Students drag triangles on a dot grid and see them named by sides (scalene, isosceles, equilateral) and by angles (acute, right, obtuse), combine the two names, and reason about impossible pairs (AC9M7SP02, 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 triangle angle sum (Angles in a triangle) and the words acute, right and obtuse for angles.
The one idea: every triangle has a sides name and an angles name, and equal sides sit opposite equal angles. The common mistake is naming by any acute angle (Zara's mistake): every triangle has at least two.
A square grid cannot make an exact equilateral triangle; the board counts sides within 2% as equal and says so.
Making a triangle with two names at once on the board. Ask students to say which name they will fix first and what has to stay true while they fix the second, rather than moving corners for them.
| What you will see | A question to ask | The fix |
|---|---|---|
| A student calls a triangle acute because it has an acute angle (Zara's mistake). | Which is the biggest angle? | The biggest angle decides: under 90° acute, 90° right, over 90° obtuse. |
| A student gives only one name. | What do the sides say, and what do the angles say? | Name the sides first, then the biggest angle. |
| A student thinks a right-angled triangle can't be isosceles. | What happens if you cut a square along its diagonal? | Two equal sides at the right angle: 45°, 45°, 90°. |
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: List all nine pairs (3 side names × 3 angle names). Which are possible? Sketch each possible one.
Support: Keep a two-column table on the board: sides names and angles names with a picture of each.
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 "Classifying triangles". The idea: Classifying triangles by sides and angles: I can Students classify triangles as scalene, isosceles or equilateral (by sides) and as acute, right-angled or obtuse (by angles), and understand that these classifications are independent. What understanding looks like: - Correctly classifies a triangle by both side and angle properties. - Understands that the two classifications are independent. - Does not assume equilateral means right-angled. Mistakes students often make here: - A student calls a triangle acute because it has an acute angle (Zara's mistake). - A student gives only one name. - A student thinks a right-angled triangle can't be isosceles. 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 "Classifying triangles".
A triangle has angles 30°, 30° and 120°. Name it by its sides and its angles.
Isosceles (two equal angles, so two equal sides) and obtuse (120°).
Next: The quadrilateral family (node 2).
Where it leads: Pythagoras' theorem (Year 8) for right-angled triangles, and congruent and similar triangles (Years 8 and 9).