Students use the angle and diagonal properties of quadrilaterals to find unknown angles and lengths, with reasons (AC9M8SP02, 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 10 min · Modify 10 min · Practise and Make 12 min
Do the Run board yourself first. Students need the quadrilateral family, co-interior angles and the angle sum of a quadrilateral (Year 7), and the proofs from the last lesson.
The one idea: each property is a rule with a reason, so a problem is a chain of rules. The common mistake is saying opposite angles of a parallelogram add to 180° (Jo's mistake); neighbouring angles do.
Reasons students should use: co-interior angles, opposite angles of a parallelogram, angle sum of a quadrilateral (360°), properties of the diagonals, congruent triangles.
Wider: the carpenter's check in the hook (equal diagonals mean a parallelogram frame is a rectangle).
Telling opposite from neighbouring angles. Ask students to trace the parallel sides with a finger before they decide which rule applies.
| What you will see | A question to ask | The fix |
|---|---|---|
| A student subtracts from 180 for the opposite angle. | Are those two angles between the same pair of parallel sides? | Opposite angles are equal; neighbours add to 180°. |
| A student uses the whole diagonal for half. | Where do the diagonals cross? | They cut each other in half: each part is half the diagonal. |
| A student gives answers with no reasons. | Which property did you use? | Write the reason after each line, such as 'co-interior angles'. |
One possible solution for each task. Other correct programs are fine.
Open task: any program that does what the step asks.
Stretch: Prove the carpenter's check: a parallelogram with equal diagonals is a rectangle.
Support: The properties table from the lesson, printed with a column for 'reason words'.
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 8 student in Australia. Help me understand ONE idea only, from the lesson "Problems with quadrilaterals". The idea: Solving problems using quadrilateral properties: I can Students use established quadrilateral properties to find unknown angles and lengths, providing full geometric reasoning. What understanding looks like: - Finds unknown angles or lengths using quadrilateral properties correctly. - States a geometric reason for each step. - Solves at least one multi-step problem without prompting for each step. Mistakes students often make here: - A student subtracts from 180 for the opposite angle. - A student uses the whole diagonal for half. - A student gives answers with no reasons. 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 (Establishing quadrilateral properties via congruent triangles), 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 "Problems with quadrilaterals".
In parallelogram ABCD, angle B = 3 × angle A. Find all four angles.
A + 3A = 180, so A = 45°. B = 135°, C = 45°, D = 135°.
This completes AC9M8SP02.
Where it leads: congruence algorithms (next lesson), and circle geometry and trigonometry in Years 9 and 10.