NUMBER Fractions Chapter 5 - misterashmore.commisterashmore.com/documents/Mathterms/Chapter5.pdf · Which recipe uses more chocolate? Vanessa’s strategy: ... Ahmed counted 10 slices

Chapter

Big IdeaUnderstanding improper fractions and mixed numbers can help me solve problems.

Learning GoalsI can relate improper fractions to mixed numbers.

Essential QuestionHow can fractions help me understand the world around me?

Important Wordsdenominatorimproper fractionmixed numbernumerator

NUMBER

5Fractions

CHAPTER 5: Fractions104

Merry Mixing

Draw, build, and write to represent mixed numbers and to find equivalent numbers. Compare and order numbers that are given as pictures, constructions, and numbers.

Example:

Order the following numbers from smallest to largest:1 , 1 , 1 , 1 .

Samina’s strategy:I drew a number line from 1 to 2 and marked it with twe lve sections.

Thirds are four sections each. For I counted eight sections because that is four twice.

Quarters are three sections. For I counted three sections. For I counted nine sections.

Nancy’s strategy:I drew each fraction in a circle and then ordered them from smal l est to biggest.

Odessa’s strategy:

I built each fraction using fraction strips and then ordered them from smal l est to largest.

Patience’s strategy:

I wrote each fraction as an equivalent fraction out of twe lve and then ordered them from smal l est to largest.

The order is: 1 , 1 , 1 , 1 .

14

34

512

23

23

14

34

1 = 1 1 = 1 1 = 1 1 = 1

14

512

23

34

312

512

812

912

14

512

23

34

141 5

12 1 231 3

41

512 1231

512 1 2

31 341

1 2121

141

141

341

CHAPTER 5: Fractions 105

Merry Mixing (continued)

11. Study the pictures below. Write a mixed number for each picture.

a.

b.

c.

d.

12. Use pattern blocks to build each fraction.

a. b.

c. 3 d. 2

13. Draw a picture to represent each fraction.

a. b.

c. 3 d. 4

14. Write two mixed numbers equivalent to each of the following.

a. b.

c. 3 d. 4

A mixed number is a number with a fraction part and a

whole number part.

12

26

45

710

15

24


Merry Mixing (continued)

7. Describe the strategies you used to compare mixed numbers.

8. How do you use mixed numbers in real life?

I can relate improper fractions to mixed numbers.

15. Write a statement using the less than symbol (<), equal to symbol (=), or greater than symbol (>) to compare the two numbers.

a.

b. ,

c. 2 ? 1 d. 4 ? 4

16. Order each set of numbers from the least to the greatest using the strategy of your choice.

a. b.

c. 4 , 4 , 4 , 4

14

712

15

35

25

45

34

18

14

78d. 3 , 3 , 3 , 3

39

36

?

?

, , , , , ,


Nice Numbers

Write, draw, or build mixed numbers. Solve problems from contexts including food, time, sports, and crafts.

Example:

Joseph went to a birthday party and saw these pizzas.

How many pizzas are there?

There is one whole pizza. There is one half of a pizza. That makes 1 pizzas.

How much of a pizza have the guests eaten so far?

If there were two pizzas to begin with, there is one half of a pizza missing. That means they ate a pizza.

11. Tanner worked in the yard for 3 hours on Saturday and 3 hours on Sunday.

a. Build a model or draw a picture to show each time.

b. On which day did Tanner work longer? How can you tell?

12. A football quarterback played 19 quarters last season. One of the wide receivers played 25 quarters last season.

a. How many games did the quarterback play? Record this amount as a mixed number.

b. How many games did the wide receiver play? Record this amount as a mixed number.

c. Who played more games last season?

13. Susie made twenty muffins using several 8-muffin trays.

a. Draw to show how many full trays of muffins she made.

b. Record the number of trays of muffins Susie made as a mixed number.

12

12

13

46


Nice Numbers (continued)

14. Mr. Sagan read to his class for of an hour each day.

a. Build a model or draw a picture to show for how many full hours he read in 11 days.

b. Record the number of hours for which Mr. Sagan read as a mixed number.

