Mathematics Grade 5 TEACHER KEY

W1 - Lesson 2: Exploring Proper Fractions

V5-07

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Mathematics Grade 5Version 5Preview/Review W1 - Lesson 2 TEACHER KEY

Publisher: Alberta Distance Learning CentreAuthor: Leslie FriesenIn-House Teacher: Sue Rees

Project Coordinator: Dennis McCarthyPreview/Review Publishing Coordinating Team: Nina Johnson, Laura Renkema, and Donna Silgard

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W1 - Lesson 1 ...................Number Sense Numbers 0 to 100 000W1 - Lesson 2 ................................... Exploring Proper FractionsW1 - Lesson 3 ................................................ Exploring DecimalsW1 - Lesson 4 .................Numbers With Up to 2 Decimal PlacesW1 - Lesson 5 ......................................................... MultiplicationW1 - QuizW2 - Lesson 1 ...................................................................DivisionW2 - Lesson 2 .............. Collecting Data and Analyzing PatternsW2 - Lesson 3 .................Estimating and Taking MeasurementsW2 - Lesson 4 ...................... Perimeter and Area MeasurementsW2 - Lesson 5 ............................................ Metric MeasurementsW2 - QuizW3 - Lesson 1 ........................ Volume, Capacity, Mass, and TimeW3 - Lesson 2 .................................. 2-D Shapes and 3-D ObjectsW3 - Lesson 3 .....................................................TransformationsW3 - Lesson 4 ...................................... Statistics and ProbabilityW3 - Lesson 5 ..........................................Chance and ProbabilityW3 - Quiz

Materials RequiredImportant Concepts of Grade 5 Mathematics

DistanceLearning

Centre

AlbertaL

EARNING

AN

YT

IME A N Y

W

HE

RE

ProtractorRulerCalculator

A textbook is not needed.

This is a stand-alone course.

W1 - Lesson 2:Exploring Proper

Fractions

Preview/Review Conceptsfor

Grade Five Mathematics

TEACHER KEY

OBJECTIVES

By the end of this lesson, you should

� understand the meaning of the numerator and denominator of afraction

� write fractions and equivalent fractions

� change fractions to their simplest forms

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Preview/Review Concepts W1 - Lesson 2 Mathematics Grade 5 - TEACHER KEY

Glossary of Terms

Denominator: The denominator is the number onthe bottom of a fraction. 4 is the

denominator in the fraction 14

.

Equivalent Fractions: Two fractions of the same valueare equivalent.

Fraction: A fraction is a way to show part ofa whole number. A fraction hastwo parts: the numerator and thedenominator.

numerator (top)denominator (bottom)

Numerator: The numerator is the number ontop. 1 is the numerator in the

fraction 14

.

Proper Fraction: In a proper fraction, the numeratoris the smaller number and thedenominator is the larger number.

34

denominator

numerator

Preview/Review Concepts W1 - Lesson 2Mathematics Grade 5 - TEACHER KEY

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Simplest Form: When a fraction is in its simplestform, the numerator and denominatorare the least whole numbers possible.

Example: 34

is the simplest

form of 68

.

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Preview/Review Concepts W1 - Lesson 2 Mathematics Grade 5 - TEACHER KEY

W1 - Lesson 2: Exploring Proper Fractions

Concepts:

• Numerator and Denominator• Representing Fractions with Pictures• Equivalent Fractions• Changing a Fraction to its Simplest Form

Numerator and Denominator

The numerator is the top number. The numerator answers the questionsHow many equal parts are left? or How many equal parts are being used?

The denominator is the bottom number. The denominator answers thequestion How many equal parts was it divided into?

Therefore, 23

means two equal pieces are left or two equal pieces are used,

but the item had been divided into three equal parts.

Here are three equal parts, and two parts are coloured grey. Therefore, 23

of

the parts are grey.

Preview/Review Concepts W1 - Lesson 2Mathematics Grade 5 - TEACHER KEY

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Fill in the missing numerator and denominator for the following questions.The grey parts represent the amount of parts left. Your fraction will showthe amount that is grey.

Allan cut an apple into 8 equal parts. He ate 6 pieces. What fraction of

the apple does Allan have left? 2 1

or8 4

⎛ ⎞⎜ ⎟⎝ ⎠

John finished reading the 4th book of a 5 book series. What fraction of books

has John read? 45

What fraction of squares are grey? 8 2

or12 3

⎛ ⎞⎜ ⎟⎝ ⎠

What fraction of squares are white? 4 1

or12 3

⎛ ⎞⎜ ⎟⎝ ⎠

45

61 2

04

22

00

815

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Preview/Review Concepts W1 - Lesson 2 Mathematics Grade 5 - TEACHER KEY

Representing Fractions with Pictures

To understand fractions, we must be able to draw a pictureof the fraction, or write a fraction by looking at a picture.

