Expanding and Factoring
5 min
Narrative
The purpose of this Warm-up is to reinforce the meaning of an area diagram, writing the area in two distinct ways to illustrate the distributive property. In this lesson, students will use the distributive property for increasingly complex expressions, and the area diagram is a useful support.
Launch
Give students 2 minutes to write as many expressions as they can think of.
Student Task
Write as many expressions as you can that represent the area of this rectangle.
Large outer rectangle partitioned into 2 smaller rectangles, vertical side 10. First rectangle top side length 6. Second rectangle top side length 3 x.
Sample Response
Sample responses:
- (6+3x)⋅10
- 60+30x
- 30(x+2)
- 10(3x+6)
- 5(6x+12)
Synthesis
The purpose of this discussion is to recall different ways to think about the area of the entire rectangle in order to write equivalent expressions. Ask a student to share an expression and record it for all to see. Ask if students agree that the expression represents the area of the rectangle, and if not, how they would amend it. Then ask for additional expressions and record them. Ensure at least one expression involves the height by the total width, such as 10(6+3x), and another expression involves the sum of the areas of the two smaller rectangles, such as 60+30x.
Standards
Building On
- 7.NS.A·Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
- 7.NS.A·Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
Building Toward
- 7.EE.1·Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
- 7.EE.A.1·Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.