Math lesson plan · 8th grade (Year 9 in England) · 60 minutes
Tell linear from nonlinear functions
Algebra
CCSS 8.F.A.3England: KS3 Algebra
Objective and success criteria
Students will: Tell linear from nonlinear 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: 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 · 6 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? {(0, 0), (9, −6), (−5, −3), (0, 2)} (Yes / No) → NoPrompt: A function gives exactly one output for each input.
- Function A: y = x + 3. Function B is shown by the table x: 0, 1, 2, 3 → y: 6, 8.5, 11, 13.5. 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 = 5/x linear or non-linear? (Linear / Non-linear) → Non-linearPrompt: A linear function can be written as y = mx + b.
Hook · 6 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Tell linear from nonlinear functions. Read the success criteria together.
I do: model it · 12 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: x: 0, 1, 2, 3, 4. y: 4, 5, 8, 13, 20. Is the function linear?
- Step 1: Differences: 1, 3, 5, 7
- Step 2: Not constant: nonlinear.
- Answer: Nonlinear
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 12 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- x: 0, 1, 2, 3, 4. y: 2, 3, 6, 11, 18. Is the function linear? (Linear / Nonlinear) → NonlinearPrompt: Find the change in y for each step in x.
- Which equation is NOT linear? (y = 7 − x / y = 3x − 2 / y = 2/x / y = x/2 + 1) → y = 2/xPrompt: A linear equation only has x to the power 1 (no x², no x in a denominator or exponent).
You do: independent practice · 17 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 · 7 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- x: 0, 1, 2, 3, 4. y: −3, −5, −7, −9, −11. Is the function linear? (Linear / Nonlinear) → LinearPrompt: Find the change in y for each step in x.
- Which equation is NOT linear? (2x + y = 5 / y = x/2 + 1 / y = x² + 1 / y = 7 − x) → y = x² + 1Prompt: A linear equation only has x to the power 1 (no x², no x in a denominator or exponent).
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