Students substitute the known values into a formula, solve the equation that is left for the unknown, and check by substituting back (AC9M7A01, 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 and Modify boards yourself first. The board lets students hunt for the answer by moving a slider: that is fine at Run, but in Investigate and Modify they should write the equation and solve it first, then use the board to check.
The new move is putting together substitution (last lesson) and backtracking (Equations unit). The common error is repeating the operation instead of undoing it (Mia's mistake: 2w = 8, so w = 16). The check catches it every time, so make checking non-negotiable.
One practise question needs only substitution, on purpose: students must decide which job each question asks for.
| What you will see | A question to ask | The fix |
|---|---|---|
| A student repeats the operation instead of undoing it (Mia's mistake). | Does your answer check? Put it back into the formula. | Undo × with ÷, and + with −. Check every answer by substituting back. |
| A student puts the known answer in for the wrong letter (45 as h). | Which letter is the cost? Which is the hours? | Write each known value next to its letter before substituting. |
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: A rectangle's length is 3 cm more than its width, and its perimeter is 30 cm. Find both sides.
Support: Give a template: formula; what I know; substitute; undo; check.
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 "Finding an unknown". The idea: Finding an unknown by substitution and backtracking: I can Students determine the value of an unknown variable in a formula by substituting known values and solving. What understanding looks like: - Correctly finds an unknown in a formula given all other values. - Verifies the solution by substituting back into the formula. - Interprets the result in context (with units and meaning). Mistakes students often make here: - A student repeats the operation instead of undoing it (Mia's mistake). - A student puts the known answer in for the wrong letter (45 as h). 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 (Substituting values into formulas), 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 "Finding an unknown".
A gym costs T = 15w + 30 dollars for w weeks. Someone paid 120 dollars. How many weeks? Check your answer.
120 = 15w + 30, so 15w = 90 and w = 6. Check: 15 × 6 + 30 = 120.
Next: the Expressions unit continues with writing expressions from words. Solving for an unknown is the Equations unit, and in Linear relations it becomes finding x for a given y on a graph.