The Savings Tracker
Students build savings equations from starting amounts and weekly deposits — one function at a time, from tables, graphs and two data points. The gentler on-ramp to Phone Plan Showdown.
Common Core standards covered
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Teacher-facing overview
Big idea: Construct a function to model a linear relationship, determining the rate of change and initial value from descriptions, tables, graphs and two (x, y) values.
Student target: “I can find a saver's weekly rate and starting amount from a table, a graph, or two data points, write y = (rate)x + (start), and use it to answer when-questions.”
Success criteria: I can identify the rate of change (per week) and initial value (week 0) in any representation. · I can write the savings equation y = mx + b with both numbers labeled. · I can find m and b from just two (week, balance) pairs. · I can predict a balance and solve for a goal week.
Essential question
A savings balance grows the same amount every week. What two numbers tell the WHOLE story — past, present and future?
Learning target: I can find a saver's weekly rate and starting amount from a table, a graph, or two data points, write y = (rate)x + (start), and use it to answer when-questions.
Success criteria
- I can identify the rate of change (per week) and initial value (week 0) in any representation.
- I can write the savings equation y = mx + b with both numbers labeled.
- I can find m and b from just two (week, balance) pairs.
- I can predict a balance and solve for a goal week.
Why this matters
This is 8.F.B.4 in its cleanest costume: every linear story is a start plus a steady change, and the two-points skill — recovering m and b from a pair of observations — is the one the standard names explicitly. It is also deliberately HALF of Phone Plan Showdown: one function, fully owned, before three functions compete. Savers who can read (2, 70) and (5, 115) into y = 15x + 40 are ready for the arena.
Students should already be able to
- y = mx + b meanings — Why Slope Never Changes.
- Evaluate an equation at a value.
- Subtraction to find differences across a table.
Vocabulary to define explicitly
- Rate of change (the deposit)
How much the balance grows per week — the m.
Example: Balances 70 then 85 a week apart: the rate is $15/week.
Not an example: The balance itself ($70) is not the rate — the CHANGE per week is.
🔒 3 more terms with examples and non-examples — Initial value (the starting amount), The savings equation, Two points determine the line — are defined in the full lesson. See plans →
Where this shows up outside the classroom
Assessment plan
Formative — for feedback during the lesson
- Warm-up shortcut: rate-times-weeks-plus-start.
- Ledger rows during club work — the b column especially.
- Sam's dual walk-back agreement.
Summative — the graded evidence: The exit ticket (two-point build, interpretations, goal), scored with the four-criterion rubric.
The task students work on
The Savings Club tracks four members. Maya tells you her plan in words. Deshawn brings a table. Lena brings a graph. Sam only remembers two balances — week 2: $70, week 5: $115. For each saver: find the weekly rate and the starting amount, write the equation, and answer their question — usually 'when do I hit my goal?'
Club ledger — one row per saver.
| Saver | Given as | Rate ($/wk) | Start ($) | Equation |
|---|---|---|---|---|
| Maya | Words: $40 start, $15 weekly | |||
| Deshawn | Table: wk 1 → 65, wk 2 → 80, wk 3 → 95 | |||
| Lena | Graph: line from (0, 40) to (8, 160) | |||
| Sam | Two points: (2, 70) and (5, 115) |
Anticipated student strategies
Table, graph, then two bare points — each representation gives a little less away, and the two-point case is the other three with the training wheels off.
- Difference column. From Deshawn's table the student computes the weekly jumps — all +15 — then walks one step back from week 1 to find week 0.
The workhorse. Share first; the walk-back to week 0 is the step that separates b from 'the first number I see'.
🔒 2 more anticipated strategies with select-and-sequence guidance are in the full lesson. See plans →
Lesson script
55, 70… and the shortcut: 15 · 10 + 40 = 190. Name the two numbers doing all the work: the $15 rate and the $40 start. Write y = 15x + 40 and label both.
Listen for: Broke start changes b to 0; faster saving changes m. The numbers have separate jobs.
Write y = 15x + 50 and verify against the table (week 3: 45 + 50 = 95 ✓). Then Lena's graph: start read at the y-axis ($40), rate from one week's climb ($15) — same plan as Maya, discovered from a picture.
- b lives at week 0 — walk the table back if it starts late.
- Verify the equation against a row you didn't use to build it.
Listen for: Going forward a week adds a deposit; rewinding a week removes one. Week 0 is week 1 minus one deposit.
🔒 The remaining 4 steps — fully scripted with teacher-says lines, discourse questions, look-fors, and interventions — are in the full lesson. See plans →
Misconceptions and how to respond
- “The first table entry is the starting amount.” Only if it's week 0. Deshawn's 65 is week ONE — rewind a deposit: b = 50. The start lives at x = 0, nowhere else.
- “Sam's rate is 45 ÷ 5.” — the teacher response is in the full lesson.
- “y = 40x + 15 says the same thing as y = 15x + 40.” — the teacher response is in the full lesson.
- “You need the whole table to find the equation.” — the teacher response is in the full lesson.
🔒 Every misconception ships with a tested classroom response. See plans →
Scaffolded practice
The workbook follows gradual release rather than a page of blank prompts: 1 fully worked, 1 partially completed, then 4 independent.
- I doDeshawn's table: week 1 → $65, week 2 → $80, week 3 → $95. Find his rate, start, and equation.
🔒 5 more prompts across all three release tiers are in the full lesson. See plans →
Worked solutions and scaffolds for every prompt are in the downloadable kit, included with membership. See plans and pricing.
Exit ticket
- A saver logs week 3 → $80 and week 7 → $140. Find the rate and starting amount, and write the equation.
🔒 2 more exit-ticket questions are in the full lesson. See plans →
Worked answers, the completed answer tables, and the scoring rubric are in the downloadable kit, included with membership. See plans and pricing.
Printable handouts in the kit
All handouts are in Printable_Handouts.pdf inside the kit download.
Materials and classroom resources
Student experience
Students enter through a low-floor prompt, build or sketch a model, test a strategy, revise their thinking, collaborate, and present a final solution. The task remains accessible while allowing for sophisticated reasoning.
Detailed facilitation notes
- Step 1: Model one saver as a table, graph and equation. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 2: Find rate and start from a table. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 3: Find rate and start from two data points. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 4: Predict a goal date. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
Differentiation and inclusion
Support: One saver at a time, whole-dollar rates, y-intercepts visible at week 0. Extend by comparing two savers — which is Phone Plan Showdown's opening move.
Language support: “I started by…”, “My model shows…”, and “I know my answer is reasonable because…”.
Extension: Require a second solution, alter a condition, or have students write a challenge for another group.
Accessibility: Manipulatives, enlarged visuals, oral response choices, partner reading, and reduced-copy student pages.
Assessment plan
Formative checks: Strategy choice, accuracy, representation, collaboration, and explanation.
End evidence: One equation built from two points, with both numbers interpreted.
Mastery: The student completes the task accurately and explains the strategy with limited prompting.