Students match rates to distances and times on a double number line, tell rates from ratios, find unit rates and convert between rate units such as km/h and m/s (AC9M8M05, 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 8 min · Modify 10 min · Practise and Make 9 min
Do the Run board yourself first. Students need ratios (Number Foundations, Ratios).
The one idea: a rate is "this much per one of that", with two different units; divide the first by the second. The common mistake is dividing the wrong way round (Mia's mistake).
The board's double number line lines up the two quantities; the dashed line marks the unit rate, and the notes give km/h in m/s.
Wider: compare several units for the same speed (km/h, m/s, knots); rates in First Nations land management, such as how fast a cool burn spreads in different conditions (teach with local knowledge where you can).
Dividing in the right order. Ask students to say the rate in words ('dollars per kilogram') before they divide: the 'per' quantity goes second.
| What you will see | A question to ask | The fix |
|---|---|---|
| A student divides the wrong way. | What is it per? That goes second. | Dollars per kilogram = dollars ÷ kilograms. |
| A student drops the units. | 60 what, per what? | A rate always has two units. |
| A student multiplies by 3.6 to get m/s. | Is a metre per second faster or slower than a kilometre per hour? | m/s is the smaller number: divide by 3.6. |
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: Express the same speed in km/h, m/s and knots (1 knot = 1.852 km/h). Which unit do ships use, and why?
Support: A card: 'rate = first quantity ÷ second quantity, units: first per second'.
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 "Rates". The idea: Rates as comparisons of different units: I can Students recognise that a rate compares two quantities with different units and express rates in standard form (quantity per unit). What understanding looks like: - Correctly identifies and writes a rate from a practical context. - Converts between related rate units. - Distinguishes a rate (different units) from a ratio (same units). Mistakes students often make here: - A student divides the wrong way. - A student drops the units. - A student multiplies by 3.6 to get m/s. 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 "Rates".
A cyclist rides 45 km in 1.5 hours. Find her speed in km/h and m/s.
45 ÷ 1.5 = 30 km/h; 30 ÷ 3.6 ≈ 8.3 m/s.
This starts AC9M8M05.
Where it leads: using rates to solve problems (next lesson), rate models, and gradient as a rate (Linear relations).