Example: can be shown by

5 =

8

Draw pictures for the following fractions.

310

612

55

26

12

28

810

13

58

Remember,all fractionsmust bemade up ofparts ofequal size!

Preview/Review Concepts W1 - Lesson 2Mathematics Grade 5 - TEACHER KEY

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Write a fraction with four as thedenominator and one as thenumerator.

Circle 5

12 of the soccer players.

Jessica made a peach pie. Shegave one tenth to her aunt. Drawa picture of the pie with one tenthgone.

Draw one set of six faces.

Make 12

of them happy and 13

of

them sad.

34

912

14

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Preview/Review Concepts W1 - Lesson 2 Mathematics Grade 5 - TEACHER KEY

Equivalent Fractions

Equivalent fractions are fractions that have the same value.

Example: James and Bertha each had a chocolate bar.

James ate 1

2 of his bar.

Bertha ate 4

8 of her bar.

You can see from looking at what is left of each chocolate bar that they each

ate the same amount. This is because 1

2 and

4

8 are equivalent

fractions.

Example: Martha and Herbert are painting wood panels for walls in newhouses.

Amount Martha has done 1216

Herbert has completed 3

4

From looking at the amount of each panel that has been completed, youcan ‘see’ that the amount of painting is the same for each person.

So, 1216

and 3

4 are the same amount, so they are equivalent fractions.

Preview/Review Concepts W1 - Lesson 2Mathematics Grade 5 - TEACHER KEY

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Changing a Fraction to its Simplest Form

Look at the following diagrams

a. b.

Both shaded areas are the same size. We know that 4

6 is the same as

2

3, or we can say that

4

6 and

2

3 are equivalent fractions.

Simplest Terms

Many times we can simplify a fraction and express it in its simplest terms.

We do this by finding numbers that will divide into both the numerator

and the denominator. With 4

6, we know that 2 will divide evenly into both

the numerator and denominator. 4 2 2

6 2 3÷ =

We can say that 2

3 is the simplest form of

4

6.

Examples of Changing Fraction into Simplest Form

9

15

A number that will divide into 9 and 15 is 3.

÷ =9 3 3

15 3 5

Therefore, 9

15 in it simplest form is

3

5.

3

5 may be represented by this diagram:

You can see that 9

15 and

3

5 are equivalent fractions.

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Preview/Review Concepts W1 - Lesson 2 Mathematics Grade 5 - TEACHER KEY

Change Each Fraction to its Simplest Form

1.2

= 4

12

2.8

= 12

23

3.5

=20

14

4.4

=12

13

5.7

=21

13

6.18

=24

34

7.14

=28

12

8.9

=12

34

9.8

=16

12

10.16

=20

45

11.11

=22

12

12.5

=40

18

13.15

=35

37

14.10

=30

13

15.12

=18

23

Preview/Review Concepts W1 - Lesson 2Mathematics Grade 5 - TEACHER KEY

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Making Equivalent Fractions

You have learned to simplify fractions. This was done by dividing thenumerator and denominator by the same number. You can makeequivalent fractions by multiplying the numerator and denominator bythe same number.

Example 1: Example 2:Fraction Diagram Look at the equivalent fractions

we can make from 23

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You can see that we have created 4equivalent fractions that are the same

value as 12

. They are2 3 4 5

, , , and 4 6 8 10

.

Of course, we could add many more!

Fraction Diagram

23

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× =

2 2 43 2 6

We can write 2 4 6 8

= = =3 6 9 12

because all these fractions areequal. (We call them equivalentfractions.)

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2 3 6× =

3 3 9

1 3 3× =

2 3 6

12

1 4 4× =

2 4 8

1 5 5× =

2 5 102 4 8

× =3 4 12

1 2 2× =

2 2 4

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Preview/Review Concepts W1 - Lesson 2 Mathematics Grade 5 - TEACHER KEY

Example 3:

How many 12ths are equivalent to 23

?

Here you are being asked to to find an equivalent fraction. The question

could be 2 ?

=3 12

Step One - Find the number that the denominator (3) must be multipliedby to make the result of 12

2× =12

3 4 You must multiply 3 by 4 to get 12.

Step Two - After you find the number, use it to multiply the numerator.

