Food Truck Friday
Students run the books for a smoothie truck's best and worst days — profits split three ways, a loss shared fairly, complex-fraction recipes, and a freezer that warms by fractions of a degree. All four rational-number operations, with money on the line.
Common Core standards covered
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Teacher-facing overview
Big idea: Solve real-world and mathematical problems involving the four operations with rational numbers, including computations with complex fractions.
Student target: “I can solve multi-step problems with rational numbers in any form, choosing operations from context, computing exactly, and checking against an estimate.”
Success criteria: I can estimate before computing and use the estimate as a check. · I can combine decimals with all four operations in a money context. · I can divide by a fraction (including complex fractions) in context. · I can interpret signed results — a negative share is money owed.
Essential question
A real business day mixes decimals, fractions, and negatives in one ledger. How do you pick the operation — and how do you know your answer is even reasonable?
Learning target: I can solve multi-step problems with rational numbers in any form, choosing operations from context, computing exactly, and checking against an estimate.
Success criteria
- I can estimate before computing and use the estimate as a check.
- I can combine decimals with all four operations in a money context.
- I can divide by a fraction (including complex fractions) in context.
- I can interpret signed results — a negative share is money owed.
Why this matters
7.NS.A.3 is where the number system stops being exercises and becomes a toolkit: no card in this ledger says which operation to use, and the numbers arrive in every form at once — the exact situation of real life and of 7.EE.B.3 one unit from now. The estimate-first ritual is the standard's own habit ('assess the reasonableness of answers'), and the loss-day division makes the signed arithmetic from The Salvage Dive earn money-world meaning.
Students should already be able to
- All four operations on signed numbers — Subzero Expedition and The Salvage Dive.
- Fraction division as multiply-by-reciprocal.
- Decimal arithmetic with money.
Vocabulary to define explicitly
- Profit and loss
Revenue minus costs; positive is profit, negative is loss — one subtraction covers both.
Example: $89.25 in, $132.75 out: 89.25 − 132.75 = −$43.50, a loss.
Not an example: Treating a loss as 'no profit' ($0) hides real money — the −$43.50 must be paid.
🔒 3 more terms with examples and non-examples — Fair share, Complex fraction, Estimate as a check — 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 ballparks and the ≈140-vs-137.25 comparison.
- Ledger columns during floor work — estimate and meaning columns especially.
- The Tuesday cash-box discussion.
Summative — the graded evidence: The exit ticket (profit-and-split, fraction division, signed share), scored with the four-criterion rubric.
The task students work on
Three friends run the Blend on Wheels smoothie truck. Friday was the best day ever: $348.50 of revenue against $127.75 in supplies, $38.50 in fuel, and a $45 permit — profit to be split three ways. Rain-day Tuesday was the worst: $89.25 in, $132.75 out, with only two partners working, sharing the damage. The kitchen has its own math: 10 1/2 cups of berries at 3/4 cup per smoothie, mangoes at $5.40 for 2 1/4 pounds, and a freezer at −18.5°C warming 3/4 of a degree every hour for 6 hours during a power flicker. Your team keeps the ledger: estimate, compute, interpret — every line.
Truck ledger — estimate before you compute.
| Entry | Numbers | Estimate | Exact | Meaning |
|---|---|---|---|---|
| Friday profit | 348.50 − (127.75 + 38.50 + 45) | |||
| Friday split (3 partners) | profit ÷ 3 | |||
| Tuesday result | 89.25 − 132.75 | |||
| Tuesday split (2 partners) | result ÷ 2 | |||
| Smoothies from berries | (21/2) ÷ (3/4) | |||
| Freezer after 6 h | −18.5 + 6 × 3/4 |
Anticipated student strategies
Estimation first because it disciplines everything after; units second because they choose the operation; the signed ledger last as the unifying notation.
- Estimate-then-verify. The student rounds every number to friendly values, computes a ballpark, then computes exactly and compares.
The ritual the standard names. Share first and enforce the ORDER — estimates written before exact work begins.
🔒 2 more anticipated strategies with select-and-sequence guidance are in the full lesson. See plans →
Lesson script
Collect estimates (≈ $350 − $210 = $140). Then compute: costs total 127.75 + 38.50 + 45 = 211.25; profit 348.50 − 211.25 = $137.25. The estimate certified it. Name the ritual: every ledger line today gets a ballpark first.
Listen for: Recheck immediately — off by a factor of ten from the ballpark means a dropped digit or misplaced decimal, and the estimate is what catches it.
Board the operation-choice chart: TOTAL from parts → add; DIFFERENCE or change → subtract; SAME thing repeated → multiply; SHARING or how-many-fit → divide. The berry problem is how-many-fit wearing fraction clothes.
- Losses split like profits — division carries the sign.
- Dividing by a fraction: multiply by the reciprocal, and let the units confirm the choice.
Listen for: Dividing by a number less than 1 asks how many small pieces fit — and small pieces fit many times. 'Division shrinks' was only ever true for divisors over 1.
🔒 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
- “A loss day just means everyone gets $0.” The $43.50 shortfall is real money the truck owes. Split it: −21.75 each. Negative shares are payments in, and pretending otherwise breaks the books.
- “Dividing always makes the answer smaller.” — the teacher response is in the full lesson.
- “Estimate after computing, to 'check the work.'” — the teacher response is in the full lesson.
- “The freezer problem is (−18.5 + 6) × 3/4.” — 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 5 independent.
- I doFriday: $348.50 revenue; costs $127.75, $38.50, $45. Estimate the profit, compute it exactly, and split it three ways.
🔒 6 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
- Saturday: $156.80 in, $94.30 out, two partners. Profit and fair share?
🔒 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: Estimate, then compute Friday's profit. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 2: Split profits — and a loss — fairly. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 3: Divide by fractions for recipes and unit prices. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 4: Audit the week and defend each line. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
Differentiation and inclusion
Support: Estimation-first is the built-in scaffold — every card demands a ballpark before the exact number. Support with the operation-choice chart; extend with the multi-week trend audit.
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 completed truck ledger with every line estimated, computed, and interpreted.
Mastery: The student completes the task accurately and explains the strategy with limited prompting.