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## Fractions: Computations and Operations

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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 ... – PowerPoint PPT presentation

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Title: Fractions: Computations and Operations

1
Fractions Computations and Operations
• Hands-On Experiences in support of Student Success

2
Addition of Fractions Fraction Factory Pattern
Blocks
• We can join these fractions and rename the region
using a common fraction piece.
• Therefore,

3
Add the Following Using Fraction Factory Show
We know that 2 - 1/8 pieces fit into a one fourth
piece, therefore
4
(No Transcript)
5
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!
6
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?
7
Repeat the following examples using Pattern Blocks
8
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.

9
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
10
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?

11
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)
12
• 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?
13
Multiplication of Fractions Fraction Factory
Pattern Blocks
14
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?

15
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.
16
Divide Using Fraction Factory Pattern Blocks
17
Problem Solving
18
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?

19
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.

20
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?
21
• 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
What fraction of the students on the track team

22
• 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?

23
• 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
24
• 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?