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Unit Fractions As Superheroes for Fraction Instruction

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Unit Fractions As Superheroes for Fraction Instruction UNIT FRACTIONS AS SUPERHEROES FOR FRACTION INSTRUCTION Vicki Jacobs 2019 Math Summit Triangle Math Alliance & NC State August 2019 Responsive Teaching in Collaborators Elementary Mathematics Susan Empson University of Missouri Gladys Krause Naomi Jessup D’Anna Pynes William & Mary Georgia State University University of Michigan Amy Hewitt Heather LindFors-Navarro University of North Carolina Cassandra Quinn at Greensboro University of Missouri SRI & Teachers Development Group What is a Unit Fraction? � � � � � � � � � �� What role do unit Fractions play in our instruction? “Starter Fractions” Ø Fractions children first learn 1/2 1/4 1/3 Ø Fractions used for defining fractions Ø Fractions used in the first few examples when operating on fractions (+ – ✕ ÷) What role could unit Fractions play in our instruction? Superheroes for Fraction Instruction A chef is making 14 pizzas. Each pizza takes 1/6 of a pound of cheese. How much cheese will the Your Turn! chef need to make all of the pizzas? Ø Review the 5 strategies with a partner Ø Think about what understanding of fractions is reflected in each strategy Ø Order the strategies from least to most understanding Ø Think about what strategy features were helpful in making your determination Unit Fractions can help build fraction understanding! Ø Unit fractions clarify the relationship to one whole Ø Unit fractions are foundational for understanding other fraction concepts • Unit fractions are building blocks for other (non-unit) fractions • Relationships between unit fractions are building blocks for understanding equivalence Unit fractions clarify the relationship to one whole One whole is the same amount as a collection oF same-sized unit Fractions 1 Sandwich (a whole) 1 whole sandwich can be partitioned into 3 one-third sandwiches 1 = 1/3 + 1/3 + 1/3 1 = 3 × 1/3 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? One whole is the same amount as a collection oF same-sized unit Fractions 1/3 of a 1/3 of a sandwich sandwich 1/3 of a sandwich Unit fractions clarify the relationship to one whole One whole is the same amount as a collection oF same-sized unit Fractions 1 Sandwich (a whole) 3 one-third sandwiches can be grouped to make 1 whole sandwich 1/3 + 1/3 + 1/3 = 1 3 × 1/3 = 1 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 cup One whole is the same of pineapple amount as a collection oF same-sized unit Fractions Unit fractions clarify the relationship to one whole One whole is the same amount as a collection oF same-sized unit Fractions 1 whole sandwich can be partitioned 4 one-fourth cups into 3 one-third can be grouped to sandwiches make 1 whole cup Noah has 4 sandwiches. He There are 10 pizzas, and wants to give 1/3 of a on each pizza is 1/4 cup sandwich to each of his of pineapple. How much friends. How many friends pineapple will we need? can he feed before he runs out of sandwiches? One whole is the same amount as a collection of same-sized unit fractions Key strategy features Ø Does the child represent each individual unit-fraction amount? Ø Does the child group unit-fraction amounts to make one whole? Continuum oF understanding One whole is the same amount as a collection of same-sized unit fractions Ø Does the child represent each individual unit-fraction amount? Ø Does the child group unit-fraction amounts to make one whole? Grouped A chef is makingtogether 14 for pizzas. Each pizza 1takes whole 1/6 cup of a There are 10 pizzas, and on each of pineapple pound of cheese. How much pizza is 1/4 cup of pineapple. cheese will the chef need to How much pineapple will we make all of the pizzas? need? Does the child represent each individual unit-fraction amount? Represents each individual unit-fraction amount Elsa’s strategy Groups to one whole Does the child group unit-fraction amounts to make one whole? Does the child represent each individual unit-fraction amount? Represents Does not each represent individual individual unit-fraction unit-fraction amount amounts Elsa’s Peyton’s strategy strategy Groups to Groups to one whole one whole Does the child group unit-fraction amounts to make one whole? Does the child represent each individual unit-fraction amount? Represents Does not each represent individual individual unit-fraction unit-fraction amount amounts Elsa’s Peyton’s strategy strategy Groups to Groups to one whole one whole Does the child group unit-fraction amounts to make one whole? Does the child represent each individual unit-fraction