Math lesson plan · 12th grade (Year 13 in England) · 30 minutes
Compare compounding periods and continuous interest
Algebra
CCSS HSF.LE.A.2CCSS HSA.SSE.B.3.CEngland: A-level Pure Mathematics
Objective and success criteria
Students will: Compare compounding periods and continuous interest.
- 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: Solve equations with e and natural logarithms; Compound interest and depreciation
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 · 4 min
- Quick retrieval from earlier learning (Solve equations with e and natural logarithms; Compound interest and depreciation). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Solve eˣ = 45. Give x to 3 decimal places. → 3.807Prompt: ln is the inverse of eˣ.
- $1500 is saved at 4% compound interest per year. How much is in the account after 3 years? Round to 2 decimal places (type the number only). → 1687.3Prompt: Each year the amount is multiplied by 1.04.
- Solve ln x = 1.5. Give x to 2 decimal places. → 4.48Prompt: Rewrite in exponential form.
Hook · 3 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Compare compounding periods and continuous interest. Read the success criteria together.
I do: model it · 7 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: $5000 is invested at 5% a year, compounded monthly. Use A = P(1 + r/n)^(nt) to find the value after 3 years, to 2 decimal places.
- Step 1: 5000(1 + 0.05/12)^36
- Step 2: ≈ 5807.36
- Answer: 5807.36
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 6 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- $5500 is invested at 5% a year, compounded monthly. Use A = P(1 + r/n)^(nt) to find the value after 9 years, to 2 decimal places. → 8617.66Prompt: r = 0.05 and n = 12.
- $6500 earns 4% a year compounded continuously: A = Pe^(rt). Find the value after 4 years, to 2 decimal places. → 7627.82Prompt: Write r as a decimal.
You do: independent practice · 7 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 6 questions are on the student sheet below, with answers in the key.
Exit ticket · 3 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- $3500 earns 6% a year compounded continuously: A = Pe^(rt). Find the value after 6 years, to 2 decimal places. → 5016.65Prompt: Write r as a decimal.
- $1000 is invested at 5% a year, compounded quarterly. Use A = P(1 + r/n)^(nt) to find the value after 3 years, to 2 decimal places. → 1160.75Prompt: r = 0.05 and n = 4.
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: Solve equations with e and natural logarithms.
- 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-12.
Free lesson plan from eurekami.com/lesson-plan-builder