Students solve area problems by choosing the base and perpendicular height, converting to one unit, and splitting composite shapes into rectangles and triangles (adding or subtracting parts), with reasoning they own (AC9M7M01, 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 15 min · Modify 12 min · Practise and Make 10 min
Do the Run board yourself first. Students need the parallelogram and triangle formulas (previous lessons) and converting cm and m.
The one idea: choose, convert, split. The common mistake is multiplying lengths in different units (Ivy's mistake); extra information (slanted sides) is planted in several tasks. 1 m² = 10 000 cm² surprises most students.
The house-wall task is a reasoning check: the working is never marked, only the final area and the reason for the roof step.
Planning a composite area before calculating. Ask students to sketch the parts and label each with its own lengths first; resist giving the split.
| What you will see | A question to ask | The fix |
|---|---|---|
| A student multiplies cm by m (Ivy's mistake). | What unit is each length in? | Change both to metres (or both to cm) first. |
| A student uses every number given. | Which lengths meet at a right angle? | Use the base and its height; ignore slanted sides. |
| A student cannot start a composite shape. | Can you see a rectangle and a triangle in it? | Sketch the parts, find each area, then add (or subtract a missing part). |
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 the area of the letter L, T or H drawn on squared paper in two different ways (adding parts, and subtracting from a rectangle).
Support: Use squared paper; convert all lengths to the smaller unit and write them on the sketch.
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 "Area problems". The idea: Applying area formulas to triangles and parallelograms: I can Students calculate the area of triangles and parallelograms using established formulas, selecting appropriate units. What understanding looks like: - Correctly calculates the area of a triangle using A = ½bh. - Correctly calculates the area of a parallelogram. - Uses appropriate units and converts if necessary. Mistakes students often make here: - A student multiplies cm by m (Ivy's mistake). - A student uses every number given. - A student cannot start a composite shape. 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 (Deriving the triangle area formula), 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 "Area problems".
A shape is a 7 m by 4 m rectangle with a triangle on top (base 7 m, height 2 m). Find its area.
28 + ½ × 7 × 2 = 28 + 7 = 35 m².
Next: Volume (AC9M7M02): the area of the base times the height.
Where it leads: area of trapeziums, circles and composite shapes with circles (Year 8), and surface area (Year 9).