Math Unit 6

Adding and SubtractingFractions

1.1 Square Numbers and Area Models

What You’ll Learn...• To write fractions in lowest terms• To show why a number cannot be divided by 0• To add and subtract fractions with like

denominators• To add and subtract fractions with unlike

denominators• To add and subtract fractions with mixed

numbers• To solve fraction problems• To compare and order positive fractions

Why is it important?• Fractions have been apart of our lives for a long time. In ancient times,

Sumerians, Babylonians, Romans, Egyptians, Greeks and Chinese all used fractions.

• The Eye of Horus was used by Egyptians to represent fractions. It was a powerful symbol that they believed protected against evil. According to an old myth, Horus’s eye was torn out, broken into pieces and then put back together.

• You can use fractions when you read gauges, shop, measurements, and work with percents and decimals, and in sports, recipes and business.

Unit 6: Fractions

+ I understand what this is and can do it very well

√ I understand and can do most of this

− I have some trouble with this

× I have a big problem with this

2

Pre-quiz

check in

Lesson Key WordsPractice Question

s/ Projects

HW CheckPost-quiz

check in

6.1 Fractions as patterns whole vs. part Representing fractions

WholeEqualparts

5-6

6.2 Adding with LIKE Denominators

Using shapes Word problems

Like denominatorCommon denominator

6.3 Subtracting with LIKE denominators

Using shapes Word problems Comparing equivalent

fractions

ThirdsFourthsFifthsHalvesEquivalent fractions

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6.4 Add and Subtract UNLIKE denominators

Review Mixed fractions Reducing fractions Adding and subtracting

mixed numbers Improper Fractions

Mixed fractionsMultiplesFactorsGCFGCDLCMMixed numbersImproper fractions

21-22Bonus 22

25

Chapter Review Activity choices x3 Unit 6

Quiz

Unit 6: Fractions

6.1 Add Fractions with Like Denominators

How can we represent fractions using models?

Fractions name ___________ parts of a whole. The pie is cut into four equal parts. 3 parts are shaded out of 4.

34 of the pie is shaded.

--------------------------------------------------------------------Parts & WholesExplore:

1. Name the following fractions:

2.Use a ruler to divide each box into equal parts:

a. 3 parts equal b. 10 parts equal

3. Using a ruler, find the fraction for each of the shaded boxes:

The numerator (3) tells you how many parts are counted.

The denominator (4) tells you how many parts are in the whole.

34

3

a. ____ b. ____ c. ____ d. ____

Unit 6: Fractions

a. ______________ is shaded b. ______________ is shaded

4. Using a ruler, complete the following images to make them whole:

a. b. c.

5. You have 45 of a pie.

a. What does the bottom of the fraction tell you?

b. What does the top of the fraction tell you?

Due Date: ___________

14

12

45

Which of the following shows 14 . Explain how you know.

4

Unit 6: Fractions

Show You Know:

1. Fill in the blanks.

a. _________ of the figures are pentagons_________ of the figures are shaded

b. _________ of the figures are pentagons_________ of the figures are shaded

2. Fill in the blanks.

a. 47 of the figures are ______________

b. 27 of the figures are ______________

c. 17 of the figures are ______________

d. 57 of the figures are ______________

3. Shade the following shapes with the appropriate fraction:

Homework Assignment TIPS & TRICKS: Visualize the problem (*sketch it out/ picture it in your head

before you do the work) Use the Guess & Check method (make a guess about the

answer; do the work; use the check back “mental math” to eliminate mistakes.

Show your work. Use the Internet, YouTube, your teacher, your friends, your

parents as resources when you get stuck. Use the textbook to T.I.F. (take it further).

5

Unit 6: Fractions

4. Kyra’s hockey team wins 6 games, loses 4 games and ties one game.What fraction of the games did the team…

a. win _________ b. lose _________ c. tie _________

5. A box contains 2 Justin Bieber posters, 3 Marianas Trench posters and 4 1D posters:What fraction of the posters do you HAVE to have?

a. Bieber _______ b. Trench ________ c. 1D ________

6.2 Add Fractions with like Denominators

Homework Reflection:

Which parts of the homework did you find pretty straightforward?

Which parts challenged you?

If you had difficulty with a certain question, what strategies did you use to solve the problem?

6

Unit 6: Fractions

Adding Fractions using shapes

1. Write the fraction for circles A and B. Imagine moving the shaded pieces from pies A and B to pie C. Show how much of pie C would be filled then write a fraction for pie C.

