Math lesson plan · 12th grade (Year 13 in England) · 45 minutes
Decide whether a function is even, odd or neither
Algebra
CCSS HSF.BF.B.3England: A-level Pure Mathematics
Objective and success criteria
Students will: Decide whether a function is even, odd or neither.
- 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: Transformations of functions
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 (Transformations of functions). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Which transformation maps y = f(x) to y = f(−x)? (translate up 4 / translate left 4 / reflect in the x-axis / reflect in the y-axis) → reflect in the y-axisPrompt: Changes outside f affect y; changes inside f affect x (and act the opposite way).
- Which transformation maps y = f(x) to y = f(x) + 5? (translate up 5 / translate left 5 / reflect in the x-axis / reflect in the y-axis) → translate up 5Prompt: Changes outside f affect y; changes inside f affect x (and act the opposite way).
- Which transformation maps y = f(x) to y = f(x) + 4? (translate up 4 / translate left 4 / reflect in the x-axis / reflect in the y-axis) → translate up 4Prompt: Changes outside f affect y; changes inside f affect x (and act the opposite way).
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Decide whether a function is even, odd or neither. 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: Is f(x) = x³ − x² + 3 even, odd or neither?
- Step 1: Neither
- Answer: Neither
- 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.
- Is f(x) = 2x³ + 5x even, odd or neither? (Even / Odd / Neither) → OddPrompt: Work out f(−x) and compare it with f(x) and −f(x).
- f is an odd function and f(5) = 0. Find f(−5). → 0Prompt: Even: f(−x) = f(x). Odd: f(−x) = −f(x).
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.
- Is f(x) = −x⁴ − 3x² + 5 even, odd or neither? (Even / Odd / Neither) → EvenPrompt: Work out f(−x) and compare it with f(x) and −f(x).
- f is an even function and f(1) = −4. Find f(−1). → -4Prompt: Even: f(−x) = f(x). Odd: f(−x) = −f(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: Transformations of functions.
- 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-12.
Free lesson plan from eurekami.com/lesson-plan-builder