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Math lesson plan · 9th grade (Year 10 in England) · 45 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 · 5 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? {(9, −8), (7, 1), (−2, −6), (9, −7)} (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: 1, 5, 9, 13. 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 = 7x − 8 linear or non-linear? (Linear / Non-linear) → LinearPrompt: A linear function can be written as y = mx + b.

Hook · 5 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 · 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? {(−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 · 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? {(6, −1), (1, −1), (0, −5), (6, 0), (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? ({(−3, 0), (5, 4), (−2, −1), (−2, −4)} / {(0, −2), (1, 4), (−4, 3), (−3, 2)} / {(0, 1), (−3, 0), (3, 3), (0, 3)} / {(−4, 7), (6, 4), (−1, −2), (6, 6)}) → {(0, −2), (1, 4), (−4, 3), (−3, 2)}Prompt: Check the first coordinates in each set.

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? {(0, 3), (−3, −3), (8, 2), (−4, 8), (−2, −1)} (Yes / No) → YesPrompt: In a function, each input (x) has exactly one output (y).
  2. Which set of ordered pairs is a function? ({(3, 7), (4, 7), (−4, 5), (−4, 4)} / {(5, 1), (0, 0), (2, 3), (0, 2)} / {(5, 6), (0, 4), (−1, 2), (−1, 1)} / {(−3, 2), (−1, 1), (5, 2), (−4, −1)}) → {(−3, 2), (−1, 1), (5, 2), (−4, −1)}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

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

    xy−66−66120(−4, 1)(−2, 6)(0, 0)(−5, 0)(−4, 4)
    • A. Yes
    • B. No

  2. Question 2

    Which set of ordered pairs is a function?

    • A. {(−3, −4), (4, 6), (−1, −2), (−3, −2)}
    • B. {(6, 5), (0, −3), (1, −3), (0, −2)}
    • C. {(6, 7), (1, −2), (5, 5), (5, 6)}
    • D. {(0, −2), (2, −3), (−2, −3), (−1, 5)}

  3. Question 3

    Is this relation a function? {(6, 7), (−5, −5), (−4, 1), (7, 6), (6, 9)}

    • A. Yes
    • B. No

  4. Question 4

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

    • A. Yes
    • B. No

  5. Question 5

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

    • A. Yes
    • B. No

  6. Question 6

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

    • A. Yes
    • B. No

  7. Question 7

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

    • A. Yes
    • B. No

  8. Question 8

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

    • A. Yes
    • B. No

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Answer key: Decide whether a relation is a function

  1. 1. B. No

  2. 2. D. {(0, −2), (2, −3), (−2, −3), (−1, 5)}

  3. 3. B. No

  4. 4. B. No

  5. 5. A. Yes

  6. 6. B. No

  7. 7. B. No

  8. 8. B. No