Students share algebra tiles into equal rows to factorise sx + t, learn to take out the highest common factor (numbers, then letters) and check by expanding (AC9M8A01, 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 15 min · Modify 12 min · Practise and Make 10 min
Do the Run board and the Make task yourself first. Students need Expanding brackets (the lesson before) and highest common factors from Year 7 Number.
The one idea: factorising divides every term by a common factor, and the factor goes outside the bracket. The common mistake is taking out a common factor that is not the highest (12x − 8 = 2(6x − 4)); it is planted after the method, in Ava's working. Her answer is equal to 12x − 8, so it is not wrong, just not finished: that is the conversation to have.
Answers are marked by form: an equal answer that could still be factorised further is told so ("could take out more") rather than marked right.
| What you will see | A question to ask | The fix |
|---|---|---|
| A student divides only the first term (6x + 9 = 3(2x + 9)). | Expand your answer. Do you get back to where you started? | Expanding is the check: 3 × 9 = 27, not 9. |
| A student stops at a common factor that is not the highest (Ava's mistake). | Look inside the bracket. Do those terms share anything? | Take out what they share as well: 2(6x − 4) = 2 × 2(3x − 2) = 4(3x − 2). |
| A student cannot find a common factor. | List the factors of each number. Which appear in both lists? | Use the board: try k = 2, 3, 4… and see which numbers of rows work. |
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.
Open task: any program that does what the step asks.
Stretch: Factorise 6x²y − 9xy² fully. (3xy(2x − 3y).) Then: write three different expressions whose full factorisation has 6 outside.
Support: Use the tiles board for every two-term question with positive numbers: try each k and read off the bracket.
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 "Factorising". The idea: Factorising linear expressions: I can Students factorise linear expressions by identifying the highest common factor and express as a product of the HCF and a bracket. What understanding looks like: - Identifies the HCF of all terms in a linear expression. - Writes the factorised form correctly. - Verifies by expanding back to the original expression. Mistakes students often make here: - A student divides only the first term (6x + 9 = 3(2x + 9)). - A student stops at a common factor that is not the highest (Ava's mistake). - A student cannot find a common factor. 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 (Expanding and simplifying linear expressions), 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 "Factorising".
Factorise 14x − 21 fully, then check by expanding.
7(2x − 3). Check: 7 × 2x = 14x and 7 × (−3) = −21.
Next: rearranging formulas (node 3), which divides every term by a number in the same way.
Where it leads: factorising quadratics in Years 9 and 10, which the same tiles show as a rectangle.