Adding and Subtracting Fractions with Common Denominatorsmryoungclassnews.weebly.com/uploads/4/0/3/5/40359489/h5_lesso… · • Adding and Subtracting Fractions with Common Denominators

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Saxon Math Intermediate 5 265 Adaptations Lesson 41

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4141

• Adding and SubtractingFractions with CommonDenominators

New ConceptNew Concept

Example

2 __ 4 + 1 __

4

14

14

14

14

14

14

2 __ 4 + 1 __ 4 = 3 __ 4 Add the numerators.

The denominator stays the same.

Example

7 ___ 10

− 4 ___ 10

110

110

110

110

110

110

110

110

110

110

110

110

1101

10

710Start with 4

10Remove 310 remains.. .

7 ___ 10

− 4 ___ 10

= 3 ___ 10

Subtract the numerators.

The denominator stays the same.

page 257

Math Language

Common denominators are denominators that are the same.

2 __ 4 and 1 __

4 have

common denominators.

SM_H5_AD_L041_FF.indd 265SM_H5_AD_L041_FF.indd 265 11/2/07 2:29:12 PM11/2/07 2:29:12 PM


New Concept,New Concept, continued continued

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• When adding mixed numbers:

1. Add the whole numbers.

2. Add the fractions.

Example

1 1 __ 4 + 1 2 __

4 =

Add the whole numbers. 1 + 1 = 2

Add the fractions. 1 __ 4 + 2 __

4 = 3 __

4

1 1 __ 4 + 1 2 __

4 = 2 3 __

4

Example

2 1 __ 2 – 1 1 __

2 = 1

122

122

We start with 122 .

We take away What is left is 1.121 .

2 1 __ 2 – 1 1 __

2 = 1



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a. 1___10

+ 2___10

= b. 3__4

− 2__4

=

c. 1 1 __ 2 + 1 1 __

2 = d. 3 4 ___

10 − 1 1 ___

10 =

Written PracticeWritten Practice page 261

1. Draw a pair of horizontal parallel line segments.

Make the upper segment longer.

Connect the ends to make a quadrilateral.

Use work area.

2. 1 out of 10

fraction and decimal

. .

3. 00001492

two centuries

4. s Sonora

4360 Colville

less340 4360

s

s − 4360 =

s =

Use work area.

5. 3 flats

plants t plants

3 × = t

t =

Use work area.



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Written Practice,Written Practice, continued continued

6. 0000805 km Alaska to Washington

km already traveled k still to travel

805 − = k

k =

Use work area.

8. 5 ___ 10

+ 4 ___ 10

= 9. 1 __ 2 − 1 __

2 = 10. 2 1 __

4 + 3 2 __

4 =

11.

10 11

12. 37842693

42997

856+ 907

13. 3106

−

14. 0000$80.00

0000$0000.0000

15. 804

×

16. Associative Property of

Multiplication

60 × 43 × 8 =

7. 3 3 ___ 10

− 1 2 ___ 10

=

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onWritten Practice,Written Practice, continued continued

17. 4w = 4008

w =

18. short division

4228 ÷ 7 =

19. short division

9635 ÷ 8 =

20. short division

$7.98 ÷ 6 =

22. 9 8 23. Draw an obtuse triangle.

Use work area.

24. 1 _ 5 of 30 ) _____

000

25. It is evening. What time will it be in 30 minutes?

time now:

3

121110

9

87 6 5

4

21

Count forward 30 minutes.

21. $4.56

$0.

+ $0.0000

$10.00

− $00.0000

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26. Show the remainder as a fraction.

1 _ 4 of 9 ) _____

27. 1 __ 2 2 __

3

Use work area.

28. Which of these angles appears to be a 90º angle?

A B

C D

29. 1 _ 4 of 100 100 ÷ 4

Use work area.

30. cm is reasonable because 61 is about and

÷ 2 = .

Use work area.

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• Short Division

• Divisibility by 3, 6, and 9

18New ConceptNew Concept

• Short division:

2 93 )

_____ 8 27

• To test for divisibility by 3, 6, and 9, add the digits:

438 4 + 3 + 8 = 15

Tests for Divisibility

A number is divisible by … 3 if the sum of its digits is divisible by 3.

6 if the number is divisible by 2 and 3.

9 if the sum of its digits is divisible by 9.

Lesson PracticeUse short division.

a. 3 ) _________

4 3 5 b. 6 ) _________

5 3 4 c. 9 ) _________

5 6 7

d. 4 ) _________

5 0 0 e. R7 )

_________ 8 0 0 f.

R10 )

_________ 8 3 6

g. 5 ) _________

6 0 0 h. R3 )

_________ 6 1 6 i.

R6 )

_________ 8 5 8

4242 Teacher Notes:

• Introduce Hint #31 “Tests for Divisibility.”

