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Math lesson plan · 8th grade (Year 9 in England) · 45 minutes

Functions: definition and comparison

Algebra

CCSS 8.F.A.1CCSS 8.F.A.2CCSS 8.F.A.3England: KS3 AlgebraEngland: GCSE Higher Algebra

Objective and success criteria

Students will: Functions: definition and comparison.

  • 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: Dependent and independent variables; Graphs of linear equations y = mx + b

Leads to: Function notation; Decide whether a relation is a function; Tell linear from nonlinear functions

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 (Dependent and independent variables; Graphs of linear equations y = mx + b). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. Yuki earns 4 for each hour of dog walking: e = 4h. How much does Yuki earn for 14 hours? → 56Prompt: Substitute the number of hours for h.
  2. Which equation matches the table? x: 1, 2, 3, 4 → y: 8, 9, 10, 11 (y = 8x / y = x + 7 / y = x − 7 / y = 7x) → y = x + 7Prompt: Test each equation with the first pair, then with another pair.
  3. Sam earns 5 for each hour of dog walking: e = 5h. How much does Sam earn for 3 hours? → 15Prompt: Substitute the number of hours for h.

Hook · 5 min

  • Show a "think of a number" puzzle and ask the class to work out the starting number.
  • Share the objective: Functions: definition and comparison. 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 this relation a function? {(5, 7), (−5, 0), (6, 7), (−2, 1)}
  • Step 1: Every input has one output: yes.
  • Answer: Yes
  • 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.
  1. Is this relation a function? {(9, 0), (8, −1), (2, 5), (9, 2)} (Yes / No) → NoPrompt: A function gives exactly one output for each input.
  2. Function A: y = 7x + 9. Function B is shown by the table x: 0, 1, 2, 3 → y: 3, 4, 5, 6. Which has the greater rate of change? (A / B / They are equal) → APrompt: The rate of change of A is the coefficient of 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.
  1. Is this relation a function? {(−2, 8), (4, 4), (6, 3), (−2, 9)} (Yes / No) → NoPrompt: A function gives exactly one output for each input.
  2. Is the function y = 4/x linear or non-linear? (Linear / Non-linear) → Non-linearPrompt: A linear function can be written as y = mx + b.

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: Dependent and independent variables.
  • 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

  • Move on to: Function notation; Decide whether a relation is a function; Tell linear from nonlinear functions.
  • 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

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Functions: definition and comparison

Name

Date

Score/ 8

  1. Question 1

    Is the function y = 5x − 9 linear or non-linear?

    • A. Linear
    • B. Non-linear

  2. Question 2

    Function A: y = 7x + 4. Function B is shown by the table x: 0, 1, 2, 3 → y: 8, 15, 22, 29. Which has the greater rate of change?

    • A. A
    • B. B
    • C. They are equal

  3. Question 3

    Is this relation a function? {(−3, −5), (9, 4), (5, 8), (−3, −3)}

    • A. Yes
    • B. No

  4. Question 4

    Is the function y = 7x − 4 linear or non-linear?

    • A. Linear
    • B. Non-linear

  5. Question 5

    Function A: y = 7x. Function B is shown by the table x: 0, 1, 2, 3 → y: 5, 12, 19, 26. Which has the greater rate of change?

    • A. A
    • B. B
    • C. They are equal

  6. Question 6

    Is this relation a function? {(1, −3), (4, 2), (0, 2), (1, −1)}

    • A. Yes
    • B. No

  7. Question 7

    Is the function y = 8x − 1 linear or non-linear?

    • A. Linear
    • B. Non-linear

  8. Question 8

    Function A: y = 3x + 3. Function B is shown by the table x: 0, 1, 2, 3 → y: 5, 13.5, 22, 30.5. Which has the greater rate of change?

    • A. A
    • B. B
    • C. They are equal

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Answer key: Functions: definition and comparison

  1. 1. A. Linear

  2. 2. C. They are equal

  3. 3. B. No

  4. 4. A. Linear

  5. 5. C. They are equal

  6. 6. B. No

  7. 7. A. Linear

  8. 8. B. B