Rebuilding the Foundation for
Fraction Understanding
Dr. Nadine Bezuk
Steve Klass, Sharon Moore, and Gail Moriarty
San Diego State University,
Encinitas Union School District,
and San Diego City Schools
Philadelphia, NCTM 2004, Session 526
April 23, 2004
The Big Questions
•
What makes fractions so difficult for
students?
•
What do students need to know and be
able to do before they can compute
meaningfully with fractions?
Fraction Topics
•
•
•
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Concepts (includes fraction sense)
Equivalence
Order and comparison
Students need to understand these topics
before they can be successful with fraction
computation.
Instructional Programs from Pre-K – Grade 12
Should Enable All Students:
To understand numbers, ways of
representing numbers,
relationships among numbers, and
number systems.
NCTM Principles and Standards for School Mathematics
In Grades 3 - 5, All Students Should:
•
develop understanding of fractions as parts of
unit wholes, as parts of a collection, as locations
on number lines, and as division of whole
numbers;
•
use models, benchmarks, and equivalent forms
to judge the size of fractions;
•
recognize and generate equivalent forms of
commonly used fractions, decimals and
percents.
NCTM, 2000, p. 148
Questions
•
What models have you used for
fractions?
•
What previous experiences
have your students had with
fractions?
Types of Models for Fractions
•
•
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Area/region
Fraction circles, pattern blocks, paper
folding, geoboards, fraction bars, fraction
strips/kits
Length/linear
Number lines, rulers, (fraction bars,
fraction strips/kits)
Set/discrete
Chips, counters, painted beans
Understanding Fraction Concepts
•
What should students understand about
fraction concepts?
Meaning of the denominator (number of
equal-sized pieces into which the whole
has been cut)
Meaning of the numerator (how many
pieces are being considered)
The more pieces a whole is divided into,
the smaller the size of the pieces
A Literature Connection
“Gator Pie” by Louise Mathews, © 1979.
People Fractions
•
Uses a set model for fractions by engaging
your students in the activity
•
•
Considerations regarding the set model
See handout for list of people fractions
questions
Fraction Topics
Concepts (includes fraction sense)
•
Equivalence
•
Order and comparison
What is Equivalence Anyway?
•
•
•
“Equivalence” means “equal value”
Names for people, for numbers
Contexts for thinking about equal values
money
measurements
•
Justify it two ways
Area / Region Models
•
•
•
•
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Pizza
Fraction Circles
Fraction Strips or Bars
Grid Paper or Dot Paper
Paper folding
Equivalence: Number Line Strips
With a number line strip we are
simultaneously developing understanding
about equivalence and connecting the area
and linear models.
Equivalence: Closing Thoughts
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Use many models, make connections
across models
•
•
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Language: use “equal value” sometimes
Simplify: when and why
Benchmarks within and across rational
numbers
Fraction Topics
Concepts (includes fraction sense)
Equivalence
•
Order and Comparison
Order and Comparison
•
Ordering Fraction Tents
Work with a group of 4 (same tent color)
Consider your ordering strategies
•
“Clothesline” Fractions Activity
Strategies for Ordering Fractions
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•
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Benchmarks: close to 0, 1, 1/2
Same denominator
Same numerator
Same number of missing parts from the
whole (Residual strategy)
The Number Line
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Relative magnitude of fractions
Benchmarks
Fraction sense
What Should “Kids” Know?
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Fractions tell you how much you have out of
how many;
•
Fractions aren’t just between zero and one, they
live between all the numbers on the number
line;
•
The more pieces the whole is cut into the
smaller the pieces get;
•
•
A fraction can have lots of different names;
A fraction is more than just a piece of pizza,
fractions are everywhere.
Resources
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See handout for list of resources
Contact us: http://pdc.sdsu.edu
.JOET UIBU NPWF UIF XPSME