Math lesson plan Β· 8th grade (Year 9 in England) Β· 30 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 Β· 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? {(0, β7), (β5, 5), (8, 1), (0, β3)} (Yes / No) β NoPrompt: A function gives exactly one output for each input.
- Function A: y = 5x. Function B is shown by the table x: 0, 1, 2, 3 β y: 7, 11, 15, 19. Which has the greater rate of change? (A / B / They are equal) β APrompt: The rate of change of A is the coefficient of x.
- Is the function y = 5x β 4 linear or non-linear? (Linear / Non-linear) β LinearPrompt: A linear function can be written as y = mx + b.
Hook Β· 3 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 Β· 7 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 Β· 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.
- x: 0, 1, 2, 3, 4. y: 5, 0, β5, β10, β15. Is the function linear? (Linear / Nonlinear) β LinearPrompt: Find the change in y for each step in x.
- Which equation is NOT linear? (y = x/2 + 1 / 2x + y = 5 / y = xΒ³ β x / y = 7 β x) β y = xΒ³ β xPrompt: A linear equation only has x to the power 1 (no xΒ², no x in a denominator or exponent).
You do: independent practice Β· 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 Β· 3 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Which equation is NOT linear? (y = 7 β x / y = 3x β 2 / 2x + y = 5 / y = 3Λ£) β y = 3Λ£Prompt: A linear equation only has x to the power 1 (no xΒ², no x in a denominator or exponent).
- x: 0, 1, 2, 3, 4. y: 1, 4, 7, 10, 13. Is the function linear? (Linear / Nonlinear) β LinearPrompt: Find the change in y for each step in 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: 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