Unit Plan 6 (Grade 7 Math): Percent Change & Multistep Problems
7th graders extend percent understanding to increases, decreases, commissions, and simple interest. They compare strategies—proportions, equations, and multipliers (1 ± r)—to solve multistep percent problems, justify method choices, and check results for accuracy and reasonableness.
Focus: Percent increase/decrease, simple interest, commission, and multistep percent scenarios; compare strategies.
Grade Level: 7
Subject Area: Mathematics (Ratios & Proportional Relationships • Expressions & Equations)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
This unit extends percent work into change and chains of operations. Students compare solution strategies—proportion/equation setups, growth-factor multipliers (1 ± r), and structured step lists—for problems involving percent increase/decrease, commission/fees, and simple interest. Emphasis: choosing the right base, sequencing steps, and writing clear conclusions with units and reasonableness checks.
Essential Questions
- How do I decide whether a situation is a percent increase or decrease, and what is the correct base?
- When is it faster to use a proportion/equation, a table, or a multiplier (1 ± r)?
- How can I manage multistep percent situations (discount → tax, commission + bonus, fees) and check if my result is reasonable?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Determine percent increase/decrease and compute final or original amounts using the correct base.
- Use multipliers (1 + r for increases, 1 − r for decreases) for single and repeated percent changes; compare with proportion/equation approaches.
- Solve multistep percent problems (discounts/markups, tax/tip, fees, commission) and justify the order of operations.
- Apply simple interest I = P × r × t and compute totals; interpret r (rate per year) and t (time in years).
- Evaluate and communicate reasonableness using estimates, benchmarks, and unit analysis.
Standards Alignment — CCSS Grade 7
- 7.RP.3: Use proportional relationships to solve multistep ratio and percent problems (markups/markdowns, gratuities/commissions, fees, percent increase/decrease, simple interest, percent error).
- 7.EE.3 (connection): Solve real-life multistep problems using positive/negative rational numbers and assess reasonableness of answers; use mental math/estimation/benchmarks.
Success Criteria — Student Language
- I can name the base and decide if the change is an increase or decrease.
- I can use a multiplier (1 + r or 1 − r) and explain what r means.
- I can solve a multistep percent problem and explain the order I used.
- I can compute commission and simple interest and state the total with units.
- I can give an estimate first and a reasonableness check at the end.