Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Function notation
Algebra
CCSS HSF.IF.A.1CCSS HSF.IF.A.2England: GCSE Higher Algebra
Objective and success criteria
Students will: Function notation.
- 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: Functions: definition and comparison; Evaluate expressions
Leads to: Composite and inverse functions; Remainder and factor theorems; Evaluate and compare two functions
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 (Functions: definition and comparison; Evaluate expressions). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Is this relation a function? {(7, −4), (6, 4), (2, 8), (9, −7)} (Yes / No) → YesPrompt: A function gives exactly one output for each input.
- Find the value of 4x + 8 when x = 4. → 24Prompt: Replace x with 4.
- Function A: y = 4x + 5. Function B is shown by the table x: 0, 1, 2, 3 → y: 3, 12.5, 22, 31.5. Which has the greater rate of change? (A / B / They are equal) → BPrompt: The rate of change of A is the coefficient of x.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Function notation. 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) = 2x² + 7. Find f(0).
- Step 1: f(0) = 2 × 0² + 0 × 0 + 7
- Step 2: = 7
- Answer: 7
- 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) = 3x² − 6x − 3. Find f(0). → -3Prompt: Replace every x with 0.
- f(x) = −4x + 6. For what value of x is f(x) = −34? → x = 10Prompt: Set the expression equal to the value.
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) = 2x² + x + 5. Find f(4). → 41Prompt: Replace every x with 4.
- f(x) = 3x − 7. For what value of x is f(x) = −13? → x = -2Prompt: Set the expression equal to the value.
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: Functions: definition and comparison.
- 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: Composite and inverse functions; Remainder and factor theorems; Evaluate and compare two functions.
- 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-9.
Free lesson plan from eurekami.com/lesson-plan-builder