2. Shade the fractions for cylinders A and B. Imagine pouring the liquid from cups A and B into C. Shade the amount of liquid that would be in C then write the fraction.

3. Add.

a. 35 + 1

5 =

b. 24 + 1

4 =

c.

37 + 2

7 =

d. 58 + 2

8 =

4. Write an addition statement for each of the fraction strips. Estimate the answer then add.

a.Adding fractions using work problems

5. Write two addition statements of your own. Draw a shape and shade it to represent your equation:

+ =

________ ________ ________

7

15

25 ________

+ =

+ =

Unit 6: Fractions

a.

b.

6. Emily has one bag of beads. She is going to make three different necklaces. For the first necklace, she needs 3

8 of a bag of beads. For the second she

needs 18 of the beads. For a third, she needs 5

8a. What fraction of a bag does she need in total?

b. Does she have enough?

7. Each performance in Allie’s dance recital was 14 h long. There were three

performances. How long did Allie’s recital take? Include a diagram to explain your answer.

5.4

8

Unit 6: Fractions

6.3 Subtract Fractions with like Denominators

Investigate (textbook p.217) How can we subtract fractions?

Explore:

1. Show how much pie would be left if you took away the amount shown. Then complete the fraction statement.

2. Subtract.

a. 23 - 1

3 =

b. 35 - 1

5 =

c. 67 - 3

7 =

d. 58 - 2

8 =

3. Calculate.9

Madi is participating in a marathon to raise money for charity. She has 2

3 of the way to go in the 3km race After she completes

another 13 marathon, how much will be left to go?

- =

Unit 6: Fractions

a. 27 + 1

7 + 37 =

b. 411 + 5

11 - 211 =

c. 1018 - 7

18 + 518 =

Comparing Equivalent Fractions4. Which fraction is greater:

5. Circle the largest fraction:28 1

8 88

6. Circle the largest fraction.28 1

2 312

7. Which is larger: 58+14 or 5

8 ? How do you know ______________________

8. Does 58+14 = 5

8 + 514 ? Explain. ___________________________________

9. Fraction A and B have the same numerators (tops) but different denominators (bottom). How can you tell which fraction is greater?

Due Date: ___________

Show You Know:

10

Unit 6: Fractions

Create a card game on index cards that helps people learn how to add and subtract fractions. Some possibilities include:

Go Fish. Question cards (to go with a

board game) Bingo Fraction pies or circles Dominoes

Check out the following websites for fun games. Record your scores for each game played:

“Fruit Shoot Fractions Addition”: http://goo.gl/zmQO2 “Race Car Fraction Addition”: http://goo.gl/EcWtd

Score Game

6.4 Add & Subtract Fractions with unlike Denominators

Investigate (textbook p.231) How can we add and subtract unlike fractions?

Write a definition in your own words for:

Common denominator: ______________________________________________________

11

Unit 6: Fractions

Multiple: ________________________________________________________________

Mixed Numbers: __________________________________________________________

Improper fractions: ________________________________________________________

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How do you make equivalent fractions? Work with a partner to find the solution:

13 = ❑6 = ❑9 = — = —

25 = ❑

10 = ❑15

Unit 6: Fractions

Time for a Story about a Story…

Early one Monday morning, Hammurabi was out surveying the canal work he had recently ordered. His vision for the world’s largest garden was about to get under way. At last, he would be more legendary than that egomaniac Gilgamesh!

He looked at the workers, quietly slaving away. He was interrupted by the squeaky voice of Hashib, the town mathematician. “Your Grace,” he squeaked. Hammurabi ignored him. “Your eminence?” he tried. Nothing. “Ruler of the Babylonian Empire, of All Assyrians; Giver of Laws, King of the Amorites…”“Ha ha ha” Hammurabi grabbed his enormous belly, “Hashib, you flatter me. King Humm, Most Esteemed Ruler of the Fertile Crescent and All That is Beyond will do… Now tell me, what is this disturbance about?”

“Oh, King Humm, Most Esteemed Ruler of the Fertile Crescent and All That is Beyond, I was looking over your accounts, and looking over the blue prints of the canals, and looking over the number of workers and… well…” Hammurabi was growing impatient. “Creating algorithms that quantified the percentage of human slavery to the source of available funds…”

“Speak Assyrian man. I can hardly understand a word you are saying.”

“You have 60 workers, and 40 canals to dig. Each slave works a 14 hour day… The Babylonians divide the days into 24 hours, each hour into 60 minutes, each minute into 60 seconds… Don’t you see what will happen?”

