Math lesson plan · 10th grade (Year 11 in England) · 45 minutes
Write the rule for a composite function
Algebra
CCSS HSF.BF.A.1.CEngland: GCSE Higher Algebra
Objective and success criteria
Students will: Write the rule for a composite 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: Evaluate composite functions f(g(a))
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 (Evaluate composite functions f(g(a))). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- f(x) = −3x − 3 and g(x) = x² + 6. Find f(g(−4)). → -69Prompt: Work from the inside out.
- x: 1, 2, 3, 4, 5 f(x): 2, 5, 3, 4, 1 g(x): 1, 5, 4, 2, 3 Find f(g(4)). → 5Prompt: Read g(4) from the table first.
- f(x) = 3x + 7 and g(x) = x² + 2. Find f(g(0)). → 13Prompt: Work from the inside out.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Write the rule for a composite function. 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: f(x) = −x + 6 and g(x) = 3x + 5. Find f(g(x)) and simplify.
- Step 1: −(3x + 5) + 6
- Step 2: −3x + 1
- Answer: -3x+1
- 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.
- f(x) = 4x + 8 and g(x) = −4x + 6. Find f(g(x)) and simplify. → -16x+32Prompt: Replace x in f with the whole of g(x).
- f(x) = x² + 5 and g(x) = 2x − 2. Find f(g(x)) and simplify. → 4x^2-8x+9Prompt: The inner function goes in place of x in the outer one.
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.
- f(x) = 2x and g(x) = x² + 4. Diego says f(g(x)) = 4x² + 4. What is f(g(x)) really? (2x² + 8 / 2x² + 4 / 2x³ + 4x / 4x² + 4) → 2x² + 8Prompt: Diego worked out g(f(x)) instead: order matters.
- f(x) = x − 5 and g(x) = 4x + 4. Find f(g(x)) and simplify. → 4x-1Prompt: Replace x in f with the whole of g(x).
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 composite functions f(g(a)).
- 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