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9-12 Extra Support Materials for Algebra 1 Unit 7 Lesson 8

Gradeband

K-5 Math 6-8 Math •9-12 Math

Course

Algebra 1 Geometry Algebra 2 •Extra Support Materials for Algebra 1

Unit

Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 •Unit 7 Unit 8

Modeling Prompts

Lesson

Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 •Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16 Lesson 17

K-5
6-8
9-12

Algebra 1
Geometry
Algebra 2
Extra Support Materials for Algebra 1

Integrated Math 1
Integrated Math 2
Integrated Math 3

Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8

Modeling Prompts

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Lesson 8

8.1 Warm-up 8.2 Activity 8.3 Activity

Unit 7, Lesson 8

Areas and Equivalent Expressions

Extra Support Materials for Algebra 1

8.1

Warm-up

Ways to Express the Area

Here are two rectangles with their side lengths labeled. Write the sum of the areas of the two rectangles.
The two rectangles can be composed into a larger rectangle as shown.
1. Write the length and width of the new, large rectangle.
2. Write an expression for the area of the new rectangle.
How are the two expressions for area alike? How are they different?

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8.2

Activity

Multiplying Two-Digit Numbers and the Distributive Property

Standards Alignment

Building On

4.NBT.5

Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

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Addressing

Building Toward

A-SSE.3

Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

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Here are two rectangles.
1. Find the area of Rectangle A.
2. Find the area of each of the 4 smaller rectangles that make up Rectangle B.
3. Use the sum of the areas of the small rectangles to find the area of Rectangle B.
4. How is finding the area of Rectangle B like multiplying ?
Find the area of this rectangle two different ways:

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8.3

Activity

Using the Distributive Property to Write Equivalent Expressions

Standards Alignment

Building On

6.EE.3

Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

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Addressing

Building Toward

Express the area of each rectangle in two ways: as a sum of the areas of the sub-rectangles, and as a product of length and width of the large rectangle.
Select all the expressions that are equivalent to . Be prepared to explain or show how you know.
Write at least three expressions that can represent the area of a rectangle that is 12 units long by units wide. If you get stuck, try drawing a diagram.
Each expression represents the area of a rectangle. Name a possible length and width of each rectangle. Be prepared to explain or show how you know.
Sort the expressions into three groups, so that all three of the expressions in a group could represent the area of the same rectangle.

<p>rectangle partitioned into 4 rectangles</p>

<p>rectangle partitioned into 4 rectangles</p>

<p>rectangle partitioned into 4 rectangles</p>

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Glossary

None

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Standards Alignment

Building On

6.EE.3

Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

View Full Standard

Addressing

Building Toward

A-SSE.3

Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

View Full Standard

A-SSE.3

Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

View Full Standard