• Review Hint #22 “Short Division.”

• Review “Tests for Divisibility” on page 20 in the Student Reference Guide.

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Lesson Practice, continued

Decide whether each of the following is divisible by 3, by 6, by 9, or by none of these numbers.

j. 1350 k. 4371 l. 1374

m. 436 n. 468 o. 765


1. Draw a pentagon.

Use work area.

2. 1 minute = seconds

shakes ________________ seconds

50 ___ 1 = t __

0

50 × = t

t =

Use work area.

3. 0000101° F later

beforen change

101 − = n

n =

Use work area.

4. 124 check out

returnedn fewer

124 − n =

n =

Use work area.



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4 ) _____

2 1

6.

3 __ 4 3 __

5

Use work area.

7. 3 ___ 10

+ 4 ___ 10

= 8. 1 1 __ 3 + 2 1 __

3 = 9. 7 ___

10 − 4 ___

10 =

10. 5 1 __ 4 − 2 1 __

4 = 11. mixed number

12. 1 5 1 13.

0 1

14. 1 _ 3 of 30 1 _ 5 of 50

Use work area.

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15.

2 __ 4 = .

Use work area.

16. $18.73$34.26

+ m$79.33

m =

17. bottom missing Subtract.

6010

− r543

r =

18. 9364718

49371

+ 82

19. 346× 80

20. $7.25× 90

21. 670× 700

22. short division

4 ) ____________

1 7 3 6

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23. short division

$8 )

_____________ $1 7 . 6 0

24. short division

R3 )

_________ 1 0 0

25. 16°C at 7:00 a.m. 5°C increased

°C at 3:00 p.m.

°C at 3:00 p.m. 2°C decreased

°C at 11:00 p.m.

26. Which of these angles appears to be an acute angle?

A B C D

27. Which number is divisible by 3, by 6, and by 9?

A 369 B 246 C 468 D 429

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28. Associative Property of Addition

3 + (4 + 5) = (3 + 4) + m

m =

29. 2 __ 12 begin with A.

3 __ 12 begin with J.

How many begin with either A or J?

30. 431 is close to .

42 ÷ 7 = 6, so ÷ 7 = 60.

Use work area.

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4343

• More Arithmetic with Mixed Numbers


• We can show a quotient as a mixed number.

Write the remainder over the divisor.

3 3 R 13 )

______ 1 0 10

3 33 )

______ 1 0 10

remainder divisor

1 __ 3

• To add or subtract whole numbers, fractions, and mixed numbers:

1. Copy the problem vertically. Line up whole numbers over whole numbers and fractions over fractions.

2. Add or subtract the fractions first.3. Add or subtract the whole numbers last.

5 3 1 __ 2

5 + 1 1__2

+ 1 __ 2

3 1__2

− 1__2 − 1 __

2

6 1 __ 2 3

Lesson Practice

a. Use fraction manipulatives.

Anil’s Pizza Shop will donate 15 pizzas. How many pizzas will there be for each of the four classes?

first class second class third class fourth class

2nd class 4th class

3rd class1st class15__

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Teacher Note:

• For additional practice, students may complete Targeted Practice 43.

1



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b. A whole circle is divided into sevenths. Each seventh is what percent of the whole circle?

(Divide 100% by 7 to find the percent for each seventh.)Show the remainder as a fraction.

100% ) _________

1 0 0

c. three and two fourths plus one fourth d. three and two fourths minus one fourth

e. 6 2 __ 3

− 3 = 6 2 __ 3 f. 3 1 __

2 + 2 = 3 1 __

2

− 3 + 2

g. 2 1__2

− 1__2 = 2 1__

2 h. 3 __

4 + 2 = 3 __

4

− 1 __ 2 + 2

i. Write a word problem for 2 1 _ 2 − 1 1 _ 2 .




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1. Draw a pair of vertical parallel line segments of the same length. Connect the ends to make a quadrilateral.

Use work area.

3. 100 cm00048 cm

n cm

100 − = n

n =

Use work area.

5. Shade all but 1 _ 4 .

What percent is not shaded? See page 19 in the Student Reference Guide.

0 __ 4 = percent

6. 158

2. ounces _______ cups 0 __ 4 = c __ 1 4c =

c =

Use work area.

4. $28.75 has m $ cost

28.75 m

34.18

$28.75 + m =

m =

Use work area.

Written PracticeWritten Practicepage 273



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7. 5 0

+

8. 12 1 __ 2

+ 12 1 __ 2

9. 1 0

+

10. 3 1 __ 2

− 0

11. 4 3 __ 5

− 0

12. 5 3 __ 8

+ 0

13. See page 19 in the Student

Reference Guide.

1 __ 8 = percent

14. 1 __ 2 = 0 __

8 15. 4080

× 70

16. two decimal places in answer

$9.670

× 60$

17. Write the “carry number.”

97000

× 900

18. $3.47$5.23$7.68

+ $2.42$

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19. r− 3977

309

r =

20. 9013− w

3608

w =

21. short division

R7 )

_________ 8 9 0

22. short division

R6 )

_________ 1 0 0

23. short division

R4 )

____________ 8 0 3 5

24. 1 hour = min

1 __ 10 of min

25. 110° Los Angeles

° Anchorage

° cooler

26.

0 1 2 3 4

Y

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27. a. right angle degrees

b. half of a right angle degrees

c. 1 __ 2 =

a.

b.

c.

28. divisible by 6 and 10

A 610 B 510 C 410 D 312

29. 1 _ 8 of 1000

30. Body of Water

Average Depth(in feet)

North Sea 308

Persian Gulf 328

Hudson Bay 305

a. shallowest

b. I would s to find the d .

c. and ;

feet and feet are both close to 300.

Use work area.

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4444 Teacher Notes:

• Introduce Hint #32 “Reading Metric Rulers,” and Hint #33 “Reading Inch Rulers.”

• Refer students to “Length” and “Equivalence Table for Units” on pages 1 and 2 in the Student Reference Guide.

• Measuring Lengthswith a Ruler


• Centimeters and millimeters are units of length in the metric system. 1 cm = 10 mm

mm 10 20 30 40 50

cm 1 2 3 4 5

40 millimeters

4 centimeters

• Inches, feet, yards, and miles are units of length in the U.S. Customary System.

• This is an inch scale divided into eighths:

321inch

Lesson Practice

Use a centimeter ruler to measure each segment both in centimeters and in millimeters.

a. centimeters: millimeters:

b. centimeters: millimeters:

c.

centimeters: millimeters:

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d. Measure the length of your math textbook to the nearest centimeter.

e. One centimeter is how many millimeters?

f. How many millimeters is 5 centimeters?

g. Write the abbreviations for “centimeter” and “millimeter.”

h. How many millimeters long is the nail?

mm 10 20 30 40

i. How many centimeters long is the arrow?

Name the mark each arrow points to.

j. k. l. m. n. o.

inch 321 4

j. k. l.

m. n. o.

Use an inch ruler to measure each segment to the nearest eighth of an inch.

p.

q.

r.

s. Is 6 1_8 inches closer to 6 inches or 7 inches?

t. Round 5 7 _ 8 inches to the nearest inch.



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1. Draw a quadrilateral that has four right angles.

Use work area.

2. $0.03$0.03$0.03$0.03$0.$0.03

3. 3 buses× b children138

3b =

b =

Use work area.

4. cm ____ mm 1 __ 0 = 6 __

t

6 × = t

t =

Use work area.

5. 18891791

d

1889 – = d

d =

Use work area.


) _____

7.

0 1 2 3 4

Z

Written PracticeWritten Practicepage 279

8. 3 3 __ 4

–



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9. 4 1 __ 2

–

10. 5 1 __ 4

–

11. 33 1 __ 3

+

12. 5 1 __ 3

+

13. 8 3 __ 8

+

14. What is the length of the rectangle?

mm 10 20 30

15. 3524287593

7684+ 9856

16. 3627

–

17. 2000

–

9104

–

18. Offset.

49100

×

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19. Associative Property of Multiplication

60 × 8 × 37 =

20. 5n = 3175 ) _____

n =

21. short division

2964 ÷ 10 =


See page 19 in the Student Reference Guide.

0 __ 3 = percent

23. The number 256 is closest to which of the following?

2 5 6

A 240 B 250 C 260 D 300

24. It is morning. What time will it be in 30 minutes?

time now:

Count forward 30 minutes.

3

121110

9

87 6 5

4

21

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25. factors of 50: 1, , , , , 50

factors of 100: 1, , , , , , , , 100

, , , , ,

26. 1 _ 4 of 12 inches

27. $3.49 is close to $3.50.

+ =

Use work area.

29. 1 __ 3 + 30. 13° warmer

F

10

10

0

28. Which number is divisible by 3 and by 5?

A 305 B 315 C 325 D 355

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4545 Teacher Notes:

• Introduce Hint #34 “Classifying Quadrilaterals.”

