Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Solve half-life problems
Algebra
CCSS HSF.LE.A.2CCSS HSF.LE.B.5England: GCSE Higher Algebra
Objective and success criteria
Students will: Solve half-life problems.
- I can answer questions on today's skill on my own, without help.
- I can explain each step and say why it works.
- I can check my answer and spot a mistake.
Before and after
Needs first: Exponential growth and decay
Leads to: the next skill in this area.
Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 5 min
- Quick retrieval from earlier learning (Exponential growth and decay). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- y = 20 × 0.5ˣ. Find y when x = 3. Round to 2 decimal places if needed. → 2.5Prompt: Work out the power first.
- Does y = 10(0.25)ˣ show exponential growth or decay? (Growth / Decay) → DecayPrompt: Look at the base b being raised to the power x.
- Daniel's bacteria culture starts with 80 cells and doubles every 2 hours. How many cells after 8 hours? → 1280Prompt: How many doubling periods fit into 8 hours?
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Solve half-life problems. Read the success criteria together.
I do: model it · 10 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: The half-life of caffeine in the body is 3 hours. Starting with 44 mg, how much is left after 6 hours?
- Step 1: 6 ÷ 3 = 2
- Step 2: 44 × (1/2)² = 11 mg
- Answer: 11
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 10 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- The half-life of caffeine in the body is 10 hours. Starting with 176 mg, how much is left after 30 hours? → 22Prompt: How many half-lives fit into 30 hours?
- A 352 mg sample decays to 11 mg in 15 days. What is its half-life in days? → 3Prompt: How many times was the amount halved?
You do: independent practice · 10 min
- Students work on the student sheet. Circulate and check the first two answers of every student early.
- Students who finish: write a question of their own for a partner, with the answer.
The 8 questions are on the student sheet below, with answers in the key.
Exit ticket · 5 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- A 80 mg sample decays to 10 mg in 27 days. What is its half-life in days? → 9Prompt: How many times was the amount halved?
- The half-life of a radioactive sample is 2 hours. Starting with 576 g, how much is left after 10 hours? → 18Prompt: How many half-lives fit into 10 hours?
Watch out for
- Doing an operation to one side of an equation but not the other.
- Reading 3x as 3 + x, or thinking x always stands for one particular number.
Support and stretch
Support
- Review first: Exponential growth and decay.
- Use concrete materials: balance scales or a balance drawing.
- Give the first step of each question, or a partly worked example to finish.
- Pair with a confident partner for the guided practice.
Stretch
- Explain a common mistake in writing and how to fix it.
- Write a word problem that uses today's skill, then solve a partner's.
Homework and more practice
Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-9.
Free lesson plan from eurekami.com/lesson-plan-builder