Do

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Five out of every four people have difficulty
with fractions.
Do Teachers Use Fractions To Make Numbers Even Mor
e Difficult?
The latest survey shows that 3 out of 4 people
make up 75 of the world's population.
87.12 of all statistics are made up on the spot.
2
Your Journals ...
Yes - education is a 'do-it-yourself' project.
Desire to Learn
Take responsibility for our own learning.
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Decimal Fractions
Percent
Equivalent
Ratio
Fractions
Part-Whole
Proportion
Rate
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Problem Of The Day 17 Rings
After an elderly woman passed away, 17 valuable
rings were left to her 3 granddaughters. The
oldest was to receive one-half of the rings, the
second eldest was to inherit one-third of the
rings and the youngest was to get a one-ninth
share. Not knowing how to divide up the rings, a
friend of the elderly woman said, Use one of
mine and then divide up the rings. When youre
done, just give mine back. How could this be
possible?
5
A fraction is completely meaningless until ...
a child knows what is being equally divided.
Remember the Division mats?
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This girl is ½ of the children in her family
. but ¼ of the whole family.
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Two Cornerstones ...
1. Part - Whole Relatioinships
OME - Scope Sequence Primary Grades
2. Equivalent Relationships
OME - Scope Sequence Junior Grades
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As a line ...
1
0
9
As a circle ...
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A Shifting Target
1 4

Are these regions equal in area?
1 2
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Divide into fourths. Use cubes to show 3/4. Put
up your hand when complete.
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Meanings of Fractions
Part of a set A region
Measure Division
Ratio
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Consider What does the 5 look like when a
child searches for 3/5?
0 1 2
3 4 4
4 4
4 4
An Elastic Fraction
Measure ½ of The two dimensions of a cupboard
door The three dimensions of your desk
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Basic Principles of Fractions

• Fractions can be compared only if they are parts
• of the _____ whole.
• 2. If two fractions have the same denominator,
  the one with the
• ________________ numerator is greater.
• 3. If two fractions have the same numerator, the
  one with the
• ________________ denominator is greater.

same
larger
smaller
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Fraction FoundationsThe story so far ..
Area / Linear Pies Fraction Strips Cuisenaire
Rods Pattern Blocks Found Material
Consider denominator first then build conceptual
models
What else might be used?
Manipulatives
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Many Ways To Represent Equivalent Fractions
Group Brainstorm (Graffiti)
Large Group Order Numbers
Pattern Block Designs
Class Project Make a Fractions Kit
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Converting Forms of Fractions
Simplify / Reduce / Lowest Terms
1
2
8
3
4
2
5
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Operation 1 Addition
Add using Fraction Pies
Add using a different manipulative.
Thats multiple representation Multi-pathing
2
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Operation 2 Subtraction
Subtract twice using your choice of different
manipulatives.
Thats multiple representation Multi-pathing
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Operation 3 Multiplication
Multiply twice using your choice of different
manipulatives.
Fish Bowl
Thats multiple representation Multi-pathing
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Use the digits 1 - 6 , once each, to make this
true.
1
6



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• Sequence
• Grade 3 tenths
• Grade 4,5,6 Hundredths
• Manipulatives include Base 10 blocks and 10 x 10
  grids
• Extend from Concepts of Fractions

Bridging To Decimal Fractions

• Think estimation first . In The Zone!
• Place Value concepts extended
• Algorithms remain consistent Line em up

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Money, Money, Money
3 x 2.58 7.74
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Lateral Development of Fractions

• Ratio Similar units to compare
• Rate Different units to compare
• Importance of Labels to Maintain Order
• Like a recipe to make lemonade
• Percent .. A Special Decimal
• (Wasnt a decimal just a special fraction?)

Proportion
Rate
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