Improper Fractions: Parts of Sets 1 - WordPress.com · proper fraction a fraction less than 1 whole...

$: Improper Fractions: Parts of Sets 1 - WordPress.com · proper fraction a fraction less than 1 whole e.g., 4 8 ... The value of is the same for ... improper fraction a fraction greater$
OPEN-ENDEDPathway 1

Markers sometimes come in boxes of 8.

A full box is 1 whole.

4 markers would fill 48 of a box.

1 marker would fill 18 of a box.

48 and 18 are proper fractions.

9 markers would fill a whole box and 18 more of a box.

So 98 5 1 18.

You can write the mixed number 1 18 or the

improper fraction 98.

• Step 1: Use the numbers 2, 3, 8, 10, 22, and 31 in the spaces below to create 6 different improper fractions.

Improper Fractions: Parts of Sets

proper fractiona fraction less than 1 whole e.g., 48mixed numbera number greater than 1 that is made up of a whole number and a fraction parte.g., 3 14improper fractiona fraction greater than 1 whole where the numerator is greater than the denominator e.g., 76

Copyright © 2011 by Nelson Education Ltd.97

Improper Fractions: Parts of Sets, Pathway 1Leaps and Bounds

Leap SR_Topic 7.indd 97Leap SR_Topic 7.indd 97 27/04/11 10:44 PM27/04/11 10:44 PM

• Step 2: Draw a picture to show each fraction from Step 1. The whole in each picture must be a package that holds more than 1 item. Label each picture with the correct mixed number.

• Step 3: Choose 2 of your fractions from Step 1.Tell how the fractions are alike. Tell how their pictures are alike.

• Step 4: Repeat Step 3 with 2 other fractions from Step 1.


Improper Fractions: Parts of Sets, Pathway 1 Leaps and Bounds

Leap SR_Topic 7.indd 98Leap SR_Topic 7.indd 98 25/04/11 10:53 AM25/04/11 10:53 AM

GUIDEDPathway 1

Light bulbs sometimes come in packages of 6.

3 light bulbs would fill 36 of a package.

1 light bulb would fill 16 of a package.

36 and 16 are proper fractions.

• If you had 11 light bulbs in packages of 6, you would have 11

6 of a package.116 is called an improper fraction.

The 11 tells you that there are 11 light bulbs. The 6 tells you that 6 light bulbs make 1 whole package.

• 116 is also 1 56.

1 56 is called a mixed number.

It means 1 whole 1 56 of another whole.

• What fraction would describe 1 whole package of light bulbs?

• What improper fraction and mixed number do you see in the picture below? The eggs in 1 carton represent 1 whole.

Improper Fractions: Parts of Sets

proper fractiona fraction less than 1 wholee.g., 48improper fractiona fraction greater than 1 whole where the numerator is greater than the denominatore.g., 76

mixed numbera number greater than 1 that is made up of a whole number and a fraction parte.g., 3 14




Try These1. In each picture below, the package shows the number

of items in 1 whole. How many full and partial packages could you fill with the loose items on the right?Use an improper fraction and a mixed number.

a)

1 whole

improper fraction: ________

mixed number: ___________

b)

1 whole



c)



d)



1 whole

1 whole




2. Cookie packages come in different sizes.One whole package might contain 4 cookies, or 6, 8, 10, or 12 cookies.How many packages would 15 cookies fill? Complete the chart for each package size.The first row is completed for you.

15 Cookies in Packages

Package size(number of cookies

in 1 whole)

Fraction of full packages

(improper fraction)

Number of full and partial packages (mixed number)

4154

3 34

6

8

10

12

3. Draw a picture to show 1 whole package in the first box. Draw a picture of the improper fraction in the second box.

a) 75 of a package of cookies

The whole: Improper fraction A75B:

b) 83 of a package of cookies

The whole: Improper fraction A83B:




4. The fraction 12j

is an improper fraction.

a) Write 3 possible denominators for the improper fraction.

12

12

12

b) Write a mixed number for each improper fraction in a).

________ ________ ________

c) Which fractions from part a) are greater than 2 wholes?

5. What could the numerator of each fraction be?

a) j6 is between 2 and 3 wholes. ❚ could be ________.

b) j4 is between 3 and 4 wholes. ❚ could be ________.

c) j5 is between 4 and 5 wholes. ❚ could be ________.

6. j4 and 23j

are both between 2 and 3 wholes.

The value of ❚ is the same for both fractions. What might ❚ be?

❚ 5 ________

7. Why might one person say that this picture shows 56 but another say that it shows 52?




8. Sketch a picture that shows each of the following.

a) 125 of a group of objects is more than 2 groups

of the objects.

b) 113 of a group of objects is less than 4 groups

of the objects.

