Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Evaluate and compare two functions
Algebra
CCSS HSF.IF.A.2England: GCSE Higher Algebra
Objective and success criteria
Students will: Evaluate and compare two functions.
- 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: 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 · 5 min
- Quick retrieval from earlier learning (Function notation). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- f(x) = 3x² − 5. Find f(−3). → 22Prompt: Replace every x with (−3).
- f(x) = −3x − 1. For what value of x is f(x) = 17? → x = -6Prompt: Set the expression equal to the value.
- f(x) = 3x² + x − 4. Find f(0). → -4Prompt: Replace every x with 0.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Evaluate and compare two functions. 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) = 2x − 1 and g(x) = x² + 1. Find f(−2) − g(3).
- Step 1: f(−2) = −5
- Step 2: g(3) = 10
- Step 3: −5 − 10 = −15
- Answer: -15
- 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) = 3x + 7 and g(x) = x² + 4. Find f(2) + g(0). → 17Prompt: Work out each function value separately.
- f(x) = −3x and g(x) = 4x − 21. For which x is f(x) = g(x)? → x = 3Prompt: Set the two expressions equal.
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) = 3x² − x. Find f(3 + 1) − f(3). → 20Prompt: f(3 + 1) means f(4): evaluate the input first.
- f(x) = 2x − 7 and g(x) = x² + 5. Find f(5) − g(2). → -6Prompt: Work out each function value separately.
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: Function notation.
- 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-9.
Free lesson plan from eurekami.com/lesson-plan-builder