Students double a triangle with a turned copy to make a parallelogram, see why A = ½bh, find heights that fall outside obtuse triangles, and work backwards from an area (AC9M7M01, 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 parallelogram area (previous lesson).
The one idea: two copies of a triangle make a parallelogram with the same base and height, so the triangle is half. The common mistake is forgetting the half (Omar's mistake). Obtuse triangles have a height outside the shape, onto the base extended.
Working backwards from an area to a height (doubling before dividing). Ask students to write ½ × 8 × h = 20 and undo one step at a time, rather than giving them the rule.
| What you will see | A question to ask | The fix |
|---|---|---|
| A student forgets to halve (Omar's mistake). | What shape has area base × height? | Two triangles make that parallelogram; one triangle is half. |
| A student says an obtuse triangle has no height. | Where would a plumb line from the top land? | Extend the base; the height meets it at a right angle. |
| A student uses the sloping side of a right-angled triangle. | Which two sides meet at the right angle? | Those two are a base and its height. |
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: Draw four different triangles on squared paper with area 12 cm², including one with its height outside.
Support: Use the board for every triangle, and cut paper triangles in half pairs.
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 of triangles". The idea: Deriving the triangle area formula: I can Students understand why the area of a triangle is half the area of a related rectangle or parallelogram, and can state the formula A = ½bh. What understanding looks like: - States the area formula for a triangle and explains its derivation. - Correctly identifies the base and corresponding perpendicular height. - Does not confuse the slant side with the perpendicular height. Mistakes students often make here: - A student forgets to halve (Omar's mistake). - A student says an obtuse triangle has no height. - A student uses the sloping side of a right-angled triangle. 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 "Area of triangles".
A triangle has base 9 cm and height 6 cm. Find its area. A triangle with area 24 cm² has base 8 cm: find its height.
½ × 9 × 6 = 27 cm². ½ × 8 × h = 24, so h = 6 cm.
Next: Area problems (node 2): choosing the base and height, units, and shapes made of rectangles and triangles.
Where it leads: area of trapeziums (Year 8), and the cross-section of triangular prisms (Volume).