Students build rectangular prisms from layers of unit cubes, see that each layer is the base area, and use V = A × h with cubic units, including working backwards to a missing length (AC9M7M02, 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 12 min · Modify 10 min · Practise and Make 10 min
Do the Run board yourself first. Students need the area of a rectangle (Area unit) and multiplying decimals.
The one idea: a prism fills up in layers, each a copy of the base, so V = A × h. The common mistake is counting only the outside (Finn's mistake), or adding the faces (a surface area). Cubic units (cm³) are new.
Seeing the box as full, not a shell of faces. Ask students to describe the hidden middle layer before they calculate, instead of counting for them.
| What you will see | A question to ask | The fix |
|---|---|---|
| A student counts only the cubes or squares they can see (Finn's mistake). | What is under the top layer? | Every layer is full: count one layer, then the layers. |
| A student adds the three lengths. | How many cubes in one layer? | Multiply length × width for a layer, then × height. |
| A student writes cm² for a volume. | Are we counting squares or cubes? | Cubes: cm³. |
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: Find every box made of 24 unit cubes (whole-number sides). Which has the least outside surface?
Support: Build with real cubes; use the board's layers for every question.
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 "Volume in layers". The idea: Volume as cross-section area times height: I can Students understand that the volume of any right prism equals the area of its cross-section multiplied by its height. What understanding looks like: - States that V = Ah for right prisms and explains what A and h represent. - Correctly identifies the cross-section and its area for a given prism. - Does not confuse the total surface area with the cross-sectional area. Mistakes students often make here: - A student counts only the cubes or squares they can see (Finn's mistake). - A student adds the three lengths. - A student writes cm² for a volume. 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 "Volume in layers".
A box is 5 cm by 4 cm by 3 cm. Find its volume. A box with base 6 cm² has volume 42 cm³: how high is it?
5 × 4 × 3 = 60 cm³. 42 ÷ 6 = 7 cm.
Next: Prisms (node 2): triangular prisms and capacity.
Where it leads: volume of cylinders (Year 9: the circle's area times the height), and surface area.