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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? {(−3, 2), (−3, 6), (2, −1), (8, 4), (−5, 1)} (Yes / No) → NoPrompt: In a function, each input (x) has exactly one output (y).
  2. Which set of ordered pairs is a function? ({(−2, 5), (2, 5), (1, −4), (−2, 7)} / {(0, −1), (−3, 3), (4, 0), (4, 2)} / {(2, −4), (3, 0), (−4, −1), (3, −3)} / {(2, 6), (−1, −2), (−3, 4), (0, −4)}) → {(2, 6), (−1, −2), (−3, 4), (0, −4)}Prompt: Check the first coordinates in each set.
  3. Is this relation a function? {(−1, 7), (−5, −6), (0, −5), (3, −3), (5, 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 = {(−1, 6), (−2, 5), (9, 2), (−3, −3)}. What is the range of R? ({−3, 2, 5} / {−3, −2, −1, 9} / {−3, −2, −1, 2, 5, 6, 9} / {−3, 2, 5, 6}) → {−3, 2, 5, 6}Prompt: Domain: all the inputs (first numbers). Range: all the outputs (second numbers).
  2. The function f = {(−2, 1), (0, 1), (2, 0), (5, −4), (9, −4), (1, 0)}. 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. R = {(−5, −4), (−6, 1), (6, −2), (8, −1)}. What is the range of R? ({−6, −5, 6, 8} / {−4, −2, −1, 1} / {−4, −2, −1} / {−6, −5, −4, −2, −1, 1, 6, 8}) → {−4, −2, −1, 1}Prompt: Domain: all the inputs (first numbers). Range: all the outputs (second numbers).
  2. The function f = {(6, 6), (0, 2), (−5, 2), (1, 6), (9, 7), (2, 7)}. How many different values are in its range? → 3Prompt: The range is the set of outputs.

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

    R = {(−2, 2), (0, −5), (−3, −1), (6, 5)}. What is the range of R?

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

  2. Question 2

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

    Answer

  3. Question 3

    R = {(5, 4), (−2, 2), (2, −1), (8, 3)}. What is the domain of R?

    • A. {−2, −1, 2, 3, 4, 5, 8}
    • B. {−1, 2, 3, 4}
    • C. {−2, 2, 5}
    • D. {−2, 2, 5, 8}

  4. Question 4

    The function f = {(8, 3), (−5, 3), (7, 2), (−2, 2), (−3, 1), (3, 1)}. How many different values are in its range?

    Answer

  5. Question 5

    R = {(9, 4), (6, 6), (8, 5), (1, −4)}. What is the domain of R?

    • A. {−4, 1, 4, 5, 6, 8, 9}
    • B. {1, 6, 8, 9}
    • C. {−4, 4, 5, 6}
    • D. {1, 6, 8}

  6. Question 6

    The function f = {(6, 3), (−4, −4), (7, 0), (5, 3), (−1, 0), (−3, −4)}. How many different values are in its range?

    Answer

  7. Question 7

    R = {(6, 0), (−3, −6), (9, −1), (−6, 1)}. What is the domain of R?

    • A. {−6, −1, 0, 1}
    • B. {−6, −3, 6, 9}
    • C. {−6, −3, 6}
    • D. {−6, −3, −1, 0, 1, 6, 9}

  8. Question 8

    The function f = {(3, −4), (9, −1), (2, −1), (−2, 8), (1, −4), (−5, 8)}. How many different values are in its range?

    Answer

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

  1. 1. B. {−5, −1, 2, 5}

  2. 2. 3

  3. 3. D. {−2, 2, 5, 8}

  4. 4. 3

  5. 5. B. {1, 6, 8, 9}

  6. 6. 3

  7. 7. B. {−6, −3, 6, 9}

  8. 8. 3