Students build triangular prisms in layers, find volume as cross-section area × length for any right prism, and link volume to capacity (1 cm³ = 1 mL, 1000 cm³ = 1 L) (AC9M7M02, node 2).
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 12 min · Modify 10 min · Practise and Make 10 min
Do the Run board yourself first. Students need V = A × h for boxes (previous lesson) and triangle area (Area unit).
The one idea: every right prism is its cross-section repeated along its length, so V = cross-section area × length. The common mistake is forgetting the triangle's half (Lena's mistake, a spiral of the triangles lesson). Capacity conversions (mL, L) are new.
Spotting the cross-section of a prism lying on its side. Ask students to imagine slicing it like bread and describe the slice, rather than pointing to the face for them.
| What you will see | A question to ask | The fix |
|---|---|---|
| A student multiplies the three lengths of a triangular prism (Lena's mistake). | What shape is the slice? What is its area? | Halve for the triangle, then multiply by the length. |
| A student calls the face it stands on the cross-section. | If you slice it like bread, what shape is each slice? | The cross-section is the slice that repeats. |
| A student divides by 100 for litres. | How many mL in a litre? | 1000 mL = 1 L, and 1 cm³ = 1 mL. |
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.
Open task: any program that does what the step asks.
Stretch: A swimming pool is a prism whose cross-section is a trapezium (shallow to deep end). Estimate how many litres it holds.
Support: Use real prisms and slices of play dough; write the cross-section area first, every time.
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 7 student in Australia. Help me understand ONE idea only, from the lesson "Prisms and capacity". The idea: Calculating volume of rectangular and triangular prisms: I can Students calculate the volume of rectangular and triangular right prisms using V = Ah with appropriate units. What understanding looks like: - Correctly calculates volume for both rectangular and triangular prisms. - Uses appropriate cubic units. - Converts between units where required (e.g. cm³ to litres). Mistakes students often make here: - A student multiplies the three lengths of a triangular prism (Lena's mistake). - A student calls the face it stands on the cross-section. - A student divides by 100 for litres. 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. - If I seem to be missing the idea that comes before this one (Volume as cross-section area times height), check it quickly, then come back. - 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 "Prisms and capacity".
A prism's triangle end has base 5 cm and height 4 cm; it is 6 cm long. Find its volume and its capacity in mL.
½ × 5 × 4 = 10 cm², × 6 = 60 cm³ = 60 mL.
Next: Circles (AC9M7M03).
Where it leads: volume of cylinders (Year 9), where the cross-section is a circle, and surface area of prisms.