Hammurabi gaped. “I am making a new law Hashib.”

Hashib looked up at the king and smiled. “I thought you would understand!”

“The law,” declared Hammurabi, “shall be the obliteration of MATH.”

-----------------------------The Babylonian system of numbers was based on 60 rather than 10, like today. Babylonian

fractions were expressed as numbers out of 60: 260

360

460

etc. Today, we still use Babylonian

math for things like time. Cool Huh?

ExploreSierra and Olivia ate three and three quarters pies together.

13¾ of the pie

Unit 6: Fractions

1. Write how many whole pies are shaded.

a. ___________ whole pies b. ___________ whole pies

2. Write the fraction as

a. _________________ b. _________

3. Shade the amount of pie in bold.

a. 2 23

b. 1 34

c. 3 14

4. Sketch:a. 3 2

3

14

3 whole pies

Unit 6: Fractions

b. 2 14

c. 1 15

Equivalent Fractions

Explore.

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Reflection:

Which parts of the homework did you find pretty straightforward?

Which parts do you find challenging?

If you had difficulty with a certain question what strategies did you use to solve the problem?

Two fractions are equivalent if they represent the same amount.

Unit 6: Fractions

1. Compare the fractions by shading to see which is more. Write > (more than) and < (less than) or = (equal to).

a.

b.

c.

d.

2. List the fractions from Question 1.

a. ❑❑ b. ❑

❑ c. ❑❑ d. ❑

❑

3. Group the squares into larger blocks to make them equivalent.

a. 610

=35 b. 4

6=❑

3 c. 106

=❑6

4. Write three equivalent fractions for the amount shaded.__________ ___________ __________

5. Draw a line to put the pies into…a. 4 equal partsb. 6 equal partsc. 8 equal parts

6. Write the fraction for a, c and c in Questions 5.

7. Make an equivalent fraction by cutting each of the shaded pieces into the same number of equal parts. The rewrite the fraction.

a.

16

36=1

2

Unit 6: Fractions

b.

c.

d.

8. Subdivide the line into ten equal parts using a ruler and then mark the fractions.

- 310

710

910

12

25

9. 56 of a pizza are covered with peperoni. 1

2 of a

pizza are covered with mushrooms. Draw a picture of the pizza to complete the order.How many toppings are there in total: _______

Adding Fractions with Different Denominators

17

23= 4

❑

23= 6

❑

25= 8

❑

Unit 6: Fractions

Explore:

1. Find the LCD for each pair of fractions. Then show what numbers you would multiply the numerator and denominator of each fraction by in order to add the fractions.

a. 3 x 13 + 1

3 x 2 LCD: _6_

b. ___ x 34 + 1

8 x ___ LCD: ___

c. ___ x 120 + 1

5 x ___ LCD: ___

d. ___ x 34 + 2

3 x ___ LCD: ___

2. Add or subtract the fractions by changing them to equivalent fractions with denominators equal to the LCD of the fractions.

a. 25 + 1

4 ==

b. 415 + 2

3 ==

c. 23 - 1

8 ==

d. 23 - 1

12 ==

18

Step 1: Find the lowest common multiple (LCM) of the denominators. 13

+ 25

Multiples of 3: 0, 3, 6, 9, 12, 15, 18…

Multiple of 5: 0, 5, 10, 15, 20…

Step 2: Create equivalent fractions with that denominator:

13 + 2

5 = 5 x 13 + 2

5 x 3 = 515 + 6

15 = 1115

The lowest common multiple of the denominator is called lowest common denominator (LCD) of the fraction.

Unit 6: Fractions

Reducing Fractions:

Explore:

1. Find the GCF of the numerator and denominator. Is the fraction in lowest terms? Write yes or no.

a. 36GCF: __3__ __yes__

b. 25GCF: ____ ____

c. 45GCF: ____ ____

d. 510GCF: ____ ____

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A fraction is reduced to lowest terms when the numerator and denominator cannot by divided by the same number anymore. The GCF of its numerator and denominator is the number 1.

68 is not in lowest terms because the GCF of 6 and 8 is 2.

34 is in lowest terms because the GCF of 3 and 4 is 1.

Reducing a Fraction to Lowest terms:

Step 1: Find the GCF of the numerator and denominator.

Step 2: Divide both the numerator and denominator by the GCF.-------------------------------------

What is a way that you can uncomplicated the above explanation? How would YOU explain to find the lowest term?

