Students solve linear equations by doing the same to both sides (the balance method), including x on both sides, and verify every answer in the first equation (AC9M7A03, 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 10 min · Investigate 12 min · Modify 12 min · Practise 10 min · Make 6 min
This is a hinge lesson: later modelling work (ratios, rates, money problems) depends on fluent solving and the checking habit. A student who skips the check will not notice a wrong answer.
Do the "x on both sides" scale yourself. The key move is taking a bag of x from both sides, which students rarely think of until they see the scale.
| What you will see | A question to ask | The fix |
|---|---|---|
| A student changes one side only (2x + 3 = 11 becomes 2x = 11). | What did you do to the left side? Did the right side get the same? | Write the step on both sides: 2x + 3 − 3 = 11 − 3. |
| A student checks in the last line (x = 4 → 4 = 4) and calls it verified. | Which equation were we asked to solve? | Check in the first equation: 2 × 4 + 3 = 11. |
| With x on both sides, the student is stuck. | You took blocks from both sides. What else is on both sides? | Take the smaller number of x from both sides first: x + 7 = 3x + 1 becomes 7 = 2x + 1. |
4x + 3 = 23
4x + 3 − 3 = 23 − 3
4x = 20
x = 5
Check: 4 × 5 + 3 = 23
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.
Stretch: 'I think of a number, double it and add 5 to get 19.' Write the equation, solve it with the balance method, and check. Then invent one where the answer must be a whole number of people, and explain why.
Support: Use the board for the Practise questions first, then write each button press as a line of algebra.
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 "The balance method". The idea: Solving algebraically and verifying: I can Students solve one-variable linear equations algebraically, using the balance model, and verify the solution by substitution. What understanding looks like: - Solves a one-variable linear equation algebraically with correct steps shown. - Verifies the solution by substituting back into the original equation. - Does not skip verification. Mistakes students often make here: - A student changes one side only (2x + 3 = 11 becomes 2x = 11). - A student checks in the last line (x = 4 → 4 = 4) and calls it verified. - With x on both sides, the student is stuck. 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 (Solving by backtracking), 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 "The balance method".
Solve 4x + 3 = 2x + 11. Show each step and check your answer in the first equation.
Take 2x from both sides: 2x + 3 = 11. Take 3: 2x = 8. Divide by 2: x = 4. Check: 4 × 4 + 3 = 19 and 2 × 4 + 11 = 19.
Next: equations from word problems, then graphing linear relations in Year 8, where the solution is where two lines meet.
Where it leads in class: rearranging formulas in science (speed = distance ÷ time), and money problems with a fixed fee plus a rate.