1

• The probability that the upturned face will be an even number is the sum of the probabilities of rolling a 2, a 4, or a 6.

1__6

+ 1__6

+ 1__6

= 3__6

= 1__2

1. What is the probability that the upturned face is either 1 or 6?

+ =

Teacher Notes:

• Review Hint #42 “Probability and Chance.”

• Each student will need a copy of Lesson Activity 30.

99

Math Language

Probability tells how likely something is to happen. It is expressed in fractions.

SM_H5_AD_Inv009_FF.indd 589SM_H5_AD_Inv009_FF.indd 589 11/2/07 3:33:46 PM11/2/07 3:33:46 PM


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I N V E S T I G A T I O N continued9

2. What is the probability that the upturned face is less than 5?

• If we rolled our dot cube 24 times, we guess that we would roll a certain number 1 _ 6 of 24 times.

24 ÷ 6 = 4 times

3. If a standard dot cube is rolled 60 times, how many times

would you guess that the upturned face will be 1?

Explain how you got your answer.

Since the outcome 1 can be expected to occur of

the time, I divided 60 by .

4. If a standard dot cube is rolled 60 times, how many times would

you guess that the upturned face will be either 1 or 6?

Explain how you got your answer.

Since one outcome can be expected to occur times

in 60 rolls, then two outcomes can be expected to

occur + , or times.



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ActivityActivity 1 1 page 593

Probability Experiment 1

• Use the tallies on Lesson Activity 30 to answer problems 5 – 8.

5. Complete the “Frequency” column on Lesson Activity 30.

6. Which outcome occurred more frequently than you

would guess?

7. How many times was the upturned face even?

8. Predict what the next roll would be.



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I N V E S T I G A T I O N continued9

2

1 3

• The table shows the results of 50 spins of the spinner shown above.

Outcome Tally RelativeFrequency

1

2

3

1750

2850

550

9. Since 28 __ 50 > 17

__ 50 , outcome 2 seems more likely than outcome 1.

How does the spinner show the same probabilities?

Region is larger than region .

Since 17 __ 50 > 5 __ 50 , outcome 1 seems more likely than outcome 3.

How does the spinner show the same probabilities?

Region is larger than region .

10. 28 __ 50 overestimates the true probability of stopping on 2.

Region 2 is slightly s

than 1 _ 2 ( or 25 __ 50 ) of the spinner.



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ActivityActivity 2 2 page 595

Probability Experiment 2

Complete Activity 2 with a partner.

Use Lesson Activity 30 to answer problems 11–16.

11. Use the tallies to complete the “Relative Frequency” column on your table.

number of tallies _______________ 30

12. Look at your “Relative Frequency” table.

Estimate the probability that you choose a T.

13. If a letter was written once, about how many times would you expect to choose it out of 30?

30 ___ 5

14. If a letter was written twice, about how many times would

you expect to choose it out of 30?

15. If a letter was written three times, about how many

times would you expect to choose it out of 30?

16. Which of the letters do you think your partner wrote

once?

twice?

three times?



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