____________________________________________________________________________________________________________________________________________________________________________________________________________

Unit 6: Fractions

2. Reduce the fractions below by dividing the numerator and the denominator by their GCF.

a. 210 ÷ 2 = 1

5

b. 26 ÷ __ = __

c. 28 ÷ __ = __

d. 69 ÷ __ = __

e. 315 ÷ __ = __

f. 412 ÷ __ = __

g. 2025 ÷ __ = __

h. 212 ÷ __ = __

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Unit 6: Fractions

Due Date: ___________

Show You Know:

1. Write the fractions in order from least to greatest.a. 1

2 25 3

10

b. 13 5

6 12

c. 12

58 3

4

2. Equivalent fractions are said to be in the same family. Write two fractions in the same family as the fractions below.

3. A recipe of soup calls for 13 of a can of tomatoes.

A recipe of spaghetti sauce calls for 56 of a can.

Which recipe uses more tomatoes? ________

4. Use the table to answer the following questions.a. What fraction of the walls were painted

green: _________b. What colour was used to paint one fifth of

the wall: ______c. What colour was used to paint one half of

the wall: _______

5. Create a fraction word problem of your own. Solve the problem with graphics.

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2/44/8

1/2

1/3

3/4

2/5

Colour Number of walls painted

White 10Yellow 5Blue 4Green 1

Unit 6: Fractions

BONUS: $10 Clement Bucks.

The Ancient Egyptians thought the fractions in the Eye of Horus added up to 1. Were they correct? Show your work.

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Reflection:Which parts of the homework did you find pretty straightforward?

Which parts do you find challenging?

If you had difficulty with a certain question, what strategies did you use to solve the problem?

Unit 6: Fractions

Adding and Subtracting Improper Fractions:

Concerting from Improper to Mixed:

1. Change these improper fractions to mixed numbers.

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After a party, Mrs. Clement’s class had 2 ½ pizzas left over.

Ms. Mo’s class had 3 13 pizzas left over.

How can you find out how many slices are left over using addition?

Hint: Draw the pizza’s…

Unit 6: Fractions

2. Change these mixed fractions to improper fractions.

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Unit 6: Fractions

Adding Improper Fractions1. Add or subtract.

a. 215 + 22

5 =

b. 336 + 21

6 =

c. 578 - 32

8 =

d. 7 915 - 4 4

15 =

2. Add or subtract by changing the fraction to equivalent fractions.

a. 212 x3 + 21

3 x2 =

= 236 + 12

6

= 356

b. 334 x3 + 11

3 x4 =

= 3❑12 + 1❑

12

= 4❑12

c. 523 x__ + 23

5 x__ =

= +

=

d. 227 x__ + 41

2 x__ =

= +

=

3. Change the improper fractions to mixed fractions.

a. 76 = 11

6

b. 115 = ❑❑

c. 137 = ❑❑

d. 74 = ❑❑

25

Math Unit 6

4. Haleigh walked 137km in the first hour of the Times Colonist Run

and 113km in the second hour. How many km did she walk?

5. Kyra ate 1 15 of the snack and Diara ate 1 1

3. What fraction of the snack did they eat together?

26

Math Unit 6

To Recap: Factor

a number that divides evenly (factors of 6 are 1, 2, 3, 6) factor rainbows are a useful visual tool for remembering factor pairs

Multiples the sequence numbers makes a patter (Ex 2, 4, 6, 8, 10…)

LCM Lowest Common Multiple refers to the lowest multiple that a pair of

numbers have in common (Ex. 2 and 3 LCM: 6)GCF

Greatest Common Factor is the highest factor that goes into both pairs. 96 and 60 both have factors of 1, 2, 3, 4, 12. Twelve is the GREATEST one in common.

Common Fractions Have common denominators (bottom) Add and subtract using the numerator (top)

Mixed Fractions Have like and unlike denominators Add and subtract once the denominators are common Common denominators are found using the lowest terms (ex ½ and

¼ ...4 is lowest common denominator)

An improper fraction Has a numerator greater than the denominator (ex 9/8) To add or subtract, create a mixed fraction and find common

denomenator

Buzz Words for Math

Word Picture Example Problem

27

Math Unit 6

Common denominator

Common factor

Denominator

Divisible

Equivalent fraction

Estimate

Fifths

Fourths

Fraction

Fraction strips

GCD

28

Math Unit 6

GCF

Halves

Improper fraction

LCM

Lowest terms

Mixed number

Multiple

Numerator

Quarters

Remainder

Simplest form

29

Math Unit 6

Thirds

Unit fraction

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