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Fractions Computations and Operations

- Hands-On Experiences in support of Student Success

Addition of Fractions Fraction Factory Pattern

Blocks

- We can join these fractions and rename the region

using a common fraction piece. - Therefore,

Add the Following Using Fraction Factory Show

Your Work!

We know that 2 - 1/8 pieces fit into a one fourth

piece, therefore

(No Transcript)

We must ask students What do we know about the

sum of these two fractions? Will the sum be

greater or less than 1? 5/6 is almost one whole

it is 1/6 shy of one whole 1/3 is greater than

1/6 therefore the sum must be greater than 1! Try

this problem with pattern blocks!

What does the common manipulative piece in this

example represent?

What sorts of questions should we be asking our

students here?

What about the similarities between the two

pieces?

How many 1/8 pieces make up the ½ piece?

Repeat the following examples using Pattern Blocks

Subtraction of Fractions Fraction Factory

Pattern Blocks

- When we subtract, we remove a portion of

something and name what we have left. - - We need to remove 1/3 of the whole from ½ of

the whole and name the portion (difference)

that remains.

Subtract Using Fraction Factory Pattern Blocks

- Complete the following using both FF PB for

each

What would the whole look like using Pattern

Blocks?

Use the hexagon as the whole

Use patterns blocks to solve and show the

solution

Multiplication of Fractions Fraction Factory

Pattern Blocks

- When we multiply, we can think of the

multiplication sign as making groups of an

amount. - 3 x 4, we can think of 3 groups of 4.
- - we can think of 1/3 of ½
- What do we really know about the product here? Do

students know what this means? - Will 1/3 of ½ be less than 1? Less than ½? Less

than 1/3?

Since I need to find 1/3 of ½, I showed ½ of the

whole, and then partitioned the ½ into thirds.

One of these partitioned parts of ½ is 1/3 of ½

which represents 1/6 of the whole. Therefore 1/3

x 1/2 1/6 (in relation to the whole)

- Multiply the following using Fraction Factory

Pattern Blocks

What does ¾ of the half look like? What is that

in relation to our indicated whole?

Multiplication of Fractions Fraction Factory

Pattern Blocks

Seeing Division of Fractions Fraction Factory

Pattern Blocks

- When we divide, we ask How many groups of?
- 12/3 How many groups of three are in 12?
- Same with fractions How many groups of ¼ are

in ½?

Divide Using Fraction Factory Pattern Blocks

1 half piece goes into 2/3, plus 1/6 of the

whole. This 1/6 of the whole is actually 1/3 of

the dividend ½. Therefore, 2/3 divided by ½ 1

1/3 or 4/3.

Divide Using Fraction Factory Pattern Blocks

Problem Solving

Teaching Through Problem Solving

- Mrs. Get Fit teaches Math and Phys-ed. To

incorporate Math into the Phys-ed class, she

divided the class into eight groups. There are

three students in each group. The first person in

the group runs ¼ of a lap of the track, the

second person runs 1/6 of the track, and the

third person runs 1/3 of a lap of the track. How

many laps of the track are run in total by all

eight teams combined?

Teaching Through Problem Solving

- Jeff acquired a recipe from his grandmother which

makes 5 dozen cookies. The recipe requires 2 ½

cups of oatmeal, 2 cups of chocolate chips, 2

cups of flour, 2 eggs, 1 cup of butter, 5 ml of

baking powder, and 5 ml of salt. - A) Adjust the recipe to make 2 dozen cookies.
- B) Adjust the recipe to make 12 dozen cookies.

Teaching Through Problem Solving

- Bills Snow Plow can plow the snow off the

schools parking lot in 4 hours. Janes plowing

company can plow the same parking lot in just 3

hours. How long would it take Bill and Jane to

plow the schools parking lot together?

Think of the math content involved with this

problem Think of some Before activities that

could be used. What would the debrief look/sound

like in the classroom after the task was complete?

- Chad made a snack by combining 1/3 of a bowl of

granola with ¼ of a bowl of chopped banana and ½

of a bowl of yoghurt. Did one bowl hold all of

the ingredients at one time? Explain. - Neptune completes 1 ½ turns about its axis each

day. How many turns does it complete in 1 week? - About 3/4 of the students on the track team are

girls. About ¾ of these girls are in grade 8.

What fraction of the students on the track team

are grade 8 girls?

- Mara spent 3/5 of her vacation in British

Columbia. While in that province, she spent ½ of

her time in Vancouver. What fraction of her

vacation did Michaela spend in Vancouver? If her

vacation lasted 20 days, how many days did she

spend in Vancouver? - Jackie used to be on the phone 3 ½ times as much

as her brother. Her parents threatened to take

away the phone, so she cut down to 2/5 of the

time she used to be on the phone. How many times

as much as her brother is Jackie now on the phone?

- A A student is sorting into stacks a room full

of food donated by the school for the local food

bank. He sorted of it before lunch and then

sorted of the remainder before school ended.

What part (fraction) of all the food will be left

for him to sort after school? - B

1 3

3 4

- Lets explore our current resources
- Grade 8 textbook pg. 57 91
- Eating Candies by Fractions
- C Use manipulatives to solve this problem
- Mark ate half of the candies in a bag. Leila ate

- of what was left. Now there are 11 candies in

the bag. How many were in the bag at the start?