Students use V = Ah for rectangular and triangular prisms, work backwards to missing lengths, and solve capacity problems in context (AC9M8M02, 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 10 min · Modify 10 min · Practise and Make 12 min
Do the Run board yourself first. Students need volume and capacity conversions (previous lesson) and composite areas.
The one idea: V = A × h for every right prism, where A is the area of the end. The common mistake is using length × width × height on a prism that is not a box (Mia's mistake).
The board's prism is built in layers of the end's area; its triangular prism has a right-triangle end.
Wider: packaging (the box with the least card for a given volume), and finding dimensions for a required capacity.
Deciding which face is the end. Ask students to point to the shape that stays the same all the way along before they calculate.
| What you will see | A question to ask | The fix |
|---|---|---|
| A student multiplies three lengths for a triangular prism. | What shape is the end, and what is its area? | V = area of the end × length. |
| A student mixes m and cm in one problem. | Are all your lengths in the same unit? | Convert first, then calculate. |
| A student multiplies when working backwards. | What times the end's area gives the volume? | Divide the volume by the end's area. |
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: A box must hold 1 L. Which whole-number dimensions use the least card? Compare at least four designs.
Support: Give a printed prism with the end shaded, and a formula card V = A × h.
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 "Prism problems". The idea: Solving practical volume and capacity problems: I can Students solve practical problems involving volume and capacity of right prisms, including optimisation and multi-step contexts. What understanding looks like: - Selects and applies the correct formula for the prism type. - Interprets the result in context with appropriate units. - Identifies which measurements are relevant to the problem. Mistakes students often make here: - A student multiplies three lengths for a triangular prism. - A student mixes m and cm in one problem. - A student multiplies when working backwards. 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 (Unit relationships between volume and capacity), 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 "Prism problems".
A tank with a 2 m by 1.5 m base holds 4500 L. How deep is the water?
4500 L = 4.5 m³; 4.5 ÷ 3 = 1.5 m.
This completes AC9M8M02.
Where it leads: cylinders (Year 9), surface area of prisms, and rates of filling (Rates).