Unit Plan 33 (Grade 8 Math): Algebra Power-Up—Equations, Functions, & Systems Spiral
8th graders review and apply key algebra and function skills—solving multi-step equations, comparing functions, and solving systems by graphing or algebraic methods. They model real situations, choose efficient strategies, and justify their reasoning with precision and clarity.
Focus: Reinforce multi-step equations, function comparisons, and systems (graphing and algebraic) with performance tasks.
Grade Level: 8
Subject Area: Mathematics (Algebra • Functions • Modeling)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
This spiral week tightens core Grade 8 algebra skills: solving multi-step linear equations, comparing and building functions, and solving systems by graphing and by algebraic methods. Students switch flexibly among equations, tables, graphs, and rules, choose efficient strategies, and justify their choices. The vibe is “train like an athlete”: short, focused workouts plus a daily mini-performance.
Essential Questions
- How do I select the most efficient method to solve an equation or system and explain why it works?
- How can I compare functions presented in different ways and decide whether a linear model is appropriate?
- When does a situation call for graphing, substitution, or elimination, and how do I communicate a clear solution with units and context?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Solve multi-step linear equations with rational coefficients, including equations with variables on both sides and equations with no solution or infinitely many solutions; check solutions and interpret structure.
- Identify and compare functions from mappings, tables, graphs, and rules; distinguish linear vs nonlinear and compare rates and initial values.
- Construct linear functions to model contexts, interpret rate of change and initial value, and sketch/interpret qualitative graphs that tell a story of change.
- Solve systems of linear equations by graphing, substitution, and elimination; interpret solutions as intersections and analyze special cases.
Standards Alignment — CCSS Grade 8
- 8.EE.7: Solve linear equations in one variable, including those with rational coefficients and special cases.
- 8.EE.8: Analyze and solve pairs of simultaneous linear equations (graphing, algebraic methods, and interpreting solution sets).
- 8.F.1: Understand a function as assigning each input exactly one output; use function notation informally.
- 8.F.2: Compare properties of two functions each represented in a different way (table, graph, equation, words).
- 8.F.3: Interpret the equation y = mx + b as defining a linear function and recognize non-linear examples.
- 8.F.4: Construct a linear function to model a relationship; interpret rate of change and initial value.
- 8.F.5: Describe qualitative features of a function from a graph and sketch a graph from a verbal description.
Success Criteria (student-friendly)
- I can solve a multi-step equation, justify each step, and identify no solution or infinitely many cases.
- I can compare two functions from different representations and decide which has a greater rate of change or larger initial value.
- I can build a linear rule from a context and explain what the slope and intercept mean.
- I can solve a system by a chosen method and explain why my answer makes sense in context.