In Grade 7 enVision Mathematics Chapter 4, Lesson 8, students learn how to write and analyze equivalent expressions to reveal relationships between quantities. Using the Distributive Property and combining like terms, they interpret what each term or factor represents in real-world contexts such as percent increase, tiled frames, and rectangular areas. Students practice rewriting expressions like 4(s + 1) and 1.25p to show that different forms can describe the same mathematical situation.
Section 1
Application: Modeling Perimeter and Borders
The total measure (e.g., area or number of units) of a border or frame is the sum of its non-overlapping parts.
For a 1-unit wide border around a square of side length , the number of unit squares in the border can be modeled by summing the four sides () and the four corner squares (), resulting in the expression .
Section 2
Application: Interpreting Dimensions by Factoring
Factoring an expression that represents the area of a rectangle creates an equivalent expression in the form of .
This allows us to interpret the possible dimensions of the rectangle.
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Section 1
Application: Modeling Perimeter and Borders
The total measure (e.g., area or number of units) of a border or frame is the sum of its non-overlapping parts.
For a 1-unit wide border around a square of side length , the number of unit squares in the border can be modeled by summing the four sides () and the four corner squares (), resulting in the expression .
Section 2
Application: Interpreting Dimensions by Factoring
Factoring an expression that represents the area of a rectangle creates an equivalent expression in the form of .
This allows us to interpret the possible dimensions of the rectangle.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter