Year Five - Understanding Fraction Multiplication Visually

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About this Big Idea

In this Big Idea students explore what it means to multiply by a fraction and the effect that this has on the answer. Students may have some experience with multiplying with fractions but have not developed an understanding of the effect this has. Students explore the concept of fraction multiplication using visuals and concrete materials to build a deep and accurate understanding of what is happening.

Understanding Goals:

Students will understand:

• fraction multiplication
• the effect that multiplication has on the size of a fraction

Background:

In Stage 3, the study of fractions is limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12 and 100 and calculations involve related denominators only

Core Content from the Syllabus:

Working Mathematically

Fraction, Decimals & Percentages

• Find a simple fraction of a quantity where the result is a whole number
• calculate a simple fraction of a collection/quantity

Language:

• In questions that require calculating a fraction or percentage of a quantity, some students may benefit from first writing an expression using the word 'of', before replacing it with the multiplication sign (×).

Connected to:

• What does it mean to divide Fractions?
• Using Fraction Equivalence
• Using Numbers and Symbols Flexibly

Mindset Mathematics Learning Activities

Visualise

Students begin to explore fraction multiplication using area models of a brownie pan. Students look for patterns in their solutions and connect these patterns to multiplication. - See page 172

Questions for reflection:

• What fraction of the pan will the person get to eat?
• How can we tell using your visual proof?
• What do the different models have in common?
• How are the brownie pans connected to multiplication? Use an example or draw a picture to make your thinking clear.

Play

In this activity, we open the door to thinking about multiplying a fraction by a whole number using the number visuals to support students in solving a fraction puzzle. - See page 180

Questions for reflection:

• What strategies did you use to find a number where ¹⁄₂, ¹⁄₃, and ¹⁄₄ of it is a whole number?
• How could we use the visuals to prove that these numbers satisfy these conditions?
• What patterns do you notice in the numbers that satisfy the conditions?
• What numbers not pictured could also satisfy these conditions? How do you know? How do the patterns in our solutions help us predict larger number solutions? How could they be drawn?
• What does it mean to find (¹⁄₂ or ¹⁄₃ or ¹⁄₄ ) of a number? Use examples or drawings to help you explain.

Investigate

We extend students' work with finding a fraction of a whole number to investigate and create visual proofs for fraction puzzles. We name finding a fraction of a whole number as multiplication. - See page 187

Questions for reflection:

• What solutions did you find?
• How did you use what you found to help you find new solutions?
• What do you notice about our solutions?
• Which numbers did we all use the most often? Why? What numbers did not get used? Why?
• How would you use these patterns to search for other solutions?
• When can you imagine needing to find a fraction of a whole number? Write your own fraction multiplication problem and solve it.

Credit:
Boaler, Munson & Williams (2018) - Mindset Mathematics: Visualizing and investigating big ideas Grade 5
NESA - Mathematics K-10 - 2012

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