Students vary one variable at a time in V = lwh, d = st and A = s², write the results as a table and describe the effect (AC9M7A06, nodes 1 and 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 8 min · Modify 10 min · Practise and Make 9 min
Do the Run board yourself first. Students need to substitute into a formula (Substituting into formulas in Algebra).
The one idea: to see what one letter does, change only that letter. Changing two at once makes it impossible to tell which did what (Tom's mistake).
The wider idea is that a variable's effect depends on the formula: in V = lwh, doubling any one factor doubles V; in A = s², doubling s makes A four times as big. The second Modify question and the last are about comparing effects.
The elaborations suggest spreadsheets. The Make task ends with a table: let students build it in a spreadsheet with a formula in the cells, so changing one cell updates the row. Machine-learning models are formulas with very many variables tuned in the same way (a talking point only).
Holding the others still. Ask students to say which letters stay the same before they move a slider.
| What you will see | A question to ask | The fix |
|---|---|---|
| A student moves two sliders and describes the result. | Which slider caused that change? | Change one, write down V, then change the next. |
| A student says doubling the side doubles the area. | What is 6 × 6 compared with 3 × 3? | A square's area has the side twice: doubling gives 4 times. |
| A student reads 2l as 2 and l side by side. | What does the working on the board show between 2 and l? | 2l means 2 × l. |
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: In d = st, find three different pairs of s and t that give d = 120. What pattern do you see? Which graph would show it?
Support: Give a printed table with l and w filled in and a blank row for V.
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 the ideas in ONE lesson only, from the lesson "Changing one thing at a time". The ideas: - Systematic variation of one variable: I can Students vary one variable in a formula while holding others constant, and describe the effect on the output. - Describing effects of variation across multiple variables: I can Students describe how changing each variable in a multi-variable formula affects the output, and identify which variables have the greatest effect. What understanding looks like: - Correctly varies one variable while holding others constant. - Describes the effect of the variation on the output in words. - Uses a table or digital tool to organise the systematic variation. - Correctly describes the effect of changing each variable on the output. - Identifies which variable produces the largest change in output for an equal proportional variation. - Uses digital tool output systematically rather than performing isolated calculations. Mistakes students often make here: - A student moves two sliders and describes the result. - A student says doubling the side doubles the area. - A student reads 2l as 2 and l side by side. 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 "Changing one thing at a time".
In V = lwh with l = 2, w = 3, h = 4, h goes to 8 and nothing else changes. What is V?
48: 2 × 3 × 8, double the 24 it was.
This completes AC9M7A06.
Where it leads: formulas in a spreadsheet, and changing the subject of a formula (Algebra, Year 8).