Download CLIP 1: Representing Simple Fractions

Fractions Representing Part/Whole Relationships
CLIPS
CLIP 1: Representing Simple Fractions
Activity 1.1: Introduction: Representing Simple Fractions
Complete the following by filling in the boxes with the words numerator, part and whole.
denominator
Choose one of the following diagrams.
Write one or more sentences using fractions that describe parts of the chosen diagram.
OR
Activity 1.2: Fractions: Area Representations
Which of the following rectangles have
4
of their area shaded? (circle your choice(s))
6
Explain how you know the rectangles that you did not circle did not have
4
of their area
6
shaded.
Divide the following octagon into equal parts
and shade some of the parts.
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What fraction of the octagon did you shade?
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Activity 1.3 Fractions: Linear Measure Representations
The following measuring cup is missing some of
its labels. To make it easier to use, add fractions
to the tick marks that are missing labels.
1 cup
2/3
Where might you use fractions for measurement
in your daily life?
1/4
Activity 1.4: Fractions: Set Representations
On the right is a picture of the fruit taken out of a fruit bowl.
Which type of fruit represents
4
of all the fruit in the fruit
10
bowl?
What fraction of the fruit bowl was bananas?
What fraction of the fruit bowl was pears?
If all of the bananas were removed from the above picture,
how many fruits will be left?
What fraction of the leftover fruit would now be pears?
Activity 1.5: Creating Visual Representations
Create a visual representation of the fraction
5
using a rectangle, circle, length or a shape of
8
your choice.
What does it mean when a fraction has 0 as its numerator?
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Activity 1.6: Quiz: Representing Simple Fractions
Complete the quiz and take notes about what you learned from any questions you answered
incorrectly.
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CLIP 2: Forming and Naming Equivalent Fractions
Activity 2.1: Recognizing Equivalent Fractions
Draw a picture to show that the fractions
1 th
2 ths
and
are equivalent.
5
10
It took 15 min for Desi to mow her neighbour’s lawn. Write at least 2 equivalent fractions to
represent how long she mowed for. Explain how you know your fractions are equivalent
Activity 2.2: Folding Circles
Use your folded circle to name some fractions equivalent to 1/2.
Name as many fractions as you can fit in the space below that are equivalent to 1.
Activity 2.3: Fraction Strips
Shade some parts of the fraction strips below to show a set of at least 3 equivalent fractions.
Is there a fraction equivalent to 4/5ths whose denominator is 8? Give reasons for your answer.
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Activity 2.4: Forming Equivalent Fractions
Start by drawing a rectangle, a circle or a line. Divide your shape into parts to show the fraction
2/3rds and at least 2 fractions that are equivalent to 2/3rds.
Why did you choose the above shape?
Activity 2.5: Practice: Forming Equivalent Fractions
Which of the 3 tools for creating fractions do you find most useful, the fraction circle, the fraction
strips or the fraction rectangles? Explain.
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CLIP 3: Comparing Simple Fractions
Activity 3.1: Introduction: Comparing Simple Fractions
For each pair of fractions below, circle the larger fraction and then give reasons for your choice.
2
5
or
2
3
1
6
or
5
6
3
5
or
1
3
Activity 3.2: Comparing Fractions: Same Denominator
Complete each of the following inequalities, by filling in a number that will make the statement
true.
3
8

8
3
7

7
1
3

2
Is it possible to make these statements true by filling in a different number? Explain
Activity 3.3: Comparing Fractions: Same Numerator
Using fraction strips, or an area model, show why the fraction
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3
3
is larger than
.
8
10
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Activity 3.4 Using the Benchmark One-Half
Why is the number
1
referred to as a benchmark?
2
Is 3/8ths less than or greater than
1
?
2
Explain the strategy that you used to answer the above question.
Activity 3.5 Benchmark Baskets/Bins Sketch
From the fractions on the right, choose 2 fractions to compare using
the benchmark 1/2. Explain the comparison.
1
8
From the fractions on the right, choose 2 that you could not compare
using the benchmark 1/2. Why does this strategy not work for those
2 fractions?
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3
4
2
3
6
10
3
6
8
9
2
5
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Activity 3.6 Practice: Comparing Fractions Strategies Sketch
For each strategy given below, name a pair of fractions that you can compare using that
strategy. State which of the fractions is greater and then given reasons for your answer.
a) Fractions with the same denominator
b) Fractions with the same numerator
c) Fractions comparable using the benchmark one-half
Name a pair of fractions, that you could not compare using any of these strategies. Can you
think of another way to compare them? Explain.
Activity 3.7: Quiz: Comparing Simple Fractions
Complete the quiz and take notes about what you learned from any questions you answered
incorrectly.
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CLIP 4: Forming Equivalent Fractions by Splitting or Merging Parts
Activity 4.1: Introduction
How do you create an equivalent fraction in higher terms?
Given an example:
How do you create an equivalent fraction in lower terms?
Give an example:
Activity 4.2: Splitting Parts
The pool below has already been split into 3 equal sections, one section for adults, one section
for teens and one section for kids. If each section is to be divided into 2 parts for games, write
2 equivalent fractions to represent the part of the pool that the teens get.
kids
adults
teens
One of your fractions is in higher terms, which one is it?
full
full
full
full
full
full
full
full
Activity 4.3: Merging Parts
Here is a different layout for a tackle box,
what fraction of the tackle box is full?
empty
empty
How could you have created the fraction in higher terms mathematically from the fraction in
lower terms?
If I remove some of the dividers to make 5 equal
trays, what fraction of the tray is now full?
How could you have created the fraction in lower
terms mathematically from the fraction in higher
terms?
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Activity 4.4: Forming Equivalent Fractions Sketch
State some fractions that are equivalent to
8
in both higher and lower terms.
12
These pairs of fractions are not equivalent. Change one number from each pair so that they
are equivalent.
3
8
and
12
16
9
12
and
3
6
Explain how you know that the pairs of fractions are now equivalent.
Activity 4.5: Practice: Forming Equivalent Fractions
Give an example of a set of equivalent fractions that you created by multiplying.
Explain why multiplying the numerator and the denominator by
the same value creates an equivalent fraction.
Give an example of a set of equivalent fractions that you created by dividing.
Explain why dividing the numerator and the denominator by the
same value creates an equivalent fraction.
Activity 4.6: Quiz: Equivalent Fractions
Complete the quiz and take notes about what you learned from any questions you answered
incorrectly.
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CLIP 5: Representing Improper Fractions as Mixed Numbers
Activity 5.1: Pizza Party
Give an example of a proper fraction and explain how you know it is a proper fraction.
Give an example of an improper fraction and explain how you know it is an improper fraction.
Give an example of a mixed number and explain how you know it is a mixed number.
Activity 5.2: Leftovers
Write each of the following as a mixed number. Explain or draw pictures to show how you
determined your answer.
7
2
13
6
Suzy says that it is not possible to write the fraction
3
as a mixed number. Do you agree with
4
her? Why or why not?
What improper fraction is equivalent to 5
2
? Explain or show how you determined your
3
answer.
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Activity 5.3: Dropball Game
Draw a number line that counts up to at least 5.
Add these numbers to your number line:
14
4
1
3
5
4
1
7
8
Create a fraction that is between 0 and 1 and add it to your number line.
Create an improper fraction greater than 2 that had a denominator of 5 and add it to your
number line.
Create a fraction that is equivalent to 3, and add it to your number line.
How many fractions can you name that are equivalent to 3? Explain/show them.
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