Interpreting Area Models for Fraction Multiplication
Interpreting Area Models for Fraction Multiplication is a Grade 5 math skill from Illustrative Mathematics Chapter 3 (Multiplying and Dividing Fractions) that teaches students to read a given area model and write the fraction multiplication expression it represents. The initially shaded region (in one direction) represents the first fraction, and the portion of that shaded area that is re-shaded or cross-hatched represents the second fraction in the expression.
Key Concepts
To find the multiplication expression $\frac{c}{d} \times \frac{a}{b}$ from an area model, identify the two fractions. The first fraction, $\frac{a}{b}$, is the area shaded in one direction. The second fraction, $\frac{c}{d}$, is the portion of that already shaded area that is re shaded or cross hatched.
Common Questions
How do you write a multiplication expression from an area model?
Identify the fraction represented by the initial shading (one direction). This is the first number in the expression. Then identify what fraction of that shaded area is cross-hatched. This is the second fraction. Write the expression as (second fraction) × (first fraction).
What is an example of reading an area model for fraction multiplication?
A model divided into 3 vertical columns with 2 shaded, then divided into 2 horizontal rows with top row cross-hatched: the initial shading shows 2/3, the cross-hatching takes 1/2 of it. Expression: (1/2) × (2/3).
What chapter covers interpreting area models in Illustrative Mathematics Grade 5?
Interpreting area models for fraction multiplication is covered in Chapter 3 of Illustrative Mathematics Grade 5, titled Multiplying and Dividing Fractions.
How do you count the divisions in an area model to find the fractions?
Count the number of equal columns to find the denominator of the first fraction, and how many are shaded for its numerator. Count the rows to find the denominator of the second fraction, and how many are shaded for its numerator.
What is the relationship between the area model and the fraction multiplication formula?
The area model visually demonstrates that (a/b) × (c/d) = (a × c)/(b × d). The cross-hatched cells are the numerator product (a × c) and the total cells are the denominator product (b × d).