UNIT FRACTIONS AS UNDERAPPRECIATED SUPERHEROES

UNIT FRACTIONS AS UNDERAPPRECIATED

SUPERHEROES

Vicki JacobsCotsen Foundation

Art of Teaching Conference 2017

University of MissouriSusan Empson

University of North Carolina at GreensboroNaomi JessupAmy Hewitt

University of Texas at AustinGladys KrauseD’Anna Pynes

Other Partners: SRI & Teachers Development Group(Joan Case!)

What is a Unit Fraction?

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What role do unit fractions play in our instruction?

ØFractions children first learn1/2 1/4 1/3

ØFractions used for naming and notating fractions & defining fraction terms (numerator, denominator)

ØFractions used in the first few examples when operating on fractions (+ – ✕ ÷)

What role do unit fractions play in our instruction?

ØFractions first learned1/2 1/4 1/3

ØFractions used for naming and notating fractions & defining fraction terms (numerator, denominator)

ØFractions used in the first few examples when doing operating on fractions (+ – ✕ ÷)

Building understanding with unit fractions

ØHelp children build understanding of:• Fractions (1/2, 1/3, 1/4, …)• Fraction quantities (1/2 apple, 1/3 can of paint,…)

• Fraction relationships (1/2 vs. 1/4, 1/3 vs. 1/9,…)

ØHelp children operate on fractions with understanding

Why are unit fractions special?

Ø Unit fractions clarify the relationship to a “whole”• A whole can be decomposed into a group of same-sized

unit fractions• Same-sized unit fractions can be grouped to make a

whole

Ø Unit fractions are building blocks for other fractions

Ø Relationships between unit fractions are building blocks for understanding equivalence

Unit fractions clarify the relationship to a “whole”

1 sandwich can be decomposed into 3 one-third sandwiches

1 = 1/3 + 1/3 + 1/31 = 3 × 1/3

3 one-third sandwiches can be grouped to make 1 sandwich

1/3 + 1/3 + 1/3 = 13 × 1/3 = 1

Sandwich(a whole)

A whole is the same as a grouping of same-sized unit fractions

Maddy (grade 3) Noah has 4 sandwiches. He wants to give 1/3 of a sandwich to each of his friends. How many friends can he feed before he runs out of sandwiches?

Maddy (grade 3) Noah has 4 sandwiches. He wants to give 1/3 of a sandwich to each of this friends. How many friends can he feed before he runs out of sandwiches?


1/3 of a sandwich1/3 of a

sandwich

1/3 of a sandwich

Maddy (grade 3) There are 10 pizzas, and on each pizza is 1/4 cup of pineapple. How much pineapple will we need?

Maddy (grade 3) There are 10 pizzas, and on each pizza is 1/4 cup of pineapple. How much pineapple will we need?


Grouped together for 1 whole


Key strategy features

ØDoes the child represent each individual unit fraction?

ØDoes the child group unit fractions to make a whole?

Continuum of understanding

A chef is making 14 pizzas. Each pizza takes 1/6 of a pound of cheese. How much cheese wil l the chef need to make all of the pizzas?

Represents each unit fraction

Groups to a

whole

Does the child represent each individual unit fraction?

Does the child group unit fractions to make a whole?

Elsa




Does notgroup to a whole

Groups to a

whole



Elsa





Groups to a

whole



ElsaPeter




Does notrepresent

unit fractions


Groups to a

whole

Groups to a

whole



Peter Elsa




Does notrepresent

unit fractions

Does notgroup

Groups to a

whole

Groups to a

whole



ElsaPeter Karisma




Does notrepresent

unit fractions


Groups to a

whole

Groups to a

whole



KarismaPeter Elsa




Represents some unit fractions

Does notrepresent

unit fractions


Groups to a

whole

Groups to a

whole

Groups to a

whole



KarismaPeter Elsa





Does notrepresent

unit fractions


Groups to a

whole

Groups to a

whole

Groups to a

whole

Groups to multiple wholes

Does notrepresent

unit fractions



KarismaPeter Elsa





Does notrepresent

unit fractions


Groups to a

whole

Groups to a

whole

Groups to a

whole

Groups to multiple wholes

Does notrepresent

unit fractions



KarismaPeter Elsa

Jamal

Grace

Peyton

DestinyJustineJasper

Lili Logan




whole



Jayden (4th): If 6 kids were going to share 4 candy bars equally, how much candy bar could each kid get?

Brian (5th) a × 1/4 = 2 1/4




whole



Gabby (4th/5th) 1/4 + 1/4 + 1/4 = b × 1/8

Take Aways

Ø Unit fractions help build fraction understanding• not just “starter” fractions• building blocks for other fraction concepts (non-

unit fractions and equivalence)

Ø Key indicators of children’s understanding of the whole as the same as a group of same-sized unit fractions (continuum of understanding)

• Does the child represent each unit fraction?• Does the child group unit fractions to make a whole

More worksheets at www.education.com/worksheetsCopyright © 2010-2011 by Education.com

Math

Fractions Equal to A fraction has two parts, a numerator and a denominator.

When the numerator is the same as the denominator, the fraction is equal to 1.Color in the shapes whose fractions are equal to 1.

Fill in the missing value.

#11

2445

20020

99

4848

9090

56

34

416

620

42

55

7117

55

=

6 1

1

=

15=

109109

=

45

numerator

denominator

More worksheets at www.education.com/worksheetsCopyright © 2010-2011 by Education.com

Math

Fractions Equal to A fraction has two parts, a numerator and a denominator.

When the numerator is the same as the denominator, the fraction is equal to 1.Color in the shapes whose fractions are equal to 1.

Fill in the missing value.

#11

2445

20020

99

4848

9090

56

34

416

620

42

55

7117

55

=

6 1

1

=

15=

109109

=

45

numerator

denominator

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UNIT FRACTIONS AS UNDERAPPRECIATED SUPERHEROES