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Multiplication of Fractions

- WMC Annual Conference
- May 2012
- Astrid Fossum, Milwaukee Public Schools
- Paige Richards, School District of South

Milwaukee

Isnt this everything I need to know?

Current Connections to Fractions

- Thinking about your current grade level of

instructiontalk to a shoulder partner - Concepts you currently teach around fractions
- Roadblocks that you encounter when you try to

work with fractions with your students.

Learning Intentions

- We are learning to
- Develop strategies related to multiplying

fractions. - Understand how estimation should be an integral

part of fraction computation development. - Read and interpret the cluster of CCSS standards

related to multiplication of fractions. - We will know we are successful when we can
- Justify our thinking when multiplying fractions

using concrete models and estimation strategies. - Clearly explain and provide examples for specific

CCSS standards

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Domain-Cluster-Standards

- Domain Number and Operations Fractions
- Cluster Apply and extend previous understandings

of multiplication and division to multiply and

divide fractions. - Standard 5.NF.6
- Solve real world problems involving

multiplication of fractions and mixed numbers,

e.g., by using visual fraction models or

equations to represent the problem.

Big Ideas for Multiplication and Division of

Fractions

- Multiplication and division of fractions are

among the most complicated fraction concepts that

elementary students encounter. - Instructional opportunities that students

encounter should include the meaning of

multiplication and division on a range of

situations and build procedural fluency with

understanding.

Launch Building on What We Know

- What do you know about multiplication and

division of whole numbers? - As a table group, make a list of what students

have learned as they interact with multiplication

and division problems. - Are they all true for fractions?

The Importance of Models

- Researchers indicate that teachers need knowledge

of concrete models to help students transition

from multiplication of whole numbers to

multiplication of fractions. (Fendel, 2000)

Thinking in Whole Numbers

- 3 X 4 12
- Write a word problem for this equation.
- What does each number mean?

Multiplication of Fraction Standards

- 4.NF.4a, 4.NF.4b, 4.NF.4c, 5.NF.4, 5.NF.5,

5.NF.6 - On your Standards Interpretation Sheet we will

rephrase these standards and provide examples.

Some Stories

- Solve these problems. Use a visual model to

record and then discuss your thinking with the

group. Then write an equation. - There are 15 cars in Dereks toy car collection.

Two-thirds of the cars are red. How many red cars

does Derek have? - Tia has 11 cookies. She wants to share them with

her three friends. How many cookies will Tia and

each of her friends get, if they share them

equally? - Jason filled 5 glasses with 1/3 liter of soda in

each glass. How much soda did Jason use?

Unpacking 4.NF.4

- 4. Apply and extend previous understandings of

multiplication to multiply a fraction by a whole

number. - a. Interpret the product (a/b) q as a parts of

a partition of q into b equal parts

equivalently, as the result of a sequence of

operations a q b. For example, use a visual

fraction model to show (2/3) 4 8/3, and

create a story context for this equation. Do the

same with (2/3) (4/5) 8/15. (In general,

(a/b) (c/d) ac/bd.) - b. Understand a multiple of a/b as a multiple of

1/b, and use this understanding to multiply a

fraction by a whole number. For example, use a

visual fraction model to express 3 (2/5) as 6

(1/5), recognizing this product as 6/5. (In

general, n (a/b) (n a)/b.) - c. Solve word problems involving multiplication

of a fraction by a whole number, e.g., by using

visual fraction models and equations to represent

the problem. For example, if each person at a

party will eat 3/8 of a pound of roast beef, and

there will be 5 people at the party, how many

pounds of roast beef will be needed? Between what

two whole numbers does your answer lie?

More Stories

- Solve these problems. Use a model to record and

then discuss your thinking with your group. Write

an equation for each problem. - You have of a pizza left. If you give of

the left-over pizza to your brother, how much of

a whole pizza will your brother get? - Frankie had 2/3 of the lawn left to cut. After

lunch, she cut 3/ 4 of the lawn she had left. How

much of the whole lawn did Frankie cut after

lunch?

Unpacking 5.NF.4a

- 4. Apply and extend previous understandings of

multiplication to multiply a fraction or whole

number by a fraction. - a. Interpret the product (a/b) q as a parts of

a partition of q into b equal parts

equivalently, as the result of a sequence of

operations a q b. For example, use a visual

fraction model to show (2/3) 4 8/3, and

create a story context for this equation. Do the

same with (2/3) (4/5) 8/15. (In general,

(a/b) (c/d) ac/bd.)

Multiplying with Mixed Numbers

- Determine the solution to these problems. Do not

use a computational algorithm. - 6 ½ x 4
- 2 ½ x 5 ¾

Unpacking 5.NF.6

- 6. Solve real world problems involving

multiplication of fractions and mixed numbers,

e.g., by using visual fraction models or

equations to represent the problem.

Revisiting Word Problems

- Examine the five problems on the handout.
- Which are story problems for 2/3 x 1/ 4 and which

are not? Why?

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Standards Interpretation Summing It All Up

- As a teacher of mathematics
- What message are you walking away with regarding

the CCSSM domain of fractions? - As a leader of mathematics
- What message will you be taking back to teachers

in your school/district?

Thank you!

- Astrid Fossum, Milwaukee Public Schools
- fossumag_at_milwaukee.k12.wi.us
- Paige Richards, School District of South

Milwaukee - prichards_at_sdsm.k12.wi.us