Unit Plan 18 (Grade 6 Math): Midyear Synthesis—Ratios, Percents, and Algebra

Focus: Mixed tasks connecting ratio/rate and percent reasoning with expressions, equations, inequalities, and coordinates.

Grade Level: 6

Subject Area: Mathematics (Integrated Review — Ratios & Percents, Algebra, Coordinates)

Total Unit Duration: 5 sessions (one week), 45–60 minutes per session

I. Introduction

This midyear synthesis weaves together the big ideas from the fall: ratio and rate, percent, algebraic expressions, equations/inequalities, and two-variable relationships on the coordinate plane. Students rotate through rigorous, real-world tasks that require modeling, representation switching (words ⇄ diagrams ⇄ symbols ⇄ graphs), and precision. Emphasis: reasoning, explanation, and decision-making with units.

Essential Questions

• How do ratio/rate and percent show up inside algebra problems and graphs?
• When do I choose x + p = q, px = q, or an inequality, and how do I check solutions?
• How can a table, graph, or equation each tell the same story about y in terms of x?
• How do units, structure, and estimation help me judge whether an answer is reasonable?

II. Objectives and Standards

Learning Objectives — Students will be able to:

1. Apply ratio/rate and percent reasoning (including unit rate, percent of, percent increase/decrease) to multistep contexts.
2. Write and evaluate expressions with whole-number exponents and use structure to interpret or rewrite them.
3. Write, solve, and check equations and inequalities from real situations; interpret solutions (value or solution set) with units.
4. Build tables, sketch graphs, and write equations that express y in terms of x; analyze rate and initial value.
5. Use substitution, error analysis, and estimation to verify results and explain reasoning.

Standards Alignment — CCSS Grade 6

• 6.RP.1–3: Understand ratio/unit rate; use ratio/percent reasoning to solve problems (including tables, tape/double-number-line, unit conversions).
• 6.EE.1–2: Evaluate expressions with exponents; write expressions from words and identify parts (term, factor, coefficient, constant).
• 6.EE.5–7: Understand solving as “which values make it true”; write/solve equations from context and check by substitution.
• 6.EE.8–9: Write/graph inequalities; represent two-variable relationships with tables/graphs/equations and analyze them.
• 6.NS.6–8 (spiral): Place/interpret rational numbers on the number line; compare using absolute value; graph points in all quadrants.
• Mathematical Practices MP.1–MP.6 emphasized (make sense, reason quantitatively, construct/critique arguments, model, use tools strategically, attend to precision).

Success Criteria — Student Language

• I can choose a model (ratio table, double-number line, tape diagram, equation, inequality, or graph) that fits the situation.
• I can write and solve an equation/inequality and check it by substitution; I can explain the meaning of the solution with units.
• I can build a table, draw a graph, and write y in terms of x; I can describe the rate and initial value.
• I can use estimation and units to decide if my answer is reasonable.
• I can explain my choices using precise terms: ratio, unit rate, percent, term, coefficient, solution set, ordered pair.