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In this lesson, we will extend your previous knowledge on writing and evaluating algebraic expressions. Moreover, we will try to use properties of operations to generate equivalent expressions through applying strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
See the fact file below for more information on the generating equivalent expressions or alternatively, you can download our 29-page Generating Equivalent Expressions worksheet pack to utilise within the classroom or home environment.
Key Facts & Information
IDENTIFYING EQUIVALENT EXPRESSIONS
- One way to test whether two expressions might be equivalent is to evaluate them using the same value for the variable.
- 5x + 65
- 5(13 + x)
- Evaluate both expressions when x = 3.
- Therefore, 5x + 65 is equivalent to 5(13 + x). When you use another value of x, these two expressions are still equal.
- Match the expressions in Column A with their equivalent expressions in Column B.
- 8(x + 1)
- 1 + 8x
- 8x + 48
- 8x + 1
- 8x + 8
- 8(6 + x)
- Evaluate each of the expressions in the two columns when x = 2.
- 8(2 + 1) = ____
- 1 + 8(2) = ____
- 8(2) + 48 = ____
- 8(2) + 1 = ____
- 8(2) + 8 = ____
- 8(6 + 2) = ____
MODELING EQUIVALENT EXPRESSIONS
- You can also use models to determine if two expressions are equivalent. Algebra tiles are one way to model expressions.
- Determine if the expression 6(x + 2) is equivalent to 6x + 12.
- Step 1. Model each expression using algebra tiles.
- Step 2. Count the algebra tiles used in each of the expressions.
- The model for 6(x + 2) has 6 x tiles and 12 1 tiles. The model for 6x + 12 has 6 x tiles and 12 1 tiles.
- Therefore, the expression 6(x + 2) is equivalent to 6x + 12.
- Use algebra tiles to determine if 4(x – 4) is equivalent to 4x – 16.
- Explain your answer.
WRITING EQUIVALENT EXPRESSIONS USING PROPERTIES
- Properties of operations can be used to identify equivalent expressions.
- Commutative Property of Addition: when adding, changing the order of the terms does not change the sum.
- Commutative Property of Multiplication: when multiplying, changing the order of the terms does not change the product.
- Associative Property of Addition: when adding more than two terms, the grouping of the terms does not change the sum.
- Associative Property of Multiplication: when multiplying more than two terms, the grouping of the terms does not change the product.
- Distributive Property: multiplying a number by a sum or difference is the same as multiplying by each number in the sum or difference and then adding or subtracting.
- Identity Property of Addition: adding zero to a term does not change its value.
- Identity Property of Multiplication: multiplying a term to one does not change its value.
- Inverse Property of Addition: the sum of a number and its opposite, or additive inverse, is zero.
GENERATING EQUIVALENT EXPRESSIONS
- When an expression contains like terms, you can use properties like terms into a single term.
Generating Equivalent Expressions Worksheets
This is a fantastic bundle which includes everything you need to know about the generating equivalent expressions across 29 in-depth pages. These are ready-to-use Generating Equivalent Expressions worksheets that are perfect for teaching students about writing and evaluating algebraic expressions. Moreover, we will try to use properties of operations to generate equivalent expressions through applying strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
Complete List Of Included Worksheets
- Lesson Plan
- Generating Equivalent Expressions
- Which is Which?
- Matching Time
- Order of Operations
- Combining Like Terms
- It’s a Match!
- Algebra Tiles
- Identifying Equivalence
- Using Properties
- Thinking Time
- Error Analysis
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Use With Any Curriculum
These worksheets have been specifically designed for use with any international curriculum. You can use these worksheets as-is, or edit them using Google Slides to make them more specific to your own student ability levels and curriculum standards.