Math lesson plan · 11th grade (Year 12 in England) · 45 minutes
Switch between exponential and logarithmic form
Algebra
CCSS HSF.LE.A.4CCSS HSF.BF.B.5England: A-level Pure Mathematics
Objective and success criteria
Students will: Switch between exponential and logarithmic form.
- 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: Logarithms
Leads to: Solve logarithmic equations
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 (Logarithms). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Evaluate log_3(1/3). → -1Prompt: Ask: 3 to what power gives 1/3?
- Lucia is revising the quotient law of logarithms. Which statement is true? (log(ab) = log a × log b / log(a + b) = log a + log b / log(a/b) = log a ÷ log b / log(a/b) = log a − log b) → log(a/b) = log a − log bPrompt: Logs turn multiplication into addition.
- Evaluate log_3(243) − log_3(27). → 2Prompt: Use log a − log b = log(a/b).
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Switch between exponential and logarithmic form. 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: Write log₁₀ 1000 = 3 in exponential form.
- Step 1: 10^3 = 1000
- Answer: 10^3 = 1000
- 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.
- Write 6^3 = 216 in logarithmic form. (log₆ 216 = 3 / log₆ 3 = 216 / log₂₁₆ 6 = 3 / log₃ 216 = 6) → log₆ 216 = 3Prompt: bˣ = N means the same as log_b N = x.
- Solve log_b 100 = 2 for the base b. → 10Prompt: Rewrite as b^n = N.
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.
- Write 6^2 = 36 in logarithmic form. (log₃₆ 6 = 2 / log₂ 36 = 6 / log₆ 2 = 36 / log₆ 36 = 2) → log₆ 36 = 2Prompt: bˣ = N means the same as log_b N = x.
- Solve log₃ x = 4. → 81Prompt: Rewrite in exponential form.
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: 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
- Move on to: Solve logarithmic equations.
- 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-11.
Free lesson plan from eurekami.com/lesson-plan-builder