Knowledge/Skill Building
Modeling Savings with Two-Variable Equations
CCSS.Math.Content.HSF-BF.A.1
CCSS.Math.Content.HSA-CED.A.2
Product
Assessment
Core Content
Essential Question
In small groups, students set up two-variable models (time and amount) to compare saving options (monthly deposits, lump sums, interest rate changes) and construct a simple matrix or table to compare scenarios. This work prepares their Day 3 Strategy Sketch & Matrix and reinforces distinguishing exponential vs linear growth and creating equations in two variables.
Plan day
Day 2
Duration
60 min
Grouping
—
Steps
5 steps
Lesson plan
5 steps · 60 min| # | What teachers do |
|---|---|
| 1 | Introduce the activity and review the essential question: "How can I use mathematical functions to model a successful savings plan for a down payment on my dream car?" (10 min) |
| 2 | Discuss the differences between linear and exponential growth with examples related to savings. (10 min) |
| 3 | Brainstorm various savings strategies as a group, considering factors such as monthly deposits, lump sums, and interest rates. (10 min) |
| 4 | Set up small group activities where students collaboratively develop two-variable equations to compare their chosen savings strategies. Provide guidance as needed. (15 min) |
| 5 | Create Strategy Sketch & Matrix where students compile and visualize their chosen models. Complete initial sketch on chart paper/table and discuss in groups. (5 min) |
Preparation (3 items)
- Prepare materials: chart paper, markers, calculator for each group, and sample savings scenarios for brainstorming.
- Arrange the classroom into collaborative groups with adequate space for group work.
- Ensure access to calculators or relevant software tools to facilitate equation modeling and calculations.
Student-facing instructions
Your task is to work in small groups to brainstorm multiple savings strategies. You will consider factors such as monthly deposits, lump sums, and changes in interest rates. Set up two-variable equations to compare scenarios and use these models to complete your Strategy Sketch & Matrix. Discuss and debate the benefits of using linear versus exponential growth models in your savings plan. Gather materials like calculators and chart paper to design your visual matrix.