2 4 8× =

3 4 12 Then multiply the numerator by 4. The result is

812

So, we know that 2 8

=3 12

. Therefore, these are equivalent fractions.

3 ?=

5 20

3× =

5 4 20

Thus, 3 12

=5 20

. These are equivalent fractions.

Example 4:

3 12=

7 ?

43 12× =

7 4 28

Therefore, 3 12

=7 28

. These are equivalent fractions.

Complete the following exercise on equivalent fractions.

a.2

=9 18

4b.

5=

6 1210

c.8

=10 40

32

d.9

=10 100

90e.

7=

8 2421

f.4

=7 21

12

43 12× =

5 4 20

Preview/Review Concepts W1 - Lesson 2Mathematics Grade 5 - TEACHER KEY

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g.3 9

=8 24

h.5 15

=7 21

i.6 24

=7 28

j.4 1

=8 2

k.4 2

=14 7

l.3 9

=8 24

2. Give two equivalent fractions for each of the following.

a. 45

8 12

10 15b.

29

4 6

18 27

Points to Remember

1. Equivalent fractions have the same values.

2. When fractions are reduced to their simplest form, the originalfraction and the fraction in simplest form are equivalent.

3. Fractions can be written as words, as pictures, or as numbers.

Which fraction of each shape is grey?a. b.

c. d.

612

04

45

59

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Preview/Review Concepts W1 - Lesson 2 Mathematics Grade 5 - TEACHER KEY

Write these fractions in number form.

1. Five-sixths 4. Three-quarters

2. Four-twelfth 5. Eleven-thirteenths

3. Nine-tenths 6. One-quarter

Write these fractions in word form.

a.7

12_____________________________________________________________

b.12

______________________________________________________________

c.2

16_____________________________________________________________

d. Many skateboarders were at the park today. Five skateboarders wereable to complete tricks off the ramp. Three skateboarders were justlearning. What fraction of skateboarders were able to complete tricksoff the ramp?

seven-twelfths

two-sixteenths

one-half

58

of the skaters could complete tricks

910

34

14

1113

56

412

Preview/Review Concepts W1 - Lesson 2Mathematics Grade 5 - TEACHER KEY

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3-Step Problem-Solving Process

1. Write the problem in a number question.

6 ? =

7 ?2. Solve the problem. SHOW YOUR

WORK!

3. Reduce your fractions to their simplestform where possible.

4. Write a sentence with the answer.

Mary had twenty pieces of candy.Her brother ate five pieces. Whatfraction of Mary’s candy did herbrother eat?

Joy is sewing buttons on a shirt.She has sewn four of the sixbuttons on the shirt. Whatfraction of buttons does she haveleft to sew?

About one-third of the studentsin Mrs. Friesen’s class arewearing blue jeans. If Mrs.Friesen has 24 students, howmany students are wearing bluejeans?

Shellie baked a dozen muffins.One-quarter were blueberry, one-quarter were banana, and therest were chocolate chip. Whatfraction were chocolate chip?

5 ÷ 5 1=

20 ÷ 5 41

Mary's brother ate 4

of her candy.

1 n=

3 24n = 8Eight students are wearing blue jeans.

2 ÷ 2 1=

6 ÷ 2 31

Joy has of the buttons3

left to sew.

2 ÷ 2 1=

4 ÷ 2 2One - half of the muffinswere chocolate chip.

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Preview/Review Concepts W1 - Lesson 2 Mathematics Grade 5 - TEACHER KEY

Draw a picture showing achocolate bar with one-sixtheaten by Mrs. Friesen. Whatfraction has she eaten, and howmuch remains to be eaten?

James wants to share some left-over pizza with his friends.James has two-thirds of hispizza left. If he gives one piece toeach of his six friends and thisleaves no pieces, how manypieces did the pizza originallyhave? Use an equivalentfraction to help solve youranswer.

Two-thirds of Mark’s soccer teamhad scrapes and bruises. Draw apicture showing how manystudents had scrapes andbruises if there were fifteenplayers on Mark’s soccer team.

John spent an hour with hishorse on Saturday. John rodehis horse for three-quarters of anhour. The rest of the time hespent brushing his horse. Whatfraction of time did John spendbrushing his horse?

X X X X X

X X X X X10 2

15 3= =

Ten-fifteenths of the soccerteam had scrapes andbruises.

John spent one-quarter ofthe time brushing hishorse.

5 1remaining, eaten

6 6Mrs. Friesen has eaten one - sixth and five - sixths remain to be eaten.

2 6=

3 nn = 9The pizza originallyhad nine pieces.