Students drag triangles of every shape on a dot grid, see that the three angles always add to 180°, and explain why by tearing off the corners to make a straight line (AC9M7M05, 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 and the tear-off task yourself first. Students should know that angles on a straight line add to 180° (Year 6).
The board measures to the nearest degree and shares out the rounding so the shown angles add to the shown total. With a real protractor, totals of 178° to 182° are normal: say so when students measure by hand (Practise has a question on it).
If you have time, do the paper version too: every student draws a different triangle, tears off the corners and lines them up. Seeing 25 different triangles all make a straight line is the strongest evidence. The formal proof with parallel lines comes with AC9M7M04.
Finding a missing angle from the other two is the next step in class (node 3), not this lesson.
| What you will see | A question to ask | The fix |
|---|---|---|
| A student thinks a bigger triangle has bigger angles (Kai's mistake). | If you make a photocopy twice as big, do the corners get pointier or blunter? | Enlarge a triangle on the board by doubling each corner's coordinates: the angles stay the same. |
| A student adds the angles and gets 179° or 181° with a protractor. | How accurately can you read a protractor? | Each reading can be a degree out, so three readings can be two or three degrees out. The true total is 180°. |
| A student says the rule only works for the triangles they tried. | Which triangle could you try that would break it? | Let them try their 'breaking' triangle on the board or on paper. Then point to the torn corners: they always fill a straight line, whatever the shape. |
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: Can a triangle have one angle that is twice the other two added together? (Yes: 120°, since 120 = 2 × 60.) What about three times? (135°.)
Support: Use the Run board throughout, and the preset buttons are on the explain clip's board. Give students paper triangles to tear.
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 "Angles in a triangle". The idea: Demonstrating the triangle angle sum: I can Students demonstrate, using concrete or dynamic methods, that the interior angles of any triangle sum to 180°. What understanding looks like: - Demonstrates the angle sum of a triangle is 180° using at least one method. - States the property applies to all triangles. - Measures angles in a triangle and verifies the sum is approximately 180°. Mistakes students often make here: - A student thinks a bigger triangle has bigger angles (Kai's mistake). - A student adds the angles and gets 179° or 181° with a protractor. - A student says the rule only works for the triangles they tried. 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 "Angles in a triangle".
A student says the angles of a very large triangle add to more than 180°. Explain why they are wrong.
Every triangle's angles add to 180°: tear off the corners and they fill a straight line. Size changes the sides, not the angles.
Next: angles in any polygon, by splitting it into triangles.
Where it leads: finding unknown angles with reasons (node 3), the proof with parallel lines (AC9M7M04), and why regular hexagons tessellate.