amount? Represents Represents Does not each each represent individual individual individual unit-fraction unit-fraction unit-fraction amount amount amounts Peter’s Elsa’s Peyton’s strategy strategy strategy Does not Groups to Groups to group to one whole one whole one whole Does the child group unit-fraction amounts to make one whole? Does the child represent each individual unit-fraction amount? Represents Represents Does not each each represent individual individual individual unit-fraction unit-fraction unit-fraction amount amount amounts Peter’s Elsa’s Peyton’s strategy strategy strategy Does not Groups to Groups to group to one whole one whole one whole Does the child group unit-fraction amounts to make one whole? Does the child represent each individual unit-fraction amount? Represents Represents Represents Does not each each some represent individual individual individual individual unit-fraction unit-fraction unit-fraction unit-fraction amount amount amounts amounts Peter’s Elsa’s Jamal’s Peyton’s strategy strategy strategy strategy Does not Groups to Groups to Groups to group to one whole one whole one whole one whole Does the child group unit-fraction amounts to make one whole? Does the child represent each individual unit-fraction amount? Represents Represents Represents Does not each each some represent individual individual individual individual unit-fraction unit-fraction unit-fraction unit-fraction amount amount amounts amounts Peter’s Elsa’s Jamal’s Peyton’s strategy strategy strategy strategy Does not Groups to Groups to Groups to group to one whole one whole one whole one whole Does the child group unit-fraction amounts to make one whole? Does the child represent each individual unit-fraction amount? Represents Represents Represents Does not Does not each each some represent represent individual individual individual individual individual unit-fraction unit-fraction unit-fraction unit-fraction unit-fraction amount amount amounts amounts amounts Peter’s Elsa’s Jamal’s Peyton’s Destiny’s strategy strategy strategy strategy strategy Does not Groups to Groups to Groups to Groups to group to one whole one whole one whole multiple one whole wholes Does the child group unit-fraction amounts to make one whole? Does the child represent each individual unit-fraction amount? Represents Represents Represents Does not Does not each each some represent represent individual individual individual individual individual unit-fraction unit-fraction unit-fraction unit-fraction unit-fraction amount amount amounts amounts amounts Peter’s Elsa’s Jamal’s Peyton’s Destiny’s strategy strategy strategy strategy strategy Does not Groups to Groups to Groups to Groups to group to one whole one whole one whole multiple one whole wholes Does the child group unit-fraction amounts to make one whole? A chef is making 14 pizzas. Each pizza takes 1/6 of a pound of cheese. How much cheese will the chef need to make all of the pizzas? Justine Logan Jasper Does the child represent each individual unit-fraction amount? Represents Represents Represents Does not Does not each each some represent represent individual individual individual individual individual unit-fraction unit-fraction unit-fraction unit-fraction unit-fraction amount amount amounts amounts amounts Peter’s Elsa’s Jamal’s Peyton’s Destiny’s strategy strategy strategy strategy strategy Jasper Logan Justine Does not Groups to Groups to Groups to Groups to group to one whole one whole one whole multiple one whole wholes Does the child group unit-fraction amounts to make one whole? Unit Fractions can help build fraction understanding! Ø Unit fractions clarify the relationship to one whole One whole is the same amount as a collection oF same-sized unit Fractions Ø Unit fractions are foundational for understanding other fraction concepts • Unit fractions are building blocks for other (non-unit) fractions Jayden (4th): If 6 kids were going to share 4 candy bars equally, how much candy bar could each kid get? I cut it into into 6…so they get 4 There are 4 candy bars and pieces. you’re taking And do you know …one sixth from what size one of each so… 1/6, those pieces is? 2/6, 3/6, 4/6 One sixth Brian (5th) a × 1/4 = 2 1/4 You can double 4 x 1/4 = 1 [4 x 1/4 = 1] to get 8 Unit Fractions can help build fraction understanding! Ø Unit fractions clarify the relationship to one whole One whole is the same amount as a collection oF same-sized unit Fractions Ø Unit fractions are foundational for understanding other fraction concepts • Unit fractions are building blocks for other fractions • Relationships between unit fractions are
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