Math lesson plan · 11th grade (Year 12 in England) · 45 minutes
Solve exponential equations by matching bases
Algebra
CCSS HSA.REI.A.1CCSS HSF.LE.A.4England: A-level Pure Mathematics
Objective and success criteria
Students will: Solve exponential equations by matching bases.
- 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: Laws of exponents (indices); Fractional and negative indices
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 (Laws of exponents (indices); Fractional and negative indices). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Simplify (y³)⁹ and write it as y to a single power. What is the power? → 27Prompt: A power of a power: multiply the exponents.
- Evaluate 32^(3/5). → 8Prompt: The denominator 5 means take the 5th root.
- Evaluate 5⁻¹ as a fraction. → 1/5Prompt: A negative exponent means 'one over' the positive power.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Solve exponential equations by matching bases. 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 3^(x + 3) = 27.
- Step 1: 27 = 3^3
- Step 2: x + 3 = 3
- Step 3: x = 0
- Answer: x = 0
- 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 3^(x − 1) = 9. → x = 3Prompt: Write 9 as a power of 3.
- Solve 9^x = 27. Give a fraction or decimal. → x = 1.5Prompt: Write both sides as powers of 3.
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 8^(x + 1) = 4^x. → x = -3Prompt: Rewrite both bases as powers of 2.
- Solve 5^(x − 3) = 625. → x = 7Prompt: Write 625 as a power of 5.
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: Laws of exponents (indices).
- 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-11.
Free lesson plan from eurekami.com/lesson-plan-builder