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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. Sofia earns 12 for each hour of dog walking: e = 12h. How much does Sofia earn for 3 hours? → 36Prompt: Substitute the number of hours for h.
  2. Which equation matches the table? x: 1, 2, 3, 4 → y: 5, 6, 7, 8 (y = 5x / y = x + 4 / y = x − 4 / y = 4x) → y = x + 4Prompt: Test each equation with the first pair, then with another pair.
  3. Ravi earns 5 for each hour of dog walking: e = 5h. How much does Ravi earn for 10 hours? → 50Prompt: 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? {(0, −9), (−5, 1), (5, −4), (1, 6)} (Yes / No) → YesPrompt: A function gives exactly one output for each input.
  2. Function A: y = 2x + 1. Function B is shown by the table x: 0, 1, 2, 3 → y: 3, 8.5, 14, 19.5. Which has the greater rate of change? (A / B / They are equal) → BPrompt: The rate of change of A is the coefficient of x.

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? {(3, 0), (−5, 0), (2, 7), (1, 1)} (Yes / No) → YesPrompt: A function gives exactly one output for each input.
  2. Is the function y = x² + 2 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 = 3x − 2 linear or non-linear?

    • A. Linear
    • B. Non-linear

  2. Question 2

    Is this relation a function? {(3, 0), (6, 5), (0, 1), (9, 0)}

    • A. Yes
    • B. No

  3. Question 3

    Function A: y = 5x + 6. Function B is shown by the table x: 0, 1, 2, 3 → y: 6, 7.5, 9, 10.5. Which has the greater rate of change?

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

  4. Question 4

    Is the function y = x² + 1 linear or non-linear?

    • A. Linear
    • B. Non-linear

  5. Question 5

    Is this relation a function? {(−5, −8), (9, 0), (3, −2), (2, 1)}

    • A. Yes
    • B. No

  6. Question 6

    Function A: y = 3x + 3. Function B is shown by the table x: 0, 1, 2, 3 → y: 5, 9, 13, 17. Which has the greater rate of change?

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

  7. Question 7

    Is the function y = x² + 3 linear or non-linear?

    • A. Linear
    • B. Non-linear

  8. Question 8

    Is this relation a function? {(−4, 6), (3, 8), (−1, 4), (2, 8)}

    • A. Yes
    • B. No

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Answer key: Functions: definition and comparison

  1. 1. A. Linear

  2. 2. A. Yes

  3. 3. A. A

  4. 4. B. Non-linear

  5. 5. A. Yes

  6. 6. B. B

  7. 7. B. Non-linear

  8. 8. A. Yes