• Refer students to “Quadrilaterals” on page 16 in the Student Reference Guide.

• Review Hint #28 “Geometry Vocabulary.”

• Classifying Quadrilaterals


• Quadrilaterals have four sides.

• Some quadrilaterals have special names.

Classifications of Quadrilaterals

Quadrilaterals 4 sides

Trapezoids Trapeziums Parallelograms

2 pairs ofparallel sides

1 pair ofparallel sides

right angles

right angles and equal sides

equal sides

no parallel sides

Rectangles Rhombuses

Squares

Lesson PracticeThe words parallelogram, trapezoid, trapezium, rectangle, rhombus, and squarewere used in this lesson to describe quadrilaterals. Describe each of the following quadrilaterals using these words.

a. b.

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c. d.

e. f.

g. Describe the difference between a parallelogram and a trapezoid.

A parallelogram has pairs of p sides.

A trapezoid has only pair of p sides.

h. Draw a rhombus with no right angles. Hint: like a diamond

1. Draw a rectangle with all equal sides.

Use work area.

2. 0000$10.00 paid m spent

got back

$10 − m =

m =

Use work area.





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3. Each state has 2 senators.

50 states

senators

U.S. senators

2 × = t

t = Use work area.

4. a people× 4 nights 2500 people

4a =

a =

Use work area.


gallons

______________ classes

8 __ 3 = ? __

1

6. 10 mm = cm

7.

321inch

9. 4 1 __ 4

+

10. 3 0

+

11. 5 3 __ 8

–

8. 3 1 __ 3

+

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12. 6 3 __ 4

−

13. 5 1 __ 2

–

14. $87.93 $35.16 $42.97+ $68.74 $

15. $50.26– $13.87 $

16. 6109– a

4937

a =

17. 9314× 70

18. $2.34× 600

19. 4287× 5

20. short division

9636 _____ 9 =

21. 8m = $34.16

) _____

000

m =

22. Shade 3 __ 5 .


5 __ 5 = percent

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23. 256

24. Which of these triangles appears to be a right triangle?

A B C D

25. Split the difference.

0 100 200

200+ 100

) _____

000

26. Measure this segment in inches.

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27. 1 2 3 R 38 )

_________ 9 8 7

Check: 8 × =

+

Correct or not?

28. Shade 1 3 _ 4 .

Use work area.

29.

A B

?

C281 in. 5

81 in.

30. Number of Small Apples 1 2 3 4

Number of Calories 65 130 195 260

a. Rule: Number of small apples ×

b. × 10 =

a. Use work area.

b.

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4646 Teacher Notes:

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

• Refer students to “Finding a Part When the Whole is Known” on page 23 in the Student Reference Guide.

• Review Hint #16 “Fraction of a Group, Part 1.”

• Word Problems About aFraction of a Group


Example

Nieve scored 2 _ 3 of her team’s 36 points. How many points did she score?

1. Draw a rectangle.This stands for the total.

36 points

The team scored36 points.

2. Divide the rectangle into the same number of parts as the denominator.

36 points

The denominator

of is 3, so 3 parts.23

3. Divide the total by thedenominator. Write that

36 points

12 points

12 points

12 points

answer in each part. 3 ) ____

3 6 12

4. Bracket the parts into fractions.Answer the question. 36 points

12 points

12 points

12 points

Nieve scored 23

Nieve did not score 13

.

. Nieve scored 24 points.

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• Shortcut: Solve the problem using an “is/of” proportion.

Example

What number is 2 _ 3 of 36?

is ____ of

2 __ 3 = ? ___

36

(36 × 2) ÷ 3 = 24

Lesson Practice

a. Two fifths of the 30 students in the class played in the band.How many students played in the band?

2 _ 5 of 30 30 students

didn’t play.35

played.25

5 ) _____

3 0

b. Susan practiced the trumpet c. Three fifths of the 30 students

for 3 _ 4 of an hour. For how were girls. How many

many minutes did Susan boys were there?practice the trumpet?

3 _ 4 of 60 0 __

5 of 30

4 ) _____

6 0 ) _____

3 0

60 min

didn’t practice.14

practiced.34

30 students

girls35

boys25



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miles ____________ hours

11 ___ 3 = ? __

1


2. 625 seats

empty f filled

625 − = f

f =

Use work area.

3. cm ________ mm 1 __ 0 = 4 __

t

4 × = t

t =

Use work area.

4. passengers× 8 ships 7000 passengers

8p = p =

Use work area.

