Students share a total in a given ratio by cutting it into equal parts (add the parts, find one part, multiply), with two and three people, and work backwards from a share to the total (AC9M7N08, 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 8 min · Investigate 12 min · Modify 12 min · Practise and Make 10 min
Do the Run board yourself first. Students need equivalent ratios (previous lesson) and division.
The one idea is the three-step routine: add the parts, divide the total by the number of parts to get one part, then multiply by each person's number. Insist on the check that the shares add back to the total. The commonest mistake is dividing the total by each term (Dee, $30 and $20), which is caught by the check.
Working backwards (Modify) finds one part from the known share first.
Starting by adding the parts, not dividing by one of the numbers. Say 'how many equal parts is the total cut into?' before any dividing.
| What you will see | A question to ask | The fix |
|---|---|---|
| A student divides the total by each term (Dee's slip). | Do the two shares add to the total? | Add the parts first: the total is cut into 5 parts, not 2 and 3 parts separately. |
| A student gives one part as the answer. | How many parts does this person have? | Multiply one part by the person's number of parts. |
| A student shares $60 in 2 : 3 and gets $30 and $30. | How many parts does each person have? | Ana has 2 parts, Ben has 3. Draw the bar. |
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: A profit is shared among three partners in the ratio 2 : 3 : 5. The biggest partner gets $1200 more than the smallest. How much was the profit?
Support: Keep the bar on screen and read each bracket aloud: 'Ana has two parts.'
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 "Sharing in a ratio". The idea: Sharing in a given ratio: I can Students share a quantity in a given ratio and solve related problems. What understanding looks like: - Correctly shares a quantity in a two-part ratio. - Identifies the total number of parts in the ratio. - Can work backwards from a share to find the total quantity. Mistakes students often make here: - A student divides the total by each term (Dee's slip). - A student gives one part as the answer. - A student shares $60 in 2 : 3 and gets $30 and $30. 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 (Equivalent ratios and simplification), 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 "Sharing in a ratio".
Share $84 between Sam and Tia in the ratio 3 : 4. How much does Tia get?
3 + 4 = 7 parts. 84 ÷ 7 = 12. Tia has 4 parts: $48.
Next: Modelling with money and with measurements, using ratios with percentages and fractions.
Where it leads: unit rates, scale drawings, similar shapes, proportion and direct variation in Years 8 and 9.