Writing Expressions from Area Models
Writing Expressions from Area Models is a Grade 5 math skill from Illustrative Mathematics Chapter 3 (Multiplying and Dividing Fractions) that teaches students to read an area model divided into rows and columns and write the corresponding unit fraction multiplication expression. A model with a rows and b columns represents (1/a) × (1/b) = 1/(a × b), where the total small rectangles in the model is the product's denominator.
Key Concepts
An area model divided into $a$ horizontal parts (rows) and $b$ vertical parts (columns) represents the multiplication of two unit fractions, $\frac{1}{a} \times \frac{1}{b}$. The product is $\frac{1}{a \times b}$.
Common Questions
How do you write a multiplication expression from an area model with rows and columns?
Count the number of rows (a) and columns (b). Write the expression as (1/a) × (1/b) = 1/(a × b). For example, a model with 4 rows and 2 columns represents (1/4) × (1/2) = 1/8.
Why is the total number of cells the denominator of the product?
The total cells represent all equal parts the whole is divided into. Since the shaded region is one cell out of all cells, the product is 1 over the total number of cells, which equals a × b.
What chapter covers writing expressions from area models in Illustrative Mathematics Grade 5?
Writing expressions from area models is covered in Chapter 3 of Illustrative Mathematics Grade 5, titled Multiplying and Dividing Fractions.
What is an example of writing a unit fraction multiplication expression from an area model?
A model divided into 3 rows and 5 columns has 15 total cells. One shaded cell = 1/15. The expression is (1/3) × (1/5) = 1/15.
How does writing expressions from models build understanding of fraction multiplication?
Reading expressions from models reinforces the visual connection to the formula: rows give one denominator, columns give the other. The total cells give the product denominator, confirming that (1/a) × (1/b) = 1/(a × b).