5. 00001976

two centuries

6. 2 _ 3 of 48

3 ) _____

4 8

48 points

___ points

___ points

___ pointsNguyet scored 23

Nguyet did not score 13

.

.

is ____ of

2 __ 3 = ? ___

48


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7. 1 _ 4 of 60 1 _ 3 of 60

8. 256


What percent is not shaded?


0 __ 5 = percent

10. three minutes before midnight

midnight:

Count back three minutes.

11.

321inch

12. 3 3 __ 7

+

13. 2 2 __ 5

−

14. 3 2 __ 3

−


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15. 4

+ 1 4 ___ 12

6 5 ___ 12

−

16. 1396727854

+ 4685

17. $15.37

− $ .00

$20.00

− $ .00

18. 97 + w = 512

w =

w =

19. 9380000

×

20. Associative Property of

Multiplication

54 × 7 × 60 =

Use work area.

21. 9n = 5445

n =

22. short division

3205 ÷ 10 =

23. 4826

24. 100%



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25. 1375

1000 2000

A B C D

26. Which shows half of 3 cups? 1 R 12 )

__ 3

– 2 ___ – 1

1 1 __ 2 2 )

__ 3

– 2 ___ – 1

Use work area.

27. A rectangle is a “right corner” polygon because each

c is a r

a .Use work area.


A 234 B 456 C 567 D 245

29. 1 3 __ 4

321inch

30. 206 is about .

350 – =

Use work area.


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4747 Teacher Notes:

• Introduce Hint #36 “Simplifying Mixed Measures.”

• Review Hint #11 “Abbreviations and Symbols.”

• Review “Length” and “Equivalence Table for Units” on pages 1 and 2 in the Student Reference Guide.

• Simplifying MixedMeasures


Example

John is 5 feet 4 inches tall. How many inches tall is John?

1. Write the formula: ( × ) + =

2. On the line, write the equivalent measure.

( × 12) + = 1 ft = 12 in.

3. Write the first number in the first space.

(5 × 12) + = 5 ft 4 in.

4. Write the last number in the last space.

(5 × 12) + 4 = 5 ft 4 in.

5. Solve.

(5 × 12) + 4 = 60 + 4 = 64 inches

Lesson Practice

a. Change 6 feet 2 inches to inches. 1 ft = in.

( × ) + =

b. Change 3 minutes 2 seconds to seconds. 1 min = s

( × ) + =

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c. Change 2 hours 30 minutes to minutes. 1 hr = min

( × ) + =

d. Change 2 pounds 12 ounces to ounces. 1 lb = oz

( × ) + =


1. one

another

third t altogether

+ + = t

t = ___

I used rounding and found that + + = .

Use work area.

2. Multiply the loop.

decades years 1 __ = 7 __ t

7 × = t

t =

Use work area.

3. 68 grandmother

Anita d older

68 − = d

d =

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4. 1 ft = in.

( × ) + =

5. 374,021

A 7 B 70 C 700 D 70,000

6. March to March 12 months

March to May

7. Shade 3 _ 8 .


__ 8 = percent

8. Measure this segment in inches.

9. 4 0

+ 0

10. 3 3 __ 5

+

11. 2 3 __ 8

+ 0

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12. 5 1 __ 3 5 1 __

3

– 1 __ 3 –

13. 2 1 __ 2

–

14. 3 5 __ 9

–

15. $48,748$37,145

+ $26,498 $

16. $63,142– $17,936 $

17. $5.63× $ 700

18. 4729× 8

19. 9006× 80

20. short division

3456 _____ 8 =

21. short division

1836 ÷ 9 =

22. short division

1405 ÷ 7 =

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23. (20 × 25) + (5 × 25) =

25× 20

25× 5

+

24. 2 _ 5 of 50 ) _____

50 seeds

____ seeds

____ seeds

____ seeds

____ seeds

____ seeds

35 are not daisies

25 are daisies

Multiply the loop.

Divide by the outside number.

is of

2 __ 5 = ? __

25. How many minutes?

time now:

3

121110

9

87 6 5

4

21

time alarm rang:

Count back minutes.

26. 115 is not

d by 3.

Use work area.


A 576 B 765 C 6057 D 7650

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28. 1 _ 5 of 10 10 ÷ 5

29. 2 1 __ 4

321inch

30. The Bottlenose Dolphin

Number of Days 1 2 3 4

Average Amount of Food Eaten (in pounds) 23 46 69 92

a. Rule: number of days by

b. About ; One week is the same as days, and

× 23 = .

Use work area.

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4848 Teacher Notes:

• Refer students to “Expanded Notation” on page 9 in the Student Reference Guide.

