• 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? {(−6, 5), (7, 5), (−6, 6), (−1, 5), (8, −5)} (Yes / No) → NoPrompt: In a function, each input (x) has exactly one output (y).
2. Which set of ordered pairs is a function? ({(5, −4), (1, 4), (4, 3), (−2, −3)} / {(4, −2), (1, −1), (6, 1), (4, 0)} / {(2, −1), (−3, 6), (−4, 2), (−4, 4)} / {(0, 6), (−3, −2), (−4, −1), (0, 7)}) → {(5, −4), (1, 4), (4, 3), (−2, −3)}Prompt: Check the first coordinates in each set.
3. Is this relation a function? {(0, 1), (5, −2), (3, −5), (4, 9), (−3, 6)} (Yes / No) → YesPrompt: In a function, each input (x) has exactly one output (y).

• 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.

• 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.

• 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 = {(−4, 1), (7, −1), (−5, −3), (−6, 8)}. What is the range of R? ({−3, −1, 1, 8} / {−6, −5, −4, 7} / {−6, −5, −4, −3, −1, 1, 7, 8} / {−3, −1, 1}) → {−3, −1, 1, 8}Prompt: Domain: all the inputs (first numbers). Range: all the outputs (second numbers).
2. The function f = {(−5, 3), (−2, −4), (7, −2), (4, 3), (0, −2), (−3, −4)}. How many different values are in its range? → 3Prompt: The range is the set of outputs.

• 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.

• Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.

1. R = {(−6, 0), (6, 2), (3, −4), (9, 6)}. What is the range of R? ({−4, 0, 2} / {−6, −