Water Tank Works
Students size the town's water tanks — one cylinder, cone or sphere at a time with step-boxed formulas — the gentler alternative to the Ice Cream Container value showdown.
Common Core standards covered
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Teacher-facing overview
Big idea: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world problems.
Student target: “I can compute the volume of a cylinder, cone, and sphere using the step box: identify r and h, square or cube, multiply, keep π, then estimate.”
Success criteria: I can pick the right formula for each tank shape. · I can run the step box: r and h → r² (or r³) → multiply → exact π-form → decimal estimate. · I can halve a diameter before anything else. · I can answer a capacity question in cubic meters with both forms.
Essential question
The town needs to know what its tanks hold — without filling a single one. What do the three formulas each need from you?
Learning target: I can compute the volume of a cylinder, cone, and sphere using the step box: identify r and h, square or cube, multiply, keep π, then estimate.
Success criteria
- I can pick the right formula for each tank shape.
- I can run the step box: r and h → r² (or r³) → multiply → exact π-form → decimal estimate.
- I can halve a diameter before anything else.
- I can answer a capacity question in cubic meters with both forms.
Why this matters
Same standard as the Ice Cream Container Challenge, half the moving parts: one tank at a time, a fixed step order, and radii chosen so the arithmetic never upstages the formula. The step box is scaffolding with a plan — by the last card students are running it mentally, which is exactly the fluency the value-comparison lesson assumes on day one.
Students should already be able to
- Area of a circle, πr².
- Squaring and cubing small numbers.
- π ≈ 3.14 as an approximation — Hunting for Irrational Numbers.
Vocabulary to define explicitly
- Cylinder formula
V = πr²h — circle base, straight sides.
Example: r = 2, h = 5: V = π · 4 · 5 = 20π ≈ 62.8 m³.
Not an example: π · 2 · 5 skips the squaring — that computes with the radius, not the base area.
🔒 3 more terms with examples and non-examples — Cone formula, Sphere formula, The step box — 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 shape sort.
- Step boxes during crew work — order and the halving step.
- Coefficient comparisons in the department review.
Summative — the graded evidence: The exit ticket (three solids, both forms), scored with the four-criterion rubric.
The task students work on
The town water department maintains four tanks: the Main (a cylinder, r = 2 m, h = 5 m), the Funnel (a cone used for filling trucks, r = 3 m, h = 4 m), the Ball (a spherical tower tank, r = 3 m), and the Reserve (a cylinder specified by DIAMETER: 8 m across, 10 m tall). Your crew computes each capacity in exact π-form and in cubic meters, then answers the department's questions — including whether the Ball outholds the Funnel.
Capacity log — run the step box on every tank.
| Tank | Shape | r (m) | Formula with values | Exact | ≈ m³ |
|---|---|---|---|---|---|
| Main | cylinder | 2 | |||
| Funnel | cone | 3 | |||
| Ball | sphere | 3 | |||
| Reserve | cylinder | ? |
Anticipated student strategies
The step box builds the habit, the coefficient comparison shows why exact form earns its keep, and the bench card fades as the cards proceed. Scaffold, payoff, release.
- Run the step box. The student fills each labeled step in order: r = 2 → r² = 4 → × h = 20 → 20π → ≈ 62.8 m³.
The scaffold doing its job. Share first and keep the boxes visible until they're internalized.
🔒 2 more anticipated strategies with select-and-sequence guidance are in the full lesson. See plans →
Lesson script
Cylinders to πr²h, the cone to its third, the sphere to (4/3)πr³ — no h, because a ball's size is set by r alone. The sort is the whole warm-up; numbers wait.
Listen for: The others get their third dimension from h. The sphere has no h — r covers all three directions, so it appears three times.
Repeat compressed for the Funnel: (1/3)π · 9 · 4 = 12π ≈ 37.7, narrating the third as the pour test from the ice-cream lesson's warm-up. The steps stay in the same order every time.
- Exact form before estimate, every tank.
- Units: cubic meters, because water fills three dimensions.
Listen for: Step one — identify. Halve the diameter before anything gets squared, or every later step inherits the error.
🔒 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
- “8 m across means r = 8.” 'Across' is the diameter. Halve first: r = 4. The error quadruples r² — check the two capacities and see.
- “The sphere needs a height.” — the teacher response is in the full lesson.
- “Skip the π-form; decimals are the real answer.” — the teacher response is in the full lesson.
- “r² means r × 2.” — 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 doThe Main tank: cylinder, r = 2 m, h = 5 m. Run the step box.
🔒 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
- A cylinder tank: r = 3 m, h = 4 m. Volume, exact and estimate.
🔒 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: Fill in the three formulas on the bench card. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 2: Compute one cylinder step by step. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 3: Compute a cone and a sphere. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 4: Answer the town's capacity questions. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
Differentiation and inclusion
Support: Each computation runs in a labeled step box (radius → r² or r³ → multiply → π-form → estimate); radii stay small and given directly at first. Extend with a diameter spec and a capacity comparison.
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 volume of each solid with the steps shown.
Mastery: The student completes the task accurately and explains the strategy with limited prompting.