-Seeing is BelievingUsing Visual Models to Support
Fraction Understanding
Jennifer DaPonte
Math Specialist, New Canaan Public Schools
[email protected]
Guiding Questions:
1. How can visual models increase the clarity
and effectiveness of our fraction
instruction?
2. How can we plan tasks for a range of
learners allowing them to reason about
mathematics?
Backwards Planning - Do The Math
A seamstress needs 1 ⅝ yards of fabric to
make a child’s dress. She needs 3 times as
much fabric to make a woman’s dress. How many
yards of fabric does she need for both
dresses?
Backwards Planning - Do The Math
Foundation Knowledge
Multiplication of a fraction by a
whole number
Addition of mixed numbers with
like denominators
Decomposition of fractions &
mixed numbers
Recognize equivalent fractions
Express whole numbers as
fractions
Backwards Planning - Do The Math
Foundation Knowledge
Multiplication of a fraction by a
whole number
Addition of mixed numbers with
like denominators
Decomposition of fractions &
mixed numbers
Recognize equivalent fractions
Express whole numbers as
fractions
Instructional Tools: Fraction Cards
Fraction Cards are tools to:
● Support all fraction content standards
● Make sense of problems
● Model with mathematics
● Reason abstractly and quantitatively
● Critique the reasoning of others
Instructional Tool: Fraction Cards
Paper-pencil task
can become an
entry to
purposeful
discourse
Fraction Cards in Action - 1
Focus for
Instruction:
Compare 2 fractions
with the same
numerator by
reasoning about
their size
Fraction Cards
in Action
-1
Cards: 6, 13, 15, 16, 18, 19
https://youtu.be/VEJOO6GVcKo
Fraction Cards in Action - 1
Reflection Notes:
● Opportunity to model precise vocabulary
● Acknowledge observations but maintain
focus of lesson purpose (revisit
equivalent fractions)
● Analyzing models that do not work can be
as powerful as studying those that do work
Fraction Cards in Action - 2
Focus for
Instruction:
Decompose fractions
and whole numbers
Fraction Cards
in Action
-2
Cards: 1, 4, 5, 13, 15, 27
https://youtu.be/tYxAIWEW0Mw
Fraction Cards in Action - 2
Reflection Notes:
● Opportunity to use labels to support
understanding and accuracy
● Highlight connections between models
(number bonds + area models)
● Have blank cards available to add
representations to the discussion
Fraction Cards in Action - 3
Focus for
Instruction:
Compare 2 fractions
with the same
numerator
Represent a fraction
on a number line
Fraction Cards
in Action
-3
Cards: 11, 12, 20, 25, 31, 35
https://youtu.be/Q_2XpoDiPKY
Fraction Cards in Action - 3
Reflection Notes:
● Highlight connections between models (area
model + number line)
● Consider revisiting same problem at a
later date with a different focus
(fraction equivalency)
Fraction Cards - Implications for the classroom
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Gather baseline data
Introduce a new model
Whole group mini lesson launch
Small group reteaching or extension
Exit card
Fraction Cards - Implications for the classroom
Consider:
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What is the standard?
Potential misconceptions?
Additional cards needed?