The Better Deal
Students compare juice prices given as a graph, a table and a sign, using unit price as slope — a store-aisle alternative to Unit Rate Racing where, for once, the flattest line wins.
Common Core standards covered
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Teacher-facing overview
Big idea: Graph proportional relationships, interpret unit rate as slope, and compare two proportional relationships represented in different ways.
Student target: “I can find the unit price from any representation, see it as the slope of the brand's line, and explain why the LOWEST line is the best deal.”
Success criteria: I can compute price per one liter from a sign, a table, and a graph. · I can graph a brand's line through the origin from its unit price. · I can explain why, on a cost graph, the lowest (flattest) line wins. · I can predict the cost of any order from the unit price.
Essential question
Three juice brands price themselves three different ways — a sign, a table, and a graph. How does a shopper compare them without buying anything?
Learning target: I can find the unit price from any representation, see it as the slope of the brand's line, and explain why the LOWEST line is the best deal.
Success criteria
- I can compute price per one liter from a sign, a table, and a graph.
- I can graph a brand's line through the origin from its unit price.
- I can explain why, on a cost graph, the lowest (flattest) line wins.
- I can predict the cost of any order from the unit price.
Why this matters
This is Unit Rate Racing at the grocery store — the same mathematics with one healthy twist: on a cost graph, the winner is the LOWEST line, which forces students to read axes instead of pattern-matching 'steeper is better.' Unit pricing is also the most-used mathematics in adult life; shelf tags compute it precisely because comparing $6-for-2 against $8.25-for-3 in your head is unfair without it.
Students should already be able to
- Division to find a per-one amount.
- Plotting points in the first quadrant.
- Unit rate as slope — Unit Rate Racing (this is its reteach twin).
Vocabulary to define explicitly
- Unit price
Dollars for exactly ONE liter — the fair-comparison number.
Example: $6 for 2 liters is $3.00 per liter.
Not an example: $6 is not comparable to $2.50 until both become per-liter prices.
🔒 3 more terms with examples and non-examples — Unit price as slope, Lowest line wins, Proportional pricing — are defined in the full lesson. See plans →
Where this shows up outside the classroom
Assessment plan
Formative — for feedback during the lesson
- The warm-up's broken reason, repaired.
- Shopper's logs during the trip: units on every rate.
- The axis-meaning exchange in checkout talk.
Summative — the graded evidence: The exit ticket (two stands, graph reading, prediction), scored with the four-criterion rubric.
The task students work on
Three brands sell the same juice. Brand A's sign: '$6 for 2 liters.' Brand B's table: 1 L → $2.50, 3 L → $7.50, 4 L → $10. Brand C's graph: a line through (0, 0) and (4, 11). You're planning a class party that needs 6 liters — find every unit price, put all three brands on one graph, and buy smart.
Shopper's log — one row per brand.
| Brand | Given as | Unit price ($/L) | Cost of 6 L |
|---|---|---|---|
| A | Sign: $6 for 2 L | ||
| B | Table: 1 → 2.50, 3 → 7.50, 4 → 10 | ||
| C | Graph: line through (4, 11) |
Anticipated student strategies
Per-one first (the life skill), same-order second (the check), the graph last (the connective tissue to slope). The deliberate contrast with Unit Rate Racing — flattest wins, not steepest — is the transfer test.
- Everything to per-liter. The student divides each brand down to one liter — 6 ÷ 2 = 3.00, table's own 2.50, graph's 11 ÷ 4 = 2.75 — and ranks the three numbers.
The shelf-tag strategy. Share first; it is the whole adult skill.
🔒 2 more anticipated strategies with select-and-sequence guidance are in the full lesson. See plans →
Lesson script
The amounts differ — $6 buys TWO liters. Per liter: A is $3.00, B is $2.50. B wins, for the right reason. Name the tool: unit price, dollars per one liter.
Listen for: Fair only when the amounts match. Different amounts need per-one prices — same denominator, fair fight.
Then graph A and B beside C: through the origin, up 3.00 per liter for A, up 2.50 for B. Read the stack: B lowest, C middle, A top. On a COST graph the cheap brand hugs the floor.
- Every brand's line starts at (0, 0): no juice, no charge.
- Steeper = pricier here. Ask what steeper meant when y was meters.
Listen for: The y-axis changed jobs: up meant distance (good), now it means dollars spent (cost). The picture is the same; the meaning lives in the axes.
🔒 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
- “$2.50 is less than $6, so B is cheaper.” Right conclusion, broken reason — the amounts differ. Per liter: 2.50 vs 3.00. The reason must survive a case where it flips.
- “The steepest line is the best, like the racers.” — the teacher response is in the full lesson.
- “Start each brand's line at its first data point.” — the teacher response is in the full lesson.
- “Unit price only matters for 1 liter.” — 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 3 independent.
- I doBrand A's sign says $6 for 2 liters. Find the unit price and the cost of 6 liters.
🔒 4 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
- Lemonade stand X charges $4.50 for 3 cups. Stand Y's graph passes through (2, 3.50). Find both unit prices — which stand is cheaper?
🔒 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: Find unit prices from a sign, a table, and a graph. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 2: Graph all brands on shared axes. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 3: Read the cheapest brand as the lowest line. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 4: Predict costs for a party order. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
Differentiation and inclusion
Support: All unit prices are quarters ($2.50, $2.75, $3.00); the graph is pre-drawn for one brand. Extend with a fourth brand and a bulk-discount twist that breaks proportionality.
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 unit-price comparison across two representations, with the graph explained.
Mastery: The student completes the task accurately and explains the strategy with limited prompting.