Math lesson plan · 12th grade (Year 13 in England) · 45 minutes
Exponential and logarithmic equations
Algebra
CCSS HSF.LE.A.4CCSS HSF.BF.B.5
Objective and success criteria
Students will: Exponential and logarithmic equations.
- 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: 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 (Logarithms). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Evaluate log(10000). → 4Prompt: Ask: 10 to what power gives 10000?
- Yuki is revising the product law of logarithms. Which statement is true? (log(a + b) = log a + log b / log(ab) = log a + log b / log(ab) = log a × log b / log(a/b) = log a ÷ log b) → log(ab) = log a + log bPrompt: Logs turn multiplication into addition.
- Evaluate log_2(4) + log_2(4). → 4Prompt: Use log a + log b = log(ab).
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Exponential and logarithmic equations. 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: Solve: 2^(x − 1) = 2
- Step 1: 2 = 2¹
- Step 2: x − 1 = 1
- Step 3: x = 2
- Answer: x = 2
- 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.
- Solve: 2^(x − 1) = 32 → x = 6Prompt: Write 32 as a power of 2.
- Solve 7ˣ = 166. Give x to 3 decimal places. → 2.627Prompt: Take logs of both sides.
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.
- Solve: log_4(x + 4) = 1. Give x as a number (fractions allowed). → 0Prompt: Rewrite in exponential form: the inside equals b to the power k.
- Solve 7ˣ = 167. Give x to 3 decimal places. → 2.63Prompt: Take logs of both sides.
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
- 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