Students predict whether a fraction's decimal terminates from the prime factors of its simplified denominator, and check on the long-division board (AC9M8N03, 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 10 min · Modify 8 min · Practise and Make 9 min
Do the Run board yourself first. Students need prime factors (Number Foundations) and the previous lesson.
The one idea: in simplest form, a denominator made only of 2s and 5s gives a terminating decimal, because terminating decimals are fractions over powers of 10 = 2 × 5. The common mistake is skipping the simplifying (Max's mistake).
The board shows the simplest form and the prime factors with the long division.
Wider: in base 12 (12 = 2 × 2 × 3), thirds would terminate and fifths would recur.
Simplifying first. Ask students to write the fraction in simplest form before they say anything about its denominator.
| What you will see | A question to ask | The fix |
|---|---|---|
| A student judges by the denominator's size or digits. | What are its prime factors? | Only the primes matter: 2s and 5s stop. |
| A student does not simplify first. | Is the fraction in simplest form? | Cancel common factors, then look at the denominator. |
| A student thinks 8 = 2 × 4 counts as other primes. | Is 4 a prime? | Break it down to primes: 8 = 2 × 2 × 2. |
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 base 12, which unit fractions from 1/2 to 1/12 would terminate? Why?
Support: A list of primes to 20 and factor trees for the denominators.
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 "Which decimals stop?". The idea: Predicting termination from prime factorisation of denominator: I can Students identify whether a fraction terminates by examining whether the prime factorisation of the denominator contains only factors of 2 and/or 5. What understanding looks like: - Correctly predicts whether a fraction terminates from its denominator's prime factorisation. - Explains why the rule works (connection to base 10). - Simplifies fractions first where necessary before applying the rule. Mistakes students often make here: - A student judges by the denominator's size or digits. - A student does not simplify first. - A student thinks 8 = 2 × 4 counts as other primes. 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 (Identifying terminating and recurring decimals), 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 "Which decimals stop?".
Does 9/24 terminate? Explain.
Yes: 9/24 = 3/8, and 8 = 2 × 2 × 2, only 2s, so it terminates (0.375).
This completes AC9M8N03.
Where it leads: irrational numbers (next unit), whose decimals never stop and never repeat.