• Review Hint #4 “Place Value (Digit Lines).”


• Reading and Writing Whole Numbers in Expanded Notation


• To write a number in expanded notation:

Name the place value of each digit.

3256 = (3 × 1000) + (2 × 100) + (5 × 10) + (6 × 1)

• When given expanded notation:

1. Count the number of places in the first parentheses:

(4 × 1000) + (6 × 10) + (2 × 1)

2. Draw digit lines for each place:

3. Fill in the digit lines. Use zeros for missing place values.

4 0 6 2

Lesson Practice

Write in expanded notation:

a. 56 = (5 × 10) + (6 × )

b. 5280 = (5 × ) + (2 × ) + (8 × )

c. 250,000 = (2 × ) + ( × )

Write in standard form:

d. (6 × 1000) + (4 × 10) =

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e. (5 × 100) + (7 × 10) =

f. (8 × 10,000) + (4 × 1000) = ,

g. (9 × 100,000) + (3 × 10,000) = ,


1. Draw a square.

Make each side 1 1 _ 2 inches long.

Use work area.

2. Aizza j Juno 6 years difference

− j = 6

j =

Use work area.

3. Which shows how much time?

16

2 __ 3

3 ) ____

5 0 − 3

2 0− 1 8

2

16 R 23 )

____ 5 0

− 3 2 0

− 1 82

4. dozens eggs 1 __ = 8 __ t

8 × = t

t =

Use work area.

5. 356,287

A 6 B 356

C 6000 D 6287

6. cm mm 1 __ = 19 ___ ?



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7. Shade 1 _ 6 .

__ 6 = percent

8. 2 8 7

9. (5 × 100) + (2 × 1)

10. 47,000

expanded notation

( × ) + ( × )

11. 98,57242,15637,428

+ 16,984

12. w− 32,436

19,724

w =

13. 10,000− y

1,746

y =

14. $34.78× 6

$14.87

15. 65490× 60

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16. 80370× 90

17. short division

3647 ÷ 6 =

18. short division

5408 ÷ 9 =

19. 10w = 1000

w =

20. 4 1 __ 3

−

3 1 __ 3

+

21. 6 × 800 = 6 × (8 × h)

(8 ? 800)

h =

22. $6.00

$6.

$6. $

$10.00

− $ . $

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24. 1 _ 4 of century

100 years

____ years

____ years

____ years

____ years

14

) ____

122

23. (20 × 62) + (3 × 62) =

× × +

25. one minute before midnight

midnight:

Count back one minute.

26.

0 100 200

200

) _____

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27. Amount of Fuel Used (in gallons) 1 2 3 4Distance Traveled (in miles) 28 56 84 112

a. Write the next three amounts in the pattern.

b. distance traveled on one gallon × number of gallons

× =

Use work area.

28. 1 dollar = dimes

) ____

000

29.

30. 42 rounds to .

13 rounds to .

– =

Use work area.

page 304


L E S S O N

Name


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4949 Teacher Notes:

• Review Hint #10 “Word Problem Cues, Part 1”, and Hint #18 “Word Problem Cues, Part 2.”

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

• Review reference chart “Word Problem Keywords.”

• Solving Multiple-StepWord Problems


• To solve a multiple-step word problem:

Write down the given information.

Draw a picture.

Example

Huang is 5 years older than Robert. Robert is 3 years older than Sally. Sally is 15 years old. How old is Huang?

Sally 15 years

Robert (Sally + 3) 15 + 3 = 18 years

Huang (Robert + 5) 18 + 5 = 23 years

Huang is 23 years old.

Lesson PracticeSolve each two-step problem:

a. The bus could carry 80 students. The 32 students from Room 8 and the 29 students from Room 12 got on the bus. How many more students can the bus carry?

Bus holds 80 Room 8 Room 12

32 29

How many empty seats are on the bus? So how many students?

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b. Mariabella collected 37 aluminum cans for school, and her brother collected 21. They decided to divide the cans evenly, so they put the cans into one big pile

and then made two equal piles. How many cans were in each pile?

2 equal piles

one big pile each small pile

Mariabella

37

one big pileBrother

21


1. Start with one pair of sides that are

not parallel.

Use work area.

2. Ciante 15

Hakim (Ciante + 5)

Kafele (Hakim + 10)

3. 1 _ 3 of 36

36 years

____ years

____ years

____ years

13

) _____

3 6



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4. 1 _ 6 of 24

) _____

2 4 24 students

___ students

___ students

___ students

___ students

___ students

___ studentsabsent16

in school56

is of

1 __ 6 = ? __

5. 754,238

A 700,000 B 700

C 7 D 754

6. (5 × 100) + (6 × 1) 7. short division

) __________

$5 . 0 0

8. 234

9. twenty-five thousand, three hundred

10. Shade 5 _ 6 .

What percent is not shaded? See page 19 in the Student Reference Guide.