15. Leah filled her glass with milk three times, and then only drank half of the third glass.

a. Write the number of glasses of milk that she drank as a mixed number.

b. Write the number of glasses of milk that Leah drank as a mixed number with a different denominator.

16. Nigel, the cat, eats of a can of cat food for breakfast and of a can again at supper.

a. How much cat food will Nigel eat in one day?

b. How much cat food will Nigel eat in one week? Record this amount as a mixed number.

17. The time it took Penny to drive from Hinton to Edmonton is shown below.

a. Express how long it took Penny to drive home as a time in minutes.

b. Use a mixed number to express in hours how long it took Penny to drive home.

c. Use as a decimal to express in hours how long it took Penny to drive home.

14

13

13

60

30

45 15

60

30

45 15

60

30

45 15

The denominator is the number of parts in a fraction,

the bottom number.


Nice Numbers (continued)

18. Victor is making beaded belts as gifts for his friends. Each of the belts uses 120 beads. How many belts can Victor make with a package of 500 beads? Record this amount as a mixed number.

19. Wesley collected sand dollars on the beach. In one week he collected 3 dozen sand dollars. How many sand dollars did Wesley collect?

10. Zavier, Yuvraj, and Zain run together on the cross country team. At one practice, the boys ran for 40 minutes. In that time, Zavier ran 7 laps, Yuvraj ran 7 laps, and Zain ran 7 laps. Put the boys in order according to the distance they ran, from least to greatest.

11. Use the clues below to solve the riddle.

• I am a mixed number between 2 and 3.

• I am larger than 2 but smaller than 2 .

• I have an even denominator.

a. What could the mystery fraction be?

b. Could there be more than one answer?

12. Write your own fraction riddle about a mixed number. Exchange riddles with a classmate and try to solve each others’ riddles.

13. How did drawing or building to show mixed numbers help you solve these problems?


47

13

12

23

78

49


Properly Improper

Draw, build, and write to represent improper fractions and to find equivalent numbers. Compare and order fractions that are given as pictures, constructions, and numbers.

Example:

Show using the strategy of your choice.

Jinee’s strategy:I drew circles with each one in four pieces. Then I coloured in 9 sections to represent .

Rachel’s strategy:I built this number using interlocking cubes. I used 9 cubes and arranged them into groups of four.

Sadie’s strategy:I showed on a number line. I made tic-marks and then labe led them with quarters. Then I put a dot at .

94

94

11. Study the pictures below. Write an improper fraction for each picture.

a.

b.

c.

d.

94

94

An improper fraction is a fraction that has a top number that is bigger

than the bottom number.

04

124

34

114

104

94

84

64

54

44

74

24

14

< >


Properly Improper (continued)

12. Use pattern blocks to build each fraction.

a.

b.

c.

d.

13. Draw a picture to represent each fraction.

a.

b.

c.

d.

14. Write two improper fractions equivalent to each of the following.

a.

b.

c.

d.

32

136

226

184

156

247


Properly Improper (continued)


a.

b.

c.

d.

16. Order each set of numbers from smallest to largest using the strategy of your choice.

a. , , ,

b. , , ,

c. , , ,

7. How do you know what the denominator will be when you are given a picture of a fraction?

8. Some people call improper fractions top-heavy fractions. Explain why this name makes sense.


83

94

63

95

73

92

43

96

198

52

1210

65

278

3012

228

309

?

?

?

?


Fraction Fun

2812

73

64

73

1812

64

73

64

73

64

Write, draw, or build the improper fractions to solve problems. Problems come from contexts including music, measurements, food, time, sports, and crafts.

Example:

Two different recipes use cups or cups of chocolate chips. Which recipe uses more chocolate?

Vanessa’s strategy:I made an equivalent fraction with a denominator of 12 for each fraction. = by multiplying both the denominator and numerator by 4. = by multiplying both the denominator and numerator by 3.

Taryn’s strategy:I drew each fraction using rectang les.

Whitney’s strategy:I built each fraction using fraction circles.

