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Mathematics Grade 5 TEACHER KEY
W1  Lesson 2: Exploring Proper Fractions
V507

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Mathematics Grade 5Version 5Preview/Review W1  Lesson 2 TEACHER KEY
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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 .................................. 2D Shapes and 3D ObjectsW3  Lesson 3 .....................................................TransformationsW3  Lesson 4 ...................................... Statistics and ProbabilityW3  Lesson 5 ..........................................Chance and ProbabilityW3  Quiz
Materials RequiredImportant Concepts of Grade 5 Mathematics
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Centre
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EARNING
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IME A N Y
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ProtractorRulerCalculator
A textbook is not needed.
This is a standalone 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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123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234
12345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345
123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234
123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234
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
1234567890123456123456789012345612345678901234561234567890123456123456789012345612345678901234561234567890123456123456789012345612345678901234561234567890123456123456789012345612345678901234561234567890123456
× =
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.)
1234567890123456712345678901234567123456789012345671234567890123456712345678901234567123456789012345671234567890123456712345678901234567123456789012345671234567890123456712345678901234567123456789012345671234567890123456712345678901234567
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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12345678901234567123456789012345671234567890123456712345678901234567123456789012345671234567890123456712345678901234567123456789012345671234567890123456712345678901234567123456789012345671234567890123456712345678901234567

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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. Fivesixths 4. Threequarters
2. Fourtwelfth 5. Eleventhirteenths
3. Ninetenths 6. Onequarter
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?
seventwelfths
twosixteenths
onehalf
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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3Step ProblemSolving 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 onethird 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.Onequarter were blueberry, onequarter 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 onesixtheaten by Mrs. Friesen. Whatfraction has she eaten, and howmuch remains to be eaten?
James wants to share some leftover pizza with his friends.James has twothirds 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.
Twothirds 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 threequarters 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= =
Tenfifteenths of the soccerteam had scrapes andbruises.
John spent onequarter 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.