The Big Questions
Rebuilding the Foundation for
Fraction Understanding
Nadine Bezuk, Steve Klass, and Sharon Moore
San Diego State University, Encinitas Union School District,
and San Diego City Schools
CMC-S 2003
November 7, 2003
Fraction Topics
Concepts (includes fraction sense)
Equivalence
Order and comparison
Students need to understand these topics
before they can be successful with fraction
computation.
What do students need to know and be
able to do before they can compute
meaningfully with fractions?
What makes fractions so difficult for
students?
From the California Standards
Grade 2: Stnd. 4.2: Recognize fractions of
a whole and parts of a group (e.g., onefourth of a pie, two-thirds of 15 balls).
Grade 3: Stnd. 3.1: Compare fractions
represented by drawings or concrete
materials to show equivalency . . . (e.g., 1/2
of a pizza is the same amount as 2/4 of
another pizza that is the same size; show
that 3/8 is larger than 1/4).
More from the CA Standards
Questions
Grade 4, Stnd. 1.5: Explain different
interpretations of fractions, for example,
parts of a whole, parts of a set, and division
of whole numbers; explain equivalents of
fractions.
What models have you used for
fractions?
Grade 4, Stnd. 1.9: Identify on a number
line the relative position of positive
fractions. . .
(see handout for complete listing)
What previous experiences have
your students had with
fractions?
Types of Models for Fractions
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
People Fractions
“Gator Pie” by Louise Mathews, © 1979.
Uses a set model for fractions by engaging
your students in the activity
(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
Equivalence: Number Line Strips
Pizza
With a number line strip we are
Fraction Circles
simultaneously developing understanding
Fraction Strips or Bars
about equivalence and connecting the area
Grid Paper or Dot Paper
and linear models.
Paper folding
Making Sense of the Set Model
12 chips
Equivalence: Closing Thoughts
Find one-third
Use many models, make connections across
models
Find two-sixths
Language: use “equal value” sometimes
Find four-twelfths
Using this model, how does two-sixths
look different from one-third?
Fraction Topics
Concepts (includes fraction sense)
Equivalence
Order and Comparison
Simplify: when and why
Benchmarks within and across rational
numbers
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
The Number Line
Same denominator
Relative magnitude of fractions
Same numerator
Benchmarks
Same number of missing parts from the
whole (”Residual strategy”)
Fraction sense
Benchmarks: close to 0, 1, 1/2
What Should “Kids” Know?
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
See handout for list of resources
Contact us: http://pdc.sdsu.edu