Math lesson plan · 11th grade (Year 12 in England) · 30 minutes
Logarithms
Algebra
CCSS HSF.BF.B.5CCSS HSF.LE.A.4
Objective and success criteria
Students will: Logarithms.
- 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; Fractional and negative indices
Leads to: Exponential and logarithmic equations; Continuous growth and the number e; Inverse functions (non-linear)
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 (Exponential growth and decay; Fractional and negative indices). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- y = 49 × 1.1ˣ. Find y when x = 3. Round to 2 decimal places if needed. → 65.22Prompt: Work out the power first.
- Evaluate 9^(2/2). → 9Prompt: The denominator 2 means take the square root.
- Does y = 45(0.25)ˣ show exponential growth or decay? (Growth / Decay) → DecayPrompt: Look at the base b being raised to the power x.
Hook · 3 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Logarithms. 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: Evaluate log_5(1/5).
- Step 1: 5⁻¹ = 1/5
- Step 2: log_5(1/5) = −1
- Answer: -1
- 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.
- Evaluate log_3(1/9). → -2Prompt: Ask: 3 to what power gives 1/9?
- Fatima is revising the quotient law of logarithms. Which statement is true? (log(a/b) = log a ÷ log b / log(a/b) = log a − log b / log(ab) = log a × log b / log(a + b) = log a + log b) → log(a/b) = log a − log bPrompt: Logs turn multiplication into addition.
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.
- Evaluate log_5(1/5). → -1Prompt: Ask: 5 to what power gives 1/5?
- Ben is revising the product law of logarithms. Which statement is true? (log(a + b) = log a + log b / log(a/b) = log a ÷ log b / log(ab) = log a × log b / log(ab) = log a + log b) → log(ab) = log a + log bPrompt: Logs turn multiplication into addition.
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
- Move on to: Exponential and logarithmic equations; Continuous growth and the number e; Inverse functions (non-linear).
- 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