Lesson plan

# 1. Understanding What Makes Expressions Equivalent Using Properties of Operations (C)

teaches Common Core State Standards CCSS.Math.Content.7.EE.A.1 http://corestandards.org/Math/Content/7/EE/A/1
teaches Common Core State Standards CCSS.Math.Content.7.EE.A.2 http://corestandards.org/Math/Content/7/EE/A/2
teaches Common Core State Standards CCSS.Math.Practice.MP3 http://corestandards.org/Math/Practice/MP3
teaches Common Core State Standards CCSS.Math.Practice.MP7 http://corestandards.org/Math/Practice/MP7

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Lesson objective: Understand that equivalent expressions always have the same value.

Students bring prior knowledge of equivalent expressions from 6.EE.A.3 and 6.EE.A.4. This prior knowledge is extended to expressions that include rational numbers as students identify more complicated equivalent expressions. A conceptual challenge students may encounter is determining that expressions are equivalent without finding a numerical value for the expressions. They may also think they're being asked to find a value for the variable in the expression, when the variable in each expression in the lesson can be any rational number.

The concept is developed through work with expressions, which allows students to experiment with the expressions and justifying why two expressions are equivalent through the use of properties of operations, including the commutative, associative, and distributive properties.

This work helps students deepen their understanding of operations because we can use the properties of operations to generate equivalent expressions.

Students engage in Mathematical Practice 3 (construct viable arguments) as they justify their choices for which expressions are equivalent. They also look for and make use of structure (MP 7) as they apply properties of operations to justify whether or not expressions are equivalent.

Key vocabulary:

• equivalent expressions
• rational number
• substitute
• variable

Special materials needed:

• expressions cards printed from task slide (optional)