Students change the number of sides and drag corners to see polygons named (pentagon to decagon), regular or irregular, and convex or concave, and reason about why equal sides alone are not enough (AC9M7SP02, node 3).
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 10 min · Modify 8 min · Practise and Make 9 min
Do the Run board yourself first. Students need the quadrilateral family (previous lesson) and the polygon angle sum (Angles in a polygon).
The one idea: regular means equal sides and equal angles; concave means a corner points in. The common mistake is equal sides alone (Kim's mistake with a rhombus).
A dart (a kite with one corner pushed in) is named a kite by the board, as its sides fit the kite's definition; some textbooks keep kites convex and call the concave one a dart.
The board starts each polygon regular (its corners are off the grid); dragging a corner puts it on the grid, so it becomes irregular.
Checking both sides and angles before calling a shape regular. Ask students to say what they checked for each, rather than confirming their answer.
| What you will see | A question to ask | The fix |
|---|---|---|
| A student calls a rhombus regular (Kim's mistake). | Are its angles all the same? | Regular needs equal sides and equal angles. |
| A student mixes up convex and concave. | Does any corner point into the shape, like a cave? | Concave has a 'cave': a corner pointing in. |
| A student confuses heptagon and hexagon. | Which has six: hex or hept? | Hex six, hept seven (like September, the old seventh month). |
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: Which regular polygons tile a floor with no gaps? Use their angles (60°, 90°, 108°, 120°) to explain.
Support: Keep the names table visible; tick 'sides equal' and 'angles equal' separately for each shape.
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 "Polygons". The idea: Classifying other polygons and reasoning about properties: I can Students classify polygons by number of sides and by regularity, and reason about properties such as line symmetry and convexity. What understanding looks like: - Correctly classifies polygons by name, regularity, and convexity. - Explains what makes a polygon regular. - Can identify whether a polygon is convex or concave and explain the difference. Mistakes students often make here: - A student calls a rhombus regular (Kim's mistake). - A student mixes up convex and concave. - A student confuses heptagon and hexagon. 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 (Classifying quadrilaterals and their relationships), 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 "Polygons".
A pentagon has angles 100°, 110°, 110°, 100° and 120°. Is it regular? Convex or concave?
Irregular (its angles are not equal), convex (every angle under 180°).
This completes AC9M7SP02.
Where it leads: tessellations, and the interior and exterior angles of regular polygons (Year 8); Pythagoras (AC9M8M06) for right-angled triangles.