R __ 6 = percent

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11. 5 2 __ 8

+ 6 + 3 __ 8 = 12. 8 5 __

6 – (3 5 __

6 – 3) = 13. 342

587463

2858

96+ 87

14. $42.01

– $ .00

$

15. 1000 − m = 1

m =

16. 50

×

17. Commutative Property of Multiplication

30 × 8 × 25 =

18. short division

1205 ÷ 6 =

19. short division

$76.32 ÷ 8 =

page 309



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20. $20 − ($12 + $4.76 + $2.89 + $0.34) =

$12.00

$ .

$ .

+ $ .

$

$20.00

− $ .

$

21. (20 × 35) + (5 × 35) =

× × +

22. 150,000

words:

Use work area.

23. 150,000

expanded notation

( × ) + ( × )

24. 185, 370, 555, 740, , ,

Use work area.

25. Which place?

203,456

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26.

1600 1700 1800

1800

) _____

27. 1998 later– 1965 earlier difference

28. odd

× 5 product

Last digit?

29. Which of these angles appears to measure 150º?

A B C D

30. See page 310.

rounds to . rounds to .

– =

Use work area.

page 309


L E S S O N

Name


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5050 Teacher Notes:

• Introduce Hint #37 “Average.”

• Refer students to “Average” on page 9 in the Student Reference Guide.


• Finding an Average


• To find an average:

1. Add the numbers.

2. Divide by the number of numbers.

• The answer must be between the smallest and largest numbers.

Lesson PracticeSolve each two-step problem by combining and then forming equal groups.

a. The number of players on the four squads was 5, 6, 9, and 8. If the squads were changed so that the same number of players were on each squad, how many players would each squad have?

5 6

9 8

569

+ 8 ) ____

122

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b. When the class lined up, there were 11 students in one line and 17 students in the other line. If the lines were made even, how many students would be in each line?

11+ 17 )

____ 122

c. This picture shows three stacks of books. If the stacks were made even, how many books would be in each stack?

57

+ 9 ) ____

122

d. Here are Shauna’s game points:

8, 9, 7, 9, 8, 10, 6, 7

What is the average of Shauna’s game points?




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5. 1 hour = minutes

( × ) + =

6. centuries years 1 __ = ? ____ 400

7. fifty-four thousand, nine hundred nineteen

8. Shade 7 _ 8 .

percent not shaded

0 __ 8 = percent


1. Draw a quadrilateral with perpendicular sides.

Use work area.

2. Miguel 13

Loh (2 years younger than Miguel)

Kimberly (5 years older than Loh)

3. average

58

+ 8 ) ____

122

4. 3 _ 5 of an hour 60 min

____ min

____ min

____ min

____ min

____ min

35 )

____ 122

is of

__ = ? ___ 60



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12. $34.28

×

$

13. 7 × 57 × 10 = 14. (4 + 7 + 7) ÷ 3 =

15. (5 + 6 + 9 + 8) ÷ 4 = 16. short division

4206 ÷ 7 =

17. short division

$60.24 ÷ 6 =

9. average

15

+ 11 ) ____

122

10. 342 + 67 + 918 + 897 + 42 = 11. $53.87

− $ .

$

18. short division

1000 ÷ 9 =

19. 6d = 180

d =

20. 1 1 __ 7

2 2 __ 7

+ 3 3 __ 7

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21. 7 7 ___ 10

−

9 9 ___ 10

−

22. (10 × 43) + (2 × 43) =

× × +

23. Don’t count July. 24. 1236

A 1100 B 1200

C 1300 D 1000

25.

4 mi

5 mi

32 mi

Arcadia Park

Safara’shouse

Legg Lake

ocean mountaincabin

98 mi

a. Count forward hours.

9:00 a.m. 4:00 p.m.

b. How far is it from Arcadia Park to Legg Lake?

c. How far did they travel from home to the mountain cabin and back home?

to the cabin+ back home

total

Use work area.

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26. average

5886

+ 8 ) ____

122

27. 700 × = a

a =

Use work area.

28. every letter

c, f, i, l, o, , , , …

Use work area.

