Unit Plan 10 (Grade 7 Math): Expressions Workout—Properties & Structure
Grade 7 unit: Build fluency with linear expressions—combine like terms, use the distributive property with rational coefficients, and rewrite forms to reveal real-world meaning.
Focus: Combine like terms; use distributive property with rational coefficients; rewrite expressions in different forms.
Grade Level: 7
Subject Area: Mathematics (Expressions & Equations • Structure)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
This unit builds fluency with linear expressions that use rational coefficients (integers, fractions, and decimals). Students combine like terms, use the distributive property to expand and factor expressions, and rewrite expressions in forms that reveal meaning in context (for example, a + 0.05a = 1.05a). Emphasis: structure over shortcuts, clear justification for each transformation, and precision with signs and rational numbers.
Essential Questions
- How do the properties of operations help me rewrite expressions quickly and correctly?
- When I rewrite an expression, what new information does the form reveal about the situation?
- How can I keep signs, units, and rational numbers organized while I simplify?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Identify like terms (same variable and exponent) and combine them accurately with rational coefficients.
- Use the distributive property to expand expressions (for example, 3/2(x − 4)) and to factor by greatest common factor, including fractional GCFs.
- Rewrite expressions into equivalent forms to highlight features in context (rate, markup/discount, fixed fee + per unit).
- Explain and justify each step using properties (commutative, associative, distributive) and maintain equivalence.
- Check reasonableness by substitution (plug in a value), mental estimates, and structure checks.
Standards Alignment — CCSS Grade 7
- 7.EE.1: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
- 7.EE.2: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities are related (for example, a + 0.05a = 1.05a).
- Mathematical Practices emphasized: MP.1 (make sense), MP.3 (justify), MP.6 (precision), MP.7 (structure).
Success Criteria — Student Language
- I can spot like terms and combine them correctly, even with fractions/decimals.
- I can expand with distribution and factor out a GCF (including fractional GCF).
- I can rewrite an expression so it tells me something new (like “start-up fee + cost per item”).
- I can justify each step by naming a property.
- I can check my work by substituting a value to see if expressions are equivalent.