Smoothie Bar Ratios
The smoothie bar's house blend is 3 parts strawberry to 2 parts mango — and every order size, price, and rival recipe question comes down to for-every reasoning. Students build ratio language, extract both unit rates, and scale recipes with equivalent-ratio tables.
Common Core standards covered
- 6.RP.A.1Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”
- 6.RP.A.2Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”
- 6.RP.A.3Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
- 6.RP.A.3.aMake tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
- 6.RP.A.3.bSolve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
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Teacher-facing overview
Big idea: Use ratio language to describe relationships, compute the unit rates associated with a ratio, and solve problems with equivalent-ratio tables.
Student target: “I can describe a ratio in words and symbols, compute both of its unit rates, and use equivalent-ratio tables to scale recipes and prices.”
Success criteria: I can write a ratio three ways and say its for-every sentence. · I can compute both unit rates a/b and b/a and match each to its question. · I can build an equivalent-ratio table and find missing values. · I can use a unit price to cost any order.
Essential question
A recipe isn't an amount — it's a RELATIONSHIP. What does 3:2 promise about every batch, glass, and gallon the bar will ever pour?
Learning target: I can describe a ratio in words and symbols, compute both of its unit rates, and use equivalent-ratio tables to scale recipes and prices.
Success criteria
- I can write a ratio three ways and say its for-every sentence.
- I can compute both unit rates a/b and b/a and match each to its question.
- I can build an equivalent-ratio table and find missing values.
- I can use a unit price to cost any order.
Why this matters
6.RP.A.1-2 is the front door of the entire middle school arc: the for-every sentence becomes Grade 7's constant of proportionality and Grade 8's slope. Getting BOTH unit rates out of one ratio — and knowing which question each answers — is the flexibility everything downstream assumes. The table habit (multiply both, never add) is where proportional reasoning splits from additive thinking, the single most consequential fork in middle school math.
Students should already be able to
- Multiplication and division fluency.
- Fractions as division.
- Reading simple tables.
Vocabulary to define explicitly
- Ratio
A for-every relationship between two quantities.
Example: 3:2 — three cups of strawberry FOR EVERY two of mango.
Not an example: '5 cups of fruit' is an amount, not a relationship.
🔒 3 more terms with examples and non-examples — Unit rate (a/b), Equivalent ratios, Ratio table — 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 sentences.
- Table factors during bar shift.
- The rival verdict.
Summative — the graded evidence: The exit ticket (language, both rates, a scale), scored with the four-criterion rubric.
The task students work on
The class runs the smoothie bar for the fair. HOUSE BLEND: 3 cups strawberry for every 2 cups mango. ORDERS: scale the blend for batches using 6, 9, and 30 cups of strawberry. THE FLIP: a supplier asks 'how much mango per cup of strawberry?' — the other unit rate. PRICING: $75 bought 15 smoothies' worth of fruit — the unit cost, and the cost of 40 smoothies. RIVAL CHECK: the stand next door blends 4:3 — is that the same drink? Prove it with the table.
Bar worksheet — for-every sentences required.
| Job | Work | Answer |
|---|---|---|
| Blend, three ways | ||
| Unit rate: strawberry per mango | ||
| Unit rate: mango per strawberry | ||
| Batches: 6, 9, 30 cups strawberry | ||
| Unit price from $75 / 15 | ||
| Rival 4:3 — same drink? |
Anticipated student strategies
Language first, scaling second, unit rates third — the sentence gives meaning, the table gives power, the division gives precision.
- For-every sentences. The student narrates every ratio as 'a of this for every b of that' before computing.
The language IS the concept — share first and require it on every row.
🔒 2 more anticipated strategies with select-and-sequence guidance are in the full lesson. See plans →
Lesson script
Collect: 3 strawberry per 2 mango; 2 mango per 3 strawberry; 3 of 5 cups are strawberry. Board the three notations: 3:2, 3 to 2, 3/2. The relationship, not the amounts, is the recipe.
Listen for: Yes — 18:12 scales down to 3:2. Same for-every, bigger pitcher.
Then the money: $75 for 15 smoothies → 75 ÷ 15 = $5 each — a unit rate wearing a price tag. Cost of 40: 40 × 5 = $200.
- Every unit rate names its per-one.
- Unit price = total ÷ count; then any order is one multiplication.
Listen for: When strawberry is the known amount — the question picks the rate, like walls-per-hour vs hours-per-wall.
🔒 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
- “4:3 is the same as 3:2 — just one more of each.” Scale to matching strawberry: 12:8 vs 12:9. Adding the same number to both parts feeds mango faster than the recipe allows — ratios scale by multiplying.
- “A ratio has one unit rate.” — the teacher response is in the full lesson.
- “3:2 means 3 cups and 2 cups, period.” — the teacher response is in the full lesson.
- “Bigger numbers mean a stronger ratio.” — 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 doThe blend is 3 strawberry : 2 mango. Write it three ways, give the for-every sentence, and find both unit rates.
🔒 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 trail mix uses 5 cups peanuts for every 2 cups raisins. Write the ratio two ways and give the for-every sentence.
🔒 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: Describe the blend in ratio language, all forms. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 2: Extract both unit rates and say what each answers. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 3: Scale the recipe with an equivalent-ratio table. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 4: Price the menu with unit rates. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
Differentiation and inclusion
Support: Color-cup diagrams ground the ratio; extend with the rival-recipe comparison and the plotted table.
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 recipe scaled by table, plus both unit rates stated with for-every sentences.
Mastery: The student completes the task accurately and explains the strategy with limited prompting.