Yara’s strategy:I divided each fraction.7 3 = more than two6 4 = less than two

73

64

2812

1812


Fraction Fun (continued)

11. Mrs. Winter bought a half-dozen cinnamon buns, eight onion buns, one dozen whole wheat buns, and a half-dozen dinner buns.

a. Draw to find the number of buns she bought.

b. Write the number of dozen of buns she bought as an improper fraction with a denominator of 12.

c. Explain what the denominator and numerator represent in this fraction.

d. Write this fraction with a different denominator.

12. David has completed laps of a 10-lap run. Blake has completed laps. Who has run further? How can you tell?

13. Moe spent of an hour cleaning the inside of his dad’s car. He spent a total of hours cleaning the entire car.

a. Build a model or draw a picture to show how long Moe spent cleaning the inside of the car.

b. Build a model or draw a picture to show how long Moe spent cleaning the entire car.

c. Write, as an improper fraction of an hour, the amount of time Moe spent cleaning the outside of the car.

d. Write, in minutes, the amount of time Moe spent cleaning the outside of the car.

e. Write, in decimals of an hour, the amount of time Moe spent cleaning the outside of the car.

358

357

34

84

The numerator is the top number in a fraction. It is the

number of parts of the whole.



14. Joel had to read a story that was pages long. He read pages before dinner. How many pages did he need to read after supper? Record this amount as an improper fraction.

15. Ahmed counted 10 slices of bread in half a loaf.

a. How many slices are in a whole loaf?

b. What fraction of a loaf is one sandwich?

c. How many loaves did Ahmed use to make 45 sandwiches? Record this amount as an improper fraction.

16. Uriah is sewing a pair of shorts. The pattern calls for yards of fabric. Uriah has yards of fabric. Does Uriah have enough fabric to make the shorts?

17. Elias cut 2.5 metres of string into 10-centimetre lengths for a craft at his birthday party.

a. Write the length of string Elias started with as an improper fraction with a denominator of 10.

b. Explain what the denominator and numerator represent in this fraction.

c. What does the fraction you wrote in part a. represent?

d. Elias decided to cut the string into 5 cm lengths instead of 10 cm lengths. Explain what denominator might make more sense in this situation.

234

84

32

85


18. Cael plays hockey. The number of periods he played in a tournament is shown by the diagram below.

Game 1 Game 2 Game 3 Game 4

1 2 3 1 2 3 1 2 3 1 2 3

a. Draw or build to show this number in another way.

b. Express the total number of games Cael played as an improper fraction.

c. Explain what the numerator and the denominator represent in this fraction.

19. Fletcher, Gabriel, Hamza, and Ian competed in a Trumpet-a-thon. Fletcher played for hours, Gabriel played for hours, Hamza played for hours, and Ian played for hours. Put the boys in order from least to greatest according to the time they played.

10. Use the clues below to solve the riddle. • I am an improper fraction.

• I am larger than but smaller than .

• I have an even denominator.

a. What could the mystery fraction be?

b. Could there be more than one answer?

247


73

4110

368

256

439

11. Write your own improper fraction riddle about an improper fraction. Exchange riddles with a classmate and try to solve each other’s riddle.

12. What strategies did you use to solve problems with improper fractions?



Real Relations

Draw, build, and write to represent improper fractions and mixed numbers. Compare and order numbers that are given as pictures, constructions, improper fractions, and mixed numbers.

Example:

Which should you choose, 1 of a pie or of a pie?

Cyndy’s strategy:I converted to a mixed number by dividing.5 3 = 1 R 2 = 11 is one quarter less than 2. 1 is one third less than 2. is bigger than because it is a whole divided into fewer pieces. 1 pie is bigger. I should choose the 1 pie.

Zainab’s strategy:I drew the fractions.

I can see that 1 1 .

Addison’s strategy:I built the fractions using fraction circles.

I can see that 1 1 .

53

34

53

34

53

23

23

14

13

34

34

23

34

23

34

11. Use ten frames to build each number.

a. b.

c. 2 d. 4 25510


Real Relations (continued)

12. Study the pictures below. Write a mixed number and an improper fraction for each picture.

a.

b.

c.

d.

13. Draw a picture to represent each number.

a.

b.

c. 1

d. 4

14. Write a mixed number equivalent to each of the following improper fractions.

a.

b.

c.

d.

