# Expressions and Equations / Visualizing Quadratic Expressions

Activity 18 of 18
In this lesson students manipulate geometric figures to explore equivalent expressions that can be expressed in the form $$x^2 + bx + c$$ where $$b$$ and $$c$$ are positive integers.

## Planning and Resources

Objectives
Students should be able to connect the distributive law to an area model, recognize quadratic expressions in many forms, and understand that the product of two binomial expressions can be determined by multiplying each term in one sum by each term in the other sum.

Vocabulary
rectangle
square
area

Standard:

## Lesson Snapshot

#### Understanding

Students understand how to recognize the structure in equivalent quadratic expressions.

### What to look for

Students make connections between the area models and algebraic expressions they represent.

### Sample Assessment

Which of the following expressions are equivalent to $$(x + 4)^2$$?

1. $$x^2 + 16$$
2. $$x^2 + 4x + 16$$
3. $$(x + 2)^2 + 4(x + 3)$$
4. $$(x + 5)^2 - 4(x + 1)^2$$

Answer: c. $$(x + 2)^2 + 4(x + 3)$$

#### The Big Idea

Using geometric shapes as tools to visualize the algebraic structure of expressions can help in thinking about equivalent expressions involving quadratics.

### What are students doing?

Students use virtual manipulatives to connect the structure of equivalent expressions

### What is teacher doing?

Help students to recognize the role of area models in illustrating the distributive property.