Students list the outcomes of two events in a grid and a tree diagram, count the outcomes in an event and find its probability (AC9M8P02, 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 10 min · Modify 12 min · Practise and Make 10 min
Do the Run board yourself first. Students need sample spaces (Year 7) and the Venn diagrams and tables from the last lesson.
The one idea: two events make pairs, and a grid or tree lists every pair once, so the outcomes are equally likely. The common mistake is merging pairs that differ only in order (Max's HH, TT, one of each), which makes unequal outcomes look equal.
Branch probabilities (multiplying along a tree) are Year 10 (AC9M10P01); here every outcome is equally likely and students count. The board lists outcomes rather than drawing spinners, so the lesson says 'equal parts' every time; point it out.
Wider: three coins on a tree (8 outcomes), and why a grid can't show them.
Counting HT and TH as different. Ask students to colour the two coins (a red coin and a blue coin) before they list.
| What you will see | A question to ask | The fix |
|---|---|---|
| A student adds the outcomes (2 + 6 = 8). | How many dice results go with heads? With tails? | Each first outcome pairs with every second outcome: multiply. |
| A student lists HT and TH once. | If one coin is red and one is blue, is red-heads blue-tails the same as red-tails blue-heads? | Order matters: both are outcomes. |
| A student says P(sum is 7) = 1/11. | Are the sums 2 to 12 equally likely? | Count pairs in the grid, not the list of sums. |
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: Three coins: draw the tree. What is P(exactly two heads)? Why can't the board's grid show this?
Support: A printed 6 by 6 grid for two dice and a blank two-level tree.
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 "Grids and tree diagrams". The idea: Representing two-event combinations: I can Students represent all possible combinations for two events using two-way tables, tree diagrams and Venn diagrams. What understanding looks like: - Correctly lists all combinations for a two-event situation. - Represents combinations accurately using at least one method. - Identifies the advantage of each representation for different questions. Mistakes students often make here: - A student adds the outcomes (2 + 6 = 8). - A student lists HT and TH once. - A student says P(sum is 7) = 1/11. 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 "Grids and tree diagrams".
A spinner shows 1, 2 or 3 (equal parts) and a coin is tossed. List the outcomes. What is P(an odd number and heads)?
1H, 1T, 2H, 2T, 3H, 3T: 6 outcomes. 1H and 3H, so 2/6 = 1/3.
This completes AC9M8P02 node 1 with the last lesson.
Where it leads: 'and', 'or' and 'not' (next), simulations, and multiplying along branches in Year 10.