9. You have 20 hockey cards in more than 3 packages. Name a possible improper fraction and a mixed number for this situation. Tell how many cards are in 1 whole package.

Lots of things come in packages. Fractions are useful for describing amounts when some packages are not full.

FYI




OPEN-ENDEDPathway 2

Raj spent 5 12 hours at soccer practice this week.

Kyle spent 2 34 hours. Alyssa spent 3 23 hours.

Each number above is a mixed number.

Each number can also be written as an improper fraction.

For example, Alyssa’s 3 23 hours is the same as 113 hours.

Count the thirds in the picture below.

1210 2

86

4

1

3

57

9

11 1210 2

86

4

1

3

57

9

11 1210 2

86

4

1

3

57

9

11 1210 2

86

4

1

3

57

9

111210

89

11

86

457

22

4

1

3

110

89

11

86

457

22

4

1

3

110

89

11

86

457

22

4

1

3

110

89

11 22

4

1

3

• Write an improper fraction for each mixed number of hours that Raj and Kyle spent at practice.

Raj: 5 12 5 ________ Kyle: 2 34 5 ________ Alyssa: 3 23 5 113

• What do you notice about the 3 improper fractions?

Fraction Set 1

• Make up a set of 3 mixed numbers that have something in common. What do the 3 mixed numbers have in common?

• Draw a picture for 1 mixed number from the set.

• Write the 3 mixed numbers as improper fractions.

• What do the 3 improper fractions have in common?

3 mixed numbers

What do the mixed numbers have in

common?Picture of

1 mixed number3 improper fractions

What do the improper fractions have in common?

Improper Fractions: Parts of Wholes

mixed numbera number greater than 1 that is made up of a whole number and a fraction parte.g., 3 14improper fractiona fraction greater than 1 whole where the numerator is greater than the denominator e.g., 76

You will need• fraction pieces


Leaps and BoundsImproper Fractions: Parts of Wholes, Pathway 2


Fraction Set 2

• Repeat the instructions for fraction set 1 with another set of 3 mixed numbers.

3 mixed numbers


common?Picture of



Fraction Set 3

• Repeat the instructions for fraction set 1 with another set of 3 mixed numbers.

3 mixed numbers


common?Picture of




Leaps and Bounds Improper Fractions: Parts of Wholes, Pathway 2


GUIDEDPathway 2

Jasmine ran around the track 2 and 14 times.

You can write 2 14 as 94, since she ran around 9 quarters of the track.

2 14 is called a mixed number.94 is called an improper fraction.

• You can show this on a number line, too.

210

04

44

84

94

once around twice around

Notice that 94 5 44 1 44 1 14.

That’s why 94 is the same as 2 14.

Try These 1. Show each fraction on the number line.

For part c), also mark the position for 1.

a) 74 210

b) 95 210

c) 73 0

Improper Fractions: Parts of Wholes

mixed numbera number greater than 1 that is made up of a whole number and a fraction parte.g., 3 14improper fractiona fraction greater than 1 whole where the numerator is greater than the denominator e.g., 76

• Fractions like 44,

33, and so on are

exactly 1.

You will need• fraction pieces




2. Shade the shapes to show each fraction.

a) 52

1 whole

b) 103

1 whole

c) 94

1 whole

3. Explain why 3 12 5 72. Use the pitchers of juice to help you.

4. How many whole pitchers would be full if you filled pitchers for each fraction?

a) 92 pitchers: ________ c) 11

3 pitchers: ________

b) 154 pitchers: ________ d) 12

5 pitchers: ________

5. 7 quarters make $1.75. How does this help you explain

why 74 5 1 34?


Leaps and Bounds Improper Fractions: Parts of Wholes, Pathway 2


6. Why might one person describe this picture as 95,

but another person might describe it as 910?

7. Draw a picture to show each relationship.

a) 1 15 of 1 whole is twice as much as 35 of that same whole.

b) 2 25 of 1 whole is 3 groups of 45 of that same whole.

8. Use an improper fraction and a mixed number to describe each number.

a) a number greater than 3 but less than 4

improper fraction: ________ mixed number: ________

b) a number a lot more than 53


c) a number closer to 5 than to 6


d) a fraction with a numerator that is 10 more than the denominator


We often use fractions to describe parts of wholes.It is helpful to have a mental picture of those fractions to understand how much the fraction represents.

FYI




OPEN-ENDEDPathway 3

Boats sometimes have 8 seats to hold 8 rowers.

4 rowers would fill 48 of the seats.

The numerator 4 tells the number of rowers there are.The denominator 8 tells how many would fill the seats.

1 rower would fill 18 of the seats.

Imagine containers that hold different numbers of things and are partly full.

For example, a package that holds 10 pencils could be 210 full.

• Think of 6 containers that hold different numbers of things. Create 6 fractions to describe how full the containers are.Use the numbers 2, 4, 5, 6, 8, and 10 for the denominators or the numerators.The numerators should not be greater than the denominators.

