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Math lesson plan · 9th grade (Year 10 in England) · 60 minutes

Decide whether a relation is a function

Algebra

CCSS HSF.IF.A.1England: GCSE Higher 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: Find the domain and range of a set of ordered pairs

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.
  1. Is this relation a function? {(−1, 9), (4, 9), (5, 5), (−1, 10)} (Yes / No) → NoPrompt: A function gives exactly one output for each input.
  2. Function A: y = 8x + 7. Function B is shown by the table x: 0, 1, 2, 3 → y: 9, 13.5, 18, 22.5. Which has the greater rate of change? (A / B / They are equal) → APrompt: The rate of change of A is the coefficient of x.
  3. Is the function y = 6x − 7 linear or non-linear? (Linear / Non-linear) → 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: Decide whether a relation is a function. 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: Is this relation a function? {(−1, 7), (7, −3), (−3, 5), (−3, 1), (4, 2)}
  • Step 1: x = −3 has two different outputs: not a function.
  • Step 2: No
  • Answer: No
  • 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.
  1. Is this relation a function? {(7, 9), (−2, −6), (−4, −5), (4, 1), (2, −2)} (Yes / No) → YesPrompt: In a function, each input (x) has exactly one output (y).
  2. Which set of ordered pairs is a function? ({(−1, 7), (2, 4), (−3, −4), (−4, 3)} / {(5, 4), (−2, −1), (6, 3), (−2, −4)} / {(4, −4), (3, −4), (−4, 2), (3, −5)} / {(−3, 0), (4, −3), (3, 3), (−3, 1)}) → {(−1, 7), (2, 4), (−3, −4), (−4, 3)}Prompt: Check the first coordinates in each set.

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.
  1. Is this relation a function? {(−3, −4), (−6, −6), (1, 1), (5, 6), (5, 8)} (Yes / No) → NoPrompt: In a function, each input (x) has exactly one output (y).
  2. Which set of ordered pairs is a function? ({(−4, 5), (6, −3), (5, −1), (−2, 5)} / {(−2, −3), (−3, 5), (−1, −1), (−3, 2)} / {(3, 4), (2, −1), (6, 3), (3, 3)} / {(3, 5), (0, 3), (−4, −1), (3, 7)}) → {(−4, 5), (6, −3), (5, −1), (−2, 5)}Prompt: Check the first coordinates in each set.

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

  • Move on to: Find the domain and range of a set of ordered pairs.
  • 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-9.

Free lesson plan from eurekami.com/lesson-plan-builder

eurekami

Decide whether a relation is a function

Name

Date

Score/ 8

  1. Question 1

    Is this relation a function? {(−4, 2), (−4, −1), (−2, 0), (7, 1), (0, −5)}

    • A. Yes
    • B. No

  2. Question 2

    Which set of ordered pairs is a function?

    • A. {(4, 3), (5, −1), (6, 7), (4, 2)}
    • B. {(1, 5), (3, −3), (2, 1), (3, −4)}
    • C. {(3, −2), (1, −2), (−4, 4), (−3, −2)}
    • D. {(6, −2), (5, 5), (4, 3), (6, −5)}

  3. Question 3

    The graph shows a set of points. Do they represent a function of x?

    xy−66−66120(1, 5)(−4, 6)(−1, −4)(5, 4)(1, 8)
    • A. Yes
    • B. No

  4. Question 4

    Is this relation a function? {(1, 0), (5, 2), (1, 4), (−4, 0), (−2, −3)}

    • A. Yes
    • B. No

  5. Question 5

    Is this relation a function? {(−2, 9), (4, 8), (3, 4), (−4, 2), (6, −2)}

    • A. Yes
    • B. No

  6. Question 6

    Is this relation a function? {(2, −5), (4, 7), (6, −6), (8, 5), (−1, 4)}

    • A. Yes
    • B. No

  7. Question 7

    Is this relation a function? {(3, 2), (6, 0), (5, −2), (2, 7), (5, 1)}

    • A. Yes
    • B. No

  8. Question 8

    Is this relation a function? {(3, −1), (2, −6), (−4, 9), (8, −6), (7, 0)}

    • A. Yes
    • B. No

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Answer key: Decide whether a relation is a function

  1. 1. B. No

  2. 2. C. {(3, −2), (1, −2), (−4, 4), (−3, −2)}

  3. 3. B. No

  4. 4. B. No

  5. 5. A. Yes

  6. 6. A. Yes

  7. 7. B. No

  8. 8. A. Yes