The Clubhouse Build
One clubhouse, four jobs: a five-sided deck measured by decomposition, a floor plan drawn on coordinates, a storage chest packed with half-foot cubes until V = lwh confesses, and a paint box unfolded into a net that adds up its own surface area.
Common Core standards covered
- 6.G.A.1Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
- 6.G.A.2Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
- 6.G.A.3Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.
- 6.G.A.4Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.
© Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
Teacher-facing overview
Big idea: Find areas by composing and decomposing into triangles and rectangles, find fractional-edge prism volumes by packing and by formula, draw polygons from coordinates and measure their sides, and use nets to find surface area.
Student target: “I can decompose polygons for area, use coordinates to draw and measure figures, justify V = lwh with fractional edges by packing, and compute surface area from a net.”
Success criteria: I can split a polygon into rectangles and triangles and total the area. · I can plot a polygon from coordinates and measure gridline sides. · I can find a fractional-edge volume by packing AND by formula, matching answers. · I can unfold a prism into a net and sum the faces.
Essential question
No formula exists for a five-sided deck, a fractional chest used to break the cube-counting rule, and a box hides its faces. How do decomposing, packing, and unfolding solve all three?
Learning target: I can decompose polygons for area, use coordinates to draw and measure figures, justify V = lwh with fractional edges by packing, and compute surface area from a net.
Success criteria
- I can split a polygon into rectangles and triangles and total the area.
- I can plot a polygon from coordinates and measure gridline sides.
- I can find a fractional-edge volume by packing AND by formula, matching answers.
- I can unfold a prism into a net and sum the faces.
Why this matters
6.G.A is one strategy taught four ways: reduce the unknown to knowns. Decomposition (A.1) becomes Grade 7's Ramp Works; the coordinate polygon (A.3) fuses the City Grid with area; the packing argument (A.2) is the rare standard that demands a formula be JUSTIFIED, not just used — fractional edges and all; and nets (A.4) make surface area un-forgettable because every face is physically there. This unit is the measurement backbone of the next two grades.
Students should already be able to
- Rectangle and triangle areas.
- Coordinate plotting and |difference| distances — The City Grid.
- Fraction multiplication — The Serving Scoop.
Vocabulary to define explicitly
- Decomposition (area)
Splitting a figure into known pieces whose areas add.
Example: The pentagon deck = a 6×4 rectangle + a triangle roof-peak: 24 + 6 = 30.
Not an example: Multiplying the two biggest sides — pentagons don't have an lw.
🔒 3 more terms with examples and non-examples — Coordinate side length, Packing argument (fractional volume), Net (surface area) — 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 seam hunt.
- Build-sheet methods during floor work.
- The finer-cubes generalization.
Summative — the graded evidence: The exit ticket (area, volume, SA), scored with the four-criterion rubric.
The task students work on
The club builds its headquarters. THE DECK (A.1 + A.3): the plan's vertices are (1,1), (7,1), (7,5), (4,7), (1,5) — plot it, measure the gridline sides by coordinates, split it into a rectangle and a triangle, and total the area. THE CHEST (A.2): the storage chest is 2½ ft × 2 ft × 1½ ft — pack it with ½-ft cubes (how many fit along each edge?), count the cubes, multiply by each cube's volume, then check that V = lwh lands identically. THE PAINT BOX (A.4): a 3 × 2 × 1 unit box — unfold it into a net, label all six faces, and total the surface area.
Build sheet — method shown before number.
| Job | Method | Work | Result |
|---|---|---|---|
| Deck sides from coordinates | |||
| Deck area | |||
| Chest volume by packing | |||
| Chest volume by formula | |||
| Paint box surface area |
Anticipated student strategies
Coordinates give the deck its numbers, the seam gives it pieces, the packing earns the formula, and the fold certifies the net — every answer grounded in something checkable.
- Seam-hunting. The student looks for the horizontal seam that splits the pentagon into rectangle + triangle.
Decomposition begins with WHERE to cut — the seam at y = 5 is visible in the coordinates themselves.
🔒 2 more anticipated strategies with select-and-sequence guidance are in the full lesson. See plans →
Lesson script
Split it into shapes we own — the class finds the seam. Strategy named: compose or decompose until every piece is a rectangle or triangle. It carried the Ramp Works... it will carry Grade 7; today it carries the deck.
Listen for: Two vertices share y = 5 — a horizontal seam already drawn in the numbers. Coordinates carry structure, not just position.
The triangle's height clarified: from y = 5 up to y = 7 is |7 − 5| = 2 — heights are gridline distances too.
- Gridline sides: |difference| of the unshared coordinate.
- Decomposition totals: pieces must tile without gap or overlap.
Listen for: Yes: the 6×6 box minus two corner triangles... both routes land 30. Compose and decompose are one strategy facing opposite ways.
🔒 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 deck's area is 6 × 7 — length times height.” That boxes the roof's empty corners in. Decompose: 24 + 6 = 30, or box-and-subtract the two corner triangles — both honest routes agree.
- “V = lwh only works for whole-number edges.” — the teacher response is in the full lesson.
- “Surface area is length × width × 6.” — the teacher response is in the full lesson.
- “Coordinate sides need a ruler.” — 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 doPlot the deck — (1,1), (7,1), (7,5), (4,7), (1,5) — measure its base and walls by coordinates, and find its area by decomposition.
🔒 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 triangle has base 10 and height 4. Area?
🔒 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: Decompose the deck into a rectangle and triangle. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 2: Plot the floor plan and measure sides by coordinates. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 3: Pack the chest with half-foot cubes; confirm with lwh. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 4: Unfold the paint box into a net and sum its faces. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
Differentiation and inclusion
Support: Physical cubes and cut-out nets ground A.2 and A.4; extend with the packing-count argument and the design-your-own deck.
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 decomposition area, one coordinate side-length, one fractional volume both ways, and one net-based surface area.
Mastery: The student completes the task accurately and explains the strategy with limited prompting.