Students model practical problems as a ratio or a rate (paint coverage, cordial, fuel, sharing, filling), solve them and interpret the answer in the situation (AC9M8M07, node 1).
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 10 min · Modify 10 min · Practise and Make 12 min
Do the Run board yourself first. Students need ratios (Year 7) and rates (previous lessons).
The one idea: same kind of quantity, ratio; different units, rate; then interpret the answer in the situation. The common mistake is rounding the wrong way for the context (Ana's mistake).
Wider: ratios in First Nations string and cordage making (fibre lengths and twisting), taught with local knowledge where you can; radiocarbon dating as a ratio of isotopes.
Choosing the model. Ask students to name the two quantities and their units before they calculate: same units, ratio; different units, rate.
| What you will see | A question to ask | The fix |
|---|---|---|
| A student multiplies area by coverage. | What units would that give? | m² ÷ (m² per L) = L: divide. |
| A student uses 4 parts for a 1 : 4 ratio. | How many parts altogether? | 1 + 4 = 5 parts. |
| A student rounds to the nearest. | Is that enough for the job? | Round to suit the situation: up for tins and buses. |
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: Plan the paint for your classroom: measure the walls, subtract the windows and door, choose a paint and tin size, and cost it.
Support: A model card: what do I need (units)? Ratio or rate? Calculation. Does the answer fit the situation?
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 "Ratio and rate models". The idea: Formulating and solving ratio/rate models: I can Students identify whether a problem requires a ratio or rate model, formulate it, and solve in context. What understanding looks like: - Correctly identifies whether the problem requires a ratio or rate model. - Formulates and solves the model correctly. - Justifies the model choice and interprets the solution in context. Mistakes students often make here: - A student multiplies area by coverage. - A student uses 4 parts for a 1 : 4 ratio. - A student rounds to the nearest. 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 "Ratio and rate models".
A recipe uses 2 cups of rice to 3 cups of water. How much water for 5 cups of rice? Is this a ratio or a rate?
A ratio (cups to cups): 5 × 1.5 = 7.5 cups of water.
This starts AC9M8M07.
Where it leads: checking models and their assumptions (next lesson), and linear models (Linear relations).