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Math lesson plan · 9th grade (Year 10 in England) · 45 minutes

Find the domain and range of a set of ordered pairs

Algebra

CCSS HSF.IF.A.1

Objective and success criteria

Students will: Find the domain and range of a set of ordered pairs.

  • 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: Decide whether a relation is a function

Leads to: the next skill in this area.

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 (Decide whether a relation is a function). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. Is this relation a function? {(−2, 2), (2, 5), (8, −6), (6, 2), (4, 8)} (Yes / No) → YesPrompt: In a function, each input (x) has exactly one output (y).
  2. Which set of ordered pairs is a function? ({(6, 5), (0, 5), (−2, 1), (4, 3)} / {(−3, −3), (6, 6), (−2, −3), (−2, −1)} / {(2, 6), (5, 3), (−4, 3), (2, 8)} / {(0, 6), (−2, 4), (3, −1), (0, 7)}) → {(6, 5), (0, 5), (−2, 1), (4, 3)}Prompt: Check the first coordinates in each set.
  3. Is this relation a function? {(−4, 5), (0, −4), (−5, −4), (7, 3), (6, 7)} (Yes / No) → YesPrompt: In a function, each input (x) has exactly one output (y).

Hook · 5 min

  • Show a "think of a number" puzzle and ask the class to work out the starting number.
  • Share the objective: Find the domain and range of a set of ordered pairs. 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: R = {(9, 0), (7, −5), (3, −4), (−1, 1)}. What is the domain of R?
  • Step 1: {−1, 3, 7, 9}
  • Answer: {−1, 3, 7, 9}
  • 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. R = {(2, −4), (4, −2), (6, 1), (9, 6)}. What is the domain of R? ({2, 4, 6} / {2, 4, 6, 9} / {−4, −2, 1, 6} / {−4, −2, 1, 2, 4, 6, 9}) → {2, 4, 6, 9}Prompt: Domain: all the inputs (first numbers). Range: all the outputs (second numbers).
  2. The function f = {(4, −2), (−3, 6), (−4, −3), (9, −2), (3, 6), (0, −3)}. How many different values are in its range? → 3Prompt: The range is the set of outputs.

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. The function f = {(4, 1), (−1, 1), (3, 0), (−3, 0), (0, −4), (8, −4)}. How many different values are in its range? → 3Prompt: The range is the set of outputs.
  2. R = {(4, −5), (5, 0), (−3, 2), (6, 8)}. What is the range of R? ({−5, 0, 2} / {−5, 0, 2, 8} / {−5, −3, 0, 2, 4, 5, 6, 8} / {−3, 4, 5, 6}) → {−5, 0, 2, 8}Prompt: Domain: all the inputs (first numbers). Range: all the outputs (second numbers).

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: Decide whether a relation is a function.
  • 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

  • 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

Find the domain and range of a set of ordered pairs

Name

Date

Score/ 8

  1. Question 1

    The function f = {(3, 3), (2, −1), (−4, −1), (−2, 7), (−5, 3), (−1, 7)}. How many different values are in its range?

    Answer

  2. Question 2

    R = {(−2, 5), (−5, 9), (7, −1), (5, −2)}. What is the domain of R?

    • A. {−5, −2, 5, 7}
    • B. {−5, −2, 5}
    • C. {−2, −1, 5, 9}
    • D. {−5, −2, −1, 5, 7, 9}

  3. Question 3

    The function f = {(−1, 7), (1, −1), (7, 7), (−2, 3), (−3, −1), (9, 3)}. How many different values are in its range?

    Answer

  4. Question 4

    R = {(0, 5), (−2, 6), (4, −3), (8, 0)}. What is the range of R?

    • A. {−3, −2, 0, 4, 5, 6, 8}
    • B. {−3, 0, 5}
    • C. {−3, 0, 5, 6}
    • D. {−2, 0, 4, 8}

  5. Question 5

    The function f = {(8, 7), (6, 8), (−4, 7), (3, −3), (1, −3), (4, 8)}. How many different values are in its range?

    Answer

  6. Question 6

    R = {(7, 7), (5, 5), (0, 3), (−3, 6)}. What is the domain of R?

    • A. {−3, 0, 3, 5, 6, 7}
    • B. {−3, 0, 5}
    • C. {3, 5, 6, 7}
    • D. {−3, 0, 5, 7}

  7. Question 7

    The function f = {(−5, 2), (0, 3), (−4, −2), (−3, −2), (7, 2), (8, 3)}. How many different values are in its range?

    Answer

  8. Question 8

    R = {(−2, 9), (2, 6), (−4, −5), (−6, 7)}. What is the range of R?

    • A. {−6, −4, −2, 2}
    • B. {−5, 6, 7, 9}
    • C. {−5, 6, 7}
    • D. {−6, −5, −4, −2, 2, 6, 7, 9}

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Answer key: Find the domain and range of a set of ordered pairs

  1. 1. 3

  2. 2. A. {−5, −2, 5, 7}

  3. 3. 3

  4. 4. C. {−3, 0, 5, 6}

  5. 5. 3

  6. 6. D. {−3, 0, 5, 7}

  7. 7. 3

  8. 8. B. {−5, 6, 7, 9}