Proper Fractions: Parts of Sets

• The numerator of the fraction is the top number.

• The denominator is the bottom number.

34

d numeratord denominator


Leaps and Bounds Proper Fractions: Parts of Sets, Pathway 3


• Sketch a picture to show each of your 6 fractions.Label each picture.

• Choose 2 of your fractions.Tell how the fractions are alike and different. Tell how their pictures are alike and different.

• Repeat with 2 other fractions.


Leaps and BoundsProper Fractions: Parts of Sets, Pathway 3


GUIDEDPathway 3

Sometimes students work in groups of 4.

The girl is 14 of the number of people in the group.

The numerator 1 tells the number of students you are talking about.

The denominator 4 tells the number of students in the whole group.

Each boy is 14 of the number of people in the group.

Together, the boys are 34 of the group.

Adults are 04 of the number of people in the group.

Students are 44 of the number of people in the group.

The items in a group do not have to be the same size to use a fraction.

• Suppose a group has 3 adults and 2 children.What fractions can you use to describe the numbers of adults and children in the group below?

Proper Fractions: Parts of Sets



34





Try These 1. What fraction of each group are oranges?

a)

________

b)

________

c)

________

d)

________

2. Why might some people say this picture shows 56 but

others say it shows 16?

3. What could the numerator of each fraction be?

a) j6 is a small part of the group of 6. ❚ could be ________.

b) j4 is most of the group of 4. ❚ could be ________.

c) j5 is around half of the group of 5. ❚ could be ________.




4. Sketch a group of circles and squares to represent each fraction given.Tell what other fraction the picture shows.

a) 45 are circles.

Picture:

Other fraction: ________

b) 06 are circles.

Picture:


c) 44 are circles.

Picture:


5. Draw a picture to show each fraction as part of a group. What do the pictures have in common?

24

25

26




6. Draw a picture to show that 45 of a group is twice as much

as 25 of that group.

7. Sketch a picture of stars and planets to fit the rules below. Name the fraction of the number of shapes that are stars.

a) There are 8 shapes altogether.

b) There are more stars than planets.

c) There are almost all planets.

Fractions are useful when a group has lots of parts and you want to describe just some of those parts.

FYI




OPEN-ENDED

You will need• linking cubes• fraction pieces

Pathway 4

Ahmed drank 13 of his glass of juice.Lisa drank 35 of her glass of juice.Yoshi drank 68 of his glass of juice.Daniella drank 8

10 of her glass of juice.

• Draw a picture for each fraction.

• What is the same about all of your pictures?

• Make up at least 3 other sets of 4 fractions that have something in common.Tell what the fractions have in common.Draw pictures for each set of fractions.

Proper Fractions: Parts of Wholes



34



Leaps and Bounds Proper Fractions: Parts of Wholes, Pathway 4


GUIDEDPathway 4

Ian has cut the grass in 23 of the lawn.The numerator 2 tells how many lawn sections are cut.The denominator 3 tells how many equal lawn sections there are altogether.

• You can show 23 on a number line or as part of a container.

1

0 13

23

33

• How can you show 35 on a number line?

• How can you show 35 as the amount of juice in a pitcher?

Try These1. Show and label each fraction on the number line.

a) 34 10

b) 25 10

c) 13 10

Proper Fractions: Parts of Wholes



34


You will need• linking cubes• fraction pieces• coloured pencils


Leaps and BoundsProper Fractions: Parts of Wholes, Pathway 4


2. Write fractions to describe the shaded and the unshaded parts of each shape.

a)

shaded: ________

unshaded: ________

d)

shaded: ________

unshaded: ________

b)

shaded: ________

unshaded: ________

e)

shaded: ________

unshaded: ________

c)

shaded: ________

unshaded: ________

f)

shaded: ________

unshaded: ________

3. Why might one person say this picture shows 45 but

another say it shows 15?




4. Colour the picture to show each fraction.

a) 16

shaded c) 58

unshaded

b) 45

shaded d) 23

unshaded

5. Sketch a shape to show each fraction.

a) 23

c) 810

b) 26

d) 68


Leaps and BoundsProper Fractions: Parts of Wholes, Pathway 4


6. Sketch a shape to show each relationship.

a) 45 of a whole is twice as much as 25 of that same whole.

b) 68 of a whole is 3 times as much as 28 of that same whole.

7. Use a fraction to describe each situation. Sketch a shape to show each fraction.

a) The fraction is almost a whole.

c) The fraction is much less than one half.

b) The numerator is 4 less than the denominator.

d) The numerator is half the denominator.

We often use fractions to describe parts of wholes.It is helpful to have a mental picture of those fractions to understand how much the fraction represents.

FYI




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