Math lesson plan · 11th grade (Year 12 in England) · 45 minutes
Combine logarithms into a single logarithm
Algebra
CCSS HSF.LE.A.4England: A-level Pure Mathematics
Objective and success criteria
Students will: Combine logarithms into a single logarithm.
- 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: Evaluate logarithms without a calculator
Leads to: Evaluate expressions with logarithm laws; Expand a logarithm using the log laws; Solve exponential equations using logarithms
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 (Evaluate logarithms without a calculator). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Evaluate log₁₀ 100. → 2Prompt: log₁₀ N asks: 10 to what power gives N?
- Evaluate log₂ (1/32). → -5Prompt: A fraction 1/bⁿ is b to a negative power.
- Evaluate log₄ 32. Give a fraction if needed. → 5/2 (2 1/2)Prompt: Write both numbers as powers of 2.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Combine logarithms into a single logarithm. 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: log 8 + log 9 − log 8 = log N. Find N.
- Step 1: log(8 × 9 ÷ 8)
- Step 2: N = 9
- Answer: 9
- 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.
- log 6 + log 3 − log 6 = log N. Find N. → 3Prompt: Adding logs multiplies the numbers; subtracting divides.
- 2 log 2 + log 8 = log N. Find N. → 32Prompt: k log a = log aᵏ (power law).
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 2 log 3 − log 3 + log 2 as a single logarithm log N. Find N. → 6Prompt: Use the power law first.
- log 9 + log 9 − log 3 = log N. Find N. → 27Prompt: Adding logs multiplies the numbers; subtracting divides.
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: Evaluate logarithms without a calculator.
- 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: Evaluate expressions with logarithm laws; Expand a logarithm using the log laws; Solve exponential equations using logarithms.
- 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