Students define half-life, work out how much of a sample is left after a number of half-lives, explain that decay is random for one nucleus but predictable for many, and link half-life to uses (AC9S9U06, node 4).
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.
Engage and Explore 9 min · Explain 11 min · Fluorine-18 4 min · Evaluate 3 min · Wider adds about 6 min
A concept tutorial for introducing or revising the idea; it pairs well with the dice (or coin) simulation in class. Set the width with ?width=minimum, typical (default) or wider. It builds on Isotopes and Alpha, beta and gamma (nodes 2 and 3).
Not a hinge node, but its misconception is stubborn: students expect a sample to be gone after two half-lives, or each nucleus to decay at its half-life. The prediction tests the first; the "one nucleus" question tests the second.
Board notes: the sample is simulated: in each tenth of a half-life every remaining nucleus decays with the same chance (about 6.7%), so the count halves on average each half-life but wobbles, more so with 100 nuclei than with 400. Each Start again is a new random sample. The dashed curve (exact halving) appears once a run has finished. Time is shown in the isotope's own unit.
Halving what is left, not the start. Ask students to write the halving ladder themselves (80, 40, …) before you confirm any answer.
| What you will see | A question to ask | The fix |
|---|---|---|
| A student says all of the sample is gone after two half-lives. | After one half-life, how many are left? What happens to those in the next half-life? | Half of them go: half of a half is a quarter. It keeps halving and never quite reaches zero. |
| A student subtracts the same number each half-life (80, 40, 0). | Is it half of the start, or half of what is left? | Half of what is left: 80, 40, 20, 10. |
| A student thinks each nucleus decays exactly at the half-life. | On the board, did all the orange squares go at once? | No: they went one by one at random. Half-life describes a large sample, not one nucleus. |
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.
Open task: any program that does what the step asks.
Open task: any program that does what the step asks.
Stretch: A sample of 1000 nuclei is down to about 30 after 5 half-lives. Why not exactly 31.25? (Decay is random, and you can't have a quarter of a nucleus: the 31.25 is the average over many samples.)
Support: Give the halving ladder: 'Start … → after 1 half-life … → after 2 … → after 3 …'.
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 science coach for a Year 9 student in Australia. Help me understand ONE idea only, from the lesson "How long does radioactivity last?". The idea: Half-life — rate of radioactive decay: I can define half-life, use half-life data to calculate remaining activity after a given number of half-lives, and explain how half-life determines the suitability of isotopes for different applications. What understanding looks like: - Defines half-life as the time for half of the nuclei in a sample to decay - Calculates the remaining quantity of a radioisotope after a given number of half-lives - Explains why half-life determines the suitability of an isotope for a named application Mistakes students often make here: - A student says all of the sample is gone after two half-lives. - A student subtracts the same number each half-life (80, 40, 0). - A student thinks each nucleus decays exactly at the half-life. 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 (Types of radioactive decay — alpha, beta and gamma), 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 "How long does radioactivity last?".
Iodine-131 has a half-life of 8 days. A hospital receives 40 g. How much is left after 24 days?
5 g (40 → 20 → 10 → 5: three half-lives).
Next: decay chains (node 5) are a class task: the decay board with isotope: uranium-238 follows the chain to lead-206. Half-life links to geological time in Earth and space.
In class: the dice simulation (each roll, remove every die showing a 6) and a class decay curve; compare with the board's.
The Wider step on dating First Peoples' presence is general: radiocarbon dates the younger layers and other methods (luminescence) the older ones. For richer context, use local resources and community guidance, and First Peoples' own accounts of their history on Country.