Students use rates both ways (total = rate × amount, amount = total ÷ rate) for petrol, speed, water and exchange rates, letting the units decide multiply or divide (AC9M8M05, node 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 rates and unit rates (previous lesson).
The one idea: a rate works both ways; the units decide whether to multiply or divide. The common mistake is multiplying distance by speed to find a time (Leo's mistake).
The exchange rate in the lesson (0.65 US dollars per Australian dollar) is a round example, not today's rate.
Wider: plan holiday spending with a current exchange rate (and its fees); compare two phone plans.
Choosing to multiply or divide. Ask students to write the units into the calculation (km ÷ km/h = h) before they press a key.
| What you will see | A question to ask | The fix |
|---|---|---|
| A student multiplies to find a time. | What units does your answer have? | km ÷ km/h gives hours: divide. |
| A student writes 2.5 hours as 2 h 50 min. | What is half an hour in minutes? | 0.5 h = 30 min. |
| A student converts money the wrong way. | Should you get more or fewer US dollars than Australian dollars? | Check the size: 1 AUD buys less than 1 USD here. |
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 a trip budget overseas: look up today's exchange rate, convert three prices, and include a 3% card fee.
Support: A card: total = rate × amount; amount = total ÷ rate; units in every line.
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 "Using rates". The idea: Applying rates to practical problems: I can Students apply rates to solve practical problems including pay rates, run rates, dilution, taxation, and unit conversions. What understanding looks like: - Correctly applies a given rate to solve a practical problem. - Shows the rate calculation clearly with appropriate units. - Interprets the result in context. Mistakes students often make here: - A student multiplies to find a time. - A student writes 2.5 hours as 2 h 50 min. - A student converts money the wrong way. 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 (Rates as comparisons of different units), 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 "Using rates".
A plane flies 2100 km at 700 km/h. How long does it take?
2100 ÷ 700 = 3 hours.
This completes AC9M8M05.
Where it leads: rate models (next lessons), gradient as a rate (Linear relations), and speed in science.