112

259

46

28


Real Relations (continued)

15. Write an improper fraction equivalent to each of the following mixed numbers.

a.

b.

c. 3

d. 4


a. 2 ?

b. ? 1

c. 1 ?

d. 2 ?

17. Order each set of numbers from smallest to largest using the strategy of your choice.

a. , 2 , , 1

b. 3 , , 1 ,

c. , 2 , , 2

18. Explain the strategies you used to write improper fractions as mixed numbers.

19. Explain the strategies you used to write mixed numbers as improper fractions.

10. When might you use mixed numbers instead of improper fractions?

11. When might you use improper fractions instead of mixed numbers?


12

58

83

94

1712

512

23

83

85

35

175

45

14

113

56

2912

73

12

94

18

16

27


Clear Comparisons

11. How old are you?

a. Write your age as a mixed number.

b. Write your age as an improper fraction.

c. Explain what the numerator represents in each number.

d. Explain what the denominator represents.

12. Raiden collected 33 eggs.

a. Draw to show the number of dozens of eggs.

b. Write the number of eggs as an improper fraction with a denominator of a dozen.

c. Explain what the numerator means.

d. Write the number of eggs as a mixed number with a denominator of a dozen.

e. Explain what the denominator means.

1

Write, draw, or build improper fractions and mixed numbers to solve problems. Explain what the numerators and denominators mean in each situation.

Example:

Andrei is 11 years and two months old. Write his age as a mixed number and as an improper fraction. I know that there are 12 months in one year, so that will be my denominator. He is 11 whole years and 2 out of 12 months.Andrei is 11 years old.

11 years is 11 x 12 months = 132 months. Andrei is 132 + 2 = 134 months old.Andrei is years old.

What do the numerator and denominator mean in this improper fraction?The numerator is 134. 134 is Andrei’s age in months.The denominator is 12. Twelve is the number of months in one year.

212

13412


Clear Comparisons (continued)

13. Your mom is making cookies and needs 3 cups of flour. She only has a cup measuring cup.

a. Build a model or draw a picture to show how many half cups of flour she needs for this recipe.

b. Express 3 cups as an improper fraction.

c. Explain what the numerator and denominator represent in the fraction.

d. How are the number of half cups and the improper fraction related?

14. Sawyer’s swimming lessons take an hour and a half.

a. Write this number as a mixed number with a denominator of 2, and explain what the whole number, numerator and denominator mean.

b. Write this number as an improper fraction with a denominator of 2, and explain what the numerator and denominator mean.

c. Write this number as an improper fraction with a denominator of 60, and explain what the numerator and denominator mean.

d. Explain which representation Sawyer should use to tell his parents how long his swimming lessons are.

15. Jackson is knitting a scarf and has completed the squares shown below.

a. Write the number of squares of the scarf that Jackson has knit as an improper fraction.

b. Write the number of squares of the scarf that Jackson has knit as a mixed number.

c. Explain the strategy you used to write the number in each form.

16. Kai and Lorenzo each play in the school band. Kai practised for 3 hours over the weekend. Lorenzo practised for hours. Compare the length of time each boy practised.1

12

12

12

26

92


Clear Comparisons (continued)

19. Write your own problem involving mixed numbers and improper fractions. Exchange problems with a classmate and try to solve each other’s problem.

10. Explain which strategy you find most useful when comparing fractions in different forms.


17. Malik has $10 to buy fabric to make a flag. The fabric costs $4 for each metre.

a. How many metres, expressed as a mixed number, can Malik buy?

b. How many metres, expressed as an improper fraction, can Malik buy?

c. Explain what each number tells you in this situation.

18. Nicolas has competed in five pie-eating contests. His results are shown in the table below.

a. Order the contests from the one in which Nicolas ate the fewest pies to the one in which he ate the most pies.

b. Describe the strategies you used to order the numbers.

Contest Number of pies eaten

Stampede 2

Capital Ex

Westerner Days

Highland Games 3

Blueberry Festival

59

298

157

510

2812

Documents

NUMBER Fractions Chapter 5 - misterashmore.commisterashmore.com/documents/Mathterms/Chapter5.pdf · Which recipe uses more chocolate? Vanessa’s strategy: ... Ahmed counted 10 slices