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### Overview

This virtual manipulative can be used to help students visualize the multiplication of two fractions using an area model. This interactive manipulative can help improve students' spatial skills and build conceptual understanding of fraction multiplication.

This learning activity was created as a result of the Girls Engaged in Math and Science University, GEMS-U Project.

## UP:MA19.5.12

### Vocabulary

• Fraction
• Fraction model
• Whole number
• Area
• Area model
• Linear model
• Set model
• Tiling
• Unit squares
• Equation

### Knowledge

Students know:
• How to write an equation involving repeated addition with fractions as a multiplication equation of a whole number times the fraction.
Example: 2/9 + 2/9 + 2/9 + 2/9 = 4 x 2/9 = 8/9.
• The relationship of partial products to an area model when multiplying by two whole numbers.
• Area of a rectangle is determined by multiplying side lengths and is found in square units.

### Skills

Students are able to:
• Use previous understandings of multiplication to
• Find products of a fraction times a whole number and products of a fraction times a fraction.
• Use area models, linear models or set models to represent products.
• Create a story context to represent equations (a/b) × q and (a/b) × (c/d) to interpret products.
• Find area of rectangles with fractional side lengths and represent products as rectangular areas.
• Find the area of a rectangle by tiling the area of a rectangle with unit squares.

### Understanding

Students understand that:
• Any whole number can be written as a fraction.
• The general rule for multiplication involving fractions can be justified through visual models.
• A variety of contextual situations can be represented by multiplication involving fractions.
• Tiling with unit squares can be used to find the area of a rectangle with fractional side lengths.

### Phase

Before/Engage
During/Explore/Explain
Learning Objectives

### Learning Objectives

Students will use an area model to multiply two fractions.

Students will reduce fractions to simplest form.

### Activity Details

This virtual manipulative may be used to introduce students to the area model for fraction multiplication or can be used by students during independent practice until the model is mastered. Users have the ability to change the numerator and denominator of both fractions.

1. Have students locate the Digital Area Model for Multiplication of Fractions.
2. Model using the manipulative and explain that the answer is where the two bar models overlap.
3. Students will use visual models and properties of operations to find and interpret the product and connect the steps with the visual models.
4. Divide students into pairs. Have students take turns completing the steps while predicting the answers and then explaining the process to multiply fractions and solve the problem to their partner.
Assessment Strategies

### Assessment Strategies

At the end of the lesson, students should be comfortable using the online virtual manipulative, as well as drawing an area model of their own on paper to demonstrate the multiplication of two fractions.

### Background / Preparation

Before using this manipulative, students should be familiar with area models for multiplication and also have experience drawing bar models to represent fractions.

Have lined paper or graph paper, as well as 2 different colored pencils for each student available, so that after they are comfortable with the virtual manipulative, they can begin practicing drawing the model on their own paper to solve a problem.

The teacher should be very comfortable with bar model representations in order to help students master this concept as it is likely their conceptual understanding will be very fragile when beginning multiplying fractions.