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Math lesson plan · 9th grade (Year 10 in England) · 30 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 · 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.
  1. Is this relation a function? {(6, −7), (−1, 6), (0, 7), (1, −1)} (Yes / No) → YesPrompt: A function gives exactly one output for each input.
  2. Function A: y = 3x + 6. Function B is shown by the table x: 0, 1, 2, 3 → y: 8, 17, 26, 35. Which has the greater rate of change? (A / B / They are equal) → BPrompt: The rate of change of A is the coefficient of x.
  3. Is the function y = 4 − 4x linear or non-linear? (Linear / Non-linear) → LinearPrompt: A linear function can be written as y = mx + b.

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

You do: independent practice · 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 · 3 min

  • Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
  1. Which set of ordered pairs is a function? ({(−1, 2), (1, 3), (6, −4), (6, −7)} / {(4, 7), (−4, 1), (−2, 6), (−2, 8)} / {(5, −4), (6, 2), (2, 3), (5, −2)} / {(−1, 0), (0, 6), (6, 5), (3, 6)}) → {(−1, 0), (0, 6), (6, 5), (3, 6)}Prompt: Check the first coordinates in each set.
  2. Is this relation a function? {(1, 3), (−2, 8), (2, 4), (6, 8), (4, −4)} (Yes / No) → YesPrompt: In a function, each input (x) has exactly one output (y).

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

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Decide whether a relation is a function

Name

Date

Score/ 6

  1. Question 1

    Is this relation a function? {(−6, −5), (2, 8), (2, 9), (−3, 1), (4, 0)}

    • A. Yes
    • B. No

  2. Question 2

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

    xy−66−66120(3, 4)(2, 5)(−5, 2)(5, −2)(3, 1)
    • A. Yes
    • B. No

  3. Question 3

    Which set of ordered pairs is a function?

    • A. {(4, −3), (5, −2), (−1, 6), (4, −4)}
    • B. {(0, −4), (2, 6), (5, 1), (5, −2)}
    • C. {(−4, −4), (2, 3), (−1, −1), (2, 2)}
    • D. {(−4, −1), (1, 4), (5, 6), (−2, −4)}

  4. Question 4

    Is this relation a function? {(8, 0), (1, −8), (1, −4), (−5, 4), (3, 6)}

    • A. Yes
    • B. No

  5. Question 5

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

    • A. Yes
    • B. No

  6. Question 6

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

    • A. Yes
    • B. No

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Answer key: Decide whether a relation is a function

  1. 1. B. No

  2. 2. B. No

  3. 3. D. {(−4, −1), (1, 4), (5, 6), (−2, −4)}

  4. 4. B. No

  5. 5. A. Yes

  6. 6. B. No