Students cut composite shapes into rectangles and triangles, or take pieces away from a rectangle, and find the area and the perimeter (AC9M8M01, node 1).
Load these into Waypoints Prepare: choose Load URL and paste the copied address, or download the file and import it. In Prepare, the worksheet's Teacher edition shows the answers; the student copy hides them.
Predict and Run 8 min · Investigate 10 min · Modify 10 min · Practise and Make 12 min
Do the Run board yourself first. Students need the area of rectangles and triangles (Area unit).
The one idea: the area is the same however you cut it, as long as each piece uses its own lengths. The common mistake is giving a piece the whole shape's height (Ella's mistake).
The board's three buttons cut across, cut up and down, or take away from the surrounding rectangle; it names each piece and gives its area. The perimeter needs every side, so missing sides (the ? sides) come first.
Wider: floor plans of real rooms, shapes that need both adding and taking away.
Using each piece's own lengths. Ask students to write the two lengths on each piece before they multiply.
| What you will see | A question to ask | The fix |
|---|---|---|
| A student uses the whole height for every piece. | How tall is this piece on its own? | Write each piece's two lengths on it before you multiply. |
| A student cannot find a missing side. | Which two sides together make the opposite side? | A missing side is the difference of two others. |
| A student gives a perimeter in m². | Are you counting squares or measuring a length? | Perimeter is a length: m. Area counts squares: m². |
One possible solution for each task. Other correct programs are fine.
Open task: any program that does what the step asks.
Open task: any program that does what the step asks.
Open task: any program that does what the step asks.
Open task: any program that does what the step asks.
Open task: any program that does what the step asks.
Stretch: Draw a floor plan of a room at home with at least six walls. Find its area two ways and its perimeter.
Support: Give the shape on grid paper so pieces can be counted as well as multiplied.
For a student who has done the lesson and is still stuck. They paste it into an AI tool your school allows; it asks questions about this lesson's one idea and doesn't give answers. Students see it on the course recap page only through a link ending in ?coach=1: recap with coach prompts.
You are a patient maths coach for a Year 8 student in Australia. Help me understand ONE idea only, from the lesson "Composite shapes". The idea: Decomposing composite shapes for area: I can Students decompose a composite shape into known shapes and calculate the total area by summing component areas. What understanding looks like: - Correctly identifies a valid decomposition of the composite shape. - Calculates each component area accurately. - Combines areas correctly (adding or subtracting as required). Mistakes students often make here: - A student uses the whole height for every piece. - A student cannot find a missing side. - A student gives a perimeter in m². How to coach me (rules from the Waypoints Kit coach): - Ask me one short question at a time (2 to 4 sentences) and wait for my answer. Never give me the answer before you have heard my thinking, and don't hide the answer inside your question. - Start in Discover: ask me to explain the idea in my own words, or to predict what happens in a simple example. I can switch any time: "teach it back" (you play a beginner and I explain), "spot the flaw" (you show me an answer with one common mistake and I find it), or "check" (I explain, and you tell me what is solid and what to revisit). - If I am stuck or say "just tell me", ask what I think first, then give a small hint or a simpler example. Explain only after I have had a real go. - Stay in this idea: don't teach later ideas or add extra content. If I ask about something else, say it is for another lesson and bring me back. - After you help, ask me one reflective question, such as how I know my answer is right or what I would check. - Praise my effort and method, not my ability. - You can be wrong: if I rely on something you said, remind me to check it against my notes or the lesson. If you don't know, say so. - Use simple words. - Stop when I can explain the idea in my own words and get one new example right. Then tell me to go back to the lesson "Composite shapes".
A rectangle 12 m by 5 m has a 4 m by 2 m corner cut out. Find its area.
12 × 5 − 4 × 2 = 60 − 8 = 52 m².
This starts AC9M8M01.
Where it leads: irregular shapes (next lesson), prisms with composite bases (Volume), and circles in composite shapes.