Math lesson plan · 10th grade (Year 11 in England) · 30 minutes
Find the inverse of a linear function
Algebra
CCSS HSF.BF.B.4.AEngland: GCSE Higher Algebra
Objective and success criteria
Students will: Find the inverse of a linear function.
- 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: Rearrange formulas (change the subject); Function notation
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 · 4 min
- Quick retrieval from earlier learning (Rearrange formulas (change the subject); Function notation). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Make x the subject of y = 3x + 5. Type the expression for x. → (y-5)/3Prompt: Undo the operations on x in reverse order.
- f(x) = 3x² + 4x + 3. Find f(0). → 3Prompt: Replace every x with 0.
- Rearrange A = πr² to make r the subject. Type the expression for r. → sqrt(A/pi)Prompt: Divide by π, then take the square root.
Hook · 3 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Find the inverse of a linear function. 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: f(x) = −6x + 6. Find f⁻¹(x).
- Step 1: x = −6y + 6
- Step 2: f⁻¹(x) = (x − 6)/(−6)
- Answer: (x-6)/(-6)
- 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.
- f(x) = 7x − 6. Find f⁻¹(x). → (x+6)/7Prompt: Write y = f(x), then swap x and y.
- f(x) = −4x + 3. Find f⁻¹(−1). → 1Prompt: f⁻¹(−1) is the input that makes f give −1.
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.
- f(x) = 6x − 1. Find f⁻¹(−37). → -6Prompt: f⁻¹(−37) is the input that makes f give −37.
- f(x) = (4x − 3)/2. Find f⁻¹(x). → (2x+3)/4Prompt: Swap x and y: x = (4y − 3)/2.
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: Rearrange formulas (change the subject).
- 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-10.
Free lesson plan from eurekami.com/lesson-plan-builder