Math lesson plan · 8th grade (Year 9 in England) · 30 minutes
Decide whether a relation is a function
Algebra
CCSS 8.F.A.1England: KS3 Algebra
Objective and success criteria
Students will: Decide whether a relation is a 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: Functions: definition and comparison
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 (Functions: definition and comparison). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Is this relation a function? {(2, 4), (9, 8), (4, −3), (−3, −6)} (Yes / No) → YesPrompt: A function gives exactly one output for each input.
- Function A: y = 5x + 4. Function B is shown by the table x: 0, 1, 2, 3 → y: 7, 15.5, 24, 32.5. Which has the greater rate of change? (A / B / They are equal) → BPrompt: The rate of change of A is the coefficient of x.
- Is the function y = 6x − 5 linear or non-linear? (Linear / Non-linear) → LinearPrompt: A linear function can be written as y = mx + b.
Hook · 3 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Decide whether a relation is a 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: Is this relation a function? (2, −1), (6, −5), (−2, −5), (1, 6)
- Step 1: Every x appears once: it is a function.
- Answer: Yes
- 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.
- Is this relation a function? (−5, −4), (7, 8), (−1, 7), (1, 7) (Yes / No) → YesPrompt: A function gives exactly ONE output for each input.
- Is this rule a function (one output for every input)? A shop's opening hour → the number of customers at that time on different days (Yes / No) → NoPrompt: Can one input lead to two different outputs?
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.
- Is this rule a function (one output for every input)? A whole number → a number whose square is it (e.g. 9 → 3 and −3) (Yes / No) → NoPrompt: Can one input lead to two different outputs?
- Is this relation a function? (5, 7), (−5, −1), (0, 0), (4, −9) (Yes / No) → YesPrompt: A function gives exactly ONE output for each input.
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
- 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-8.
Free lesson plan from eurekami.com/lesson-plan-builder