Students rearrange formulas to change the subject by undoing the steps in reverse order on both sides, and check each rearrangement by substituting numbers, on a formula board that works the original forwards (AC9M8A01, 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 15 min · Modify 12 min · Practise and Make 10 min
Do the Run board and the working check yourself first. Students need solving equations by backtracking and the balance method (Year 7 equations unit), substituting into formulas, and the two lessons before (expanding and factorising).
The one idea: changing the subject is solving an equation with letters. Undo what was done to the letter, last step first, doing the same to both sides. The common mistake is dividing only one term (y = 4x − 3 becomes y ÷ 4 = x − 3); it is planted after the method, in Jo's working. Undoing the − 3 first avoids it.
Answers are marked by form and value: the subject must be on its own on the left, and the formula must agree with the original for every value. An equal formula in another shape, such as x = y/2 − 7/2 for (y − 7)/2, is marked right.
| What you will see | A question to ask | The fix |
|---|---|---|
| A student divides only one term (Jo's mistake). | Put in x = 2. Does your formula give back the y you started with? | Undo the add or subtract first, so there is only one term left to divide. |
| A student undoes the steps in the wrong order (x = y/3 − 5 from y = 3x + 5). | What was done to x first? What was done last? | Draw the flow: x → × 3 → + 5 → y. Go back along it from y. |
| A student gets lost with letters. | What would you do if the formula were 11 = 3x + 5? | Solve it with the number, then do exactly the same steps with y. |
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.
Open task: any program that does what the step asks.
Stretch: Make l the subject of P = 2l + 2w, then r the subject of C = 2πr, then x the subject of ax + b = c.
Support: Give a number version first (11 = 3x + 5), then the letter version beside it, step for step.
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 "Changing the subject". The idea: Rearranging linear expressions: I can Students rearrange linear expressions and formulas using inverse operations and algebraic properties, maintaining equivalence. What understanding looks like: - Correctly rearranges a linear formula to make a specified variable the subject. - Applies inverse operations in the correct order. - Verifies the rearranged formula by substitution. Mistakes students often make here: - A student divides only one term (Jo's mistake). - A student undoes the steps in the wrong order (x = y/3 − 5 from y = 3x + 5). - A student gets lost with letters. 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 (Factorising 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 "Changing the subject".
Make x the subject of y = 6x − 2, then check it with x = 3.
x = (y + 2)/6. Check: x = 3 gives y = 16, and (16 + 2)/6 = 3.
This completes AC9M8A01: expanding, factorising and changing the subject.
Where it leads: formulas in science (v = d/t, F = ma, ρ = m/V), linear relations (y = mx + c rearranged for x), and in Years 9 and 10 rearranging formulas with the subject in more than one term (factorise it out).