29. 300× 2 + 200

30. I can use c numbers. 984 is close to .

– 885 =

Use work area.

page 316


Saxon Math Intermediate 5 325 Adaptations Investigation 5

Name I N V E S T I G A T I O N©

200

8 S

axon

page 317

Focus onFocus on• Organizing and Analyzing

Data

• To make a frequency table of activities:

1. List the possible activities in the first column.2. Tally the number of students who completed each activity

in the second column.3. The frequency is given by the tallies. List the frequency in

the third column.4. Check your answer by adding the numbers in the frequency

column. The sum should match the total number of tallies.

Frequency Table

Activity Tally Frequency

1

4

7

5

5

3

1

2

3

4

5

6

1. Twenty children were asked how many brothers and sisters each had. The responses were these numbers:

2, 3, 0, 1, 1, 3, 0, 4, 1, 2,

0, 1, 1, 2, 2, 3, 0, 2, 1, 1

Represent Complete the frequency table on the next page to show the numbers of brothers and sisters.

55

Math Language

• Data are all types of gathered information.

SM_H5_AD_Inv05_FF.indd 325SM_H5_AD_Inv05_FF.indd 325 11/2/07 2:26:58 PM11/2/07 2:26:58 PM


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I N V E S T I G A T I O N continued5

Frequency Table

Number of Brothers and Sisters Tally Frequency

ABC market offers 22 turkeys for sale. The weights of the turkeys in pounds are given below:

11, 18, 21, 23, 16, 20, 22, 14, 16, 20, 17,

19, 13, 14, 22, 19, 22, 18, 20, 12, 25, 23

Sometimes we group data in intervals of equal length.

2. Represent Use the raw data about the turkey weights at ABC Market to complete the frequency table. Instead of the weight intervals shown in the table on page 319 in your textbook, use the intervals 11–15 lb, 16–20 lb, and 21–25 lb.

Frequency Table

Weight Tally Frequency

11—15 lb

16—20 lb

21—25 lb

3. The annual rainfall in a certain Texas city for each of the last fifteen years is recorded below. Each of these data is in inches.

17, 24, 32, 27, 18, 30, 22, 18, 24, 31, 32, 26, 18, 19, 22

Represent Complete the frequency table on the next page for the data, using five-inch intervals. Begin with the interval 15–19 in.



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Frequency Table

Rainfall Tally Frequency

15—19 in.

20—24 in.

25—29 in.

30—34 in.

• To make a line plot:

1. Draw a number line to include the highest and lowest values collected.

2. Place an X above each number for each data point that matches a number.

Jean-Paul recorded the ages of the first 20 people who went down a certain water slide after the water park opened at 9 a.m. Their ages were:

11, 9, 8, 11, 12, 15, 13, 12, 17, 12,

12, 22, 13, 11, 21, 9, 16, 12, 13, 9

Use the line plot Jean-Paul made to answer these problems.

5 10 15 20 25

X

Age

XXXX

XXXXX

XXX

XXX

X X XX

4. Which age was recorded most frequently?

5. How many people who went down the slide were over 15?

6. Which ages were recorded exactly three times?

, ,

Math Language

• A line plot lets us see each data point.



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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

The Lizard Emporium pet store tracks the life span of the iguanas it sells. The data for some of the iguanas are displayed in this line plot:

Life Span (in years)

10 15 20 25 30

XX

XXX

XXXX

XXXX

XXX

XXX

XX

Use the line plot above to answer problems 7–11.

7. What was the most frequent life span (mode) of the iguanas

that were tracked?

8. How many iguanas were tracked?

9. How many iguanas lived between 17 and 25 years?



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10. What is the range of the life spans? range span

– =

11. What is the median life span of the iguanas? median middle

12. The teacher recorded the number of papers she graded each day for 15 days.

19, 18, 17, 15, 18, 20, 14, 17,

19, 11, 18, 17, 16, 18, 16

Represent Make a line plot for the number of papers graded each day.

Papers Graded

201510

13. Which number is an outlier?

14. Which number occurs most often (mode)?

15. What is the median for this set of data? median middle

Math Language

cluster – a group of data points that are very close together

outlier – a data point that is far from most of the data points



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Tuesday

Wednesday

Thursday

Friday

Saturday

Sunday

Dinners Served

represents 10 dinners

Use the pictograph above to answer these problems.

16. What is the range of the number of dinners served? range span

– =

17. What is the median of the number of dinners served?

median middle

Use your textbook to complete problems 18–21.

ActivityActivity page 323

Graphing

• This activity is optional.


Documents

Adding and Subtracting Fractions with Common Denominatorsmryoungclassnews.weebly.com/uploads/4/0/3/5/40359489/h5_lesso… · • Adding and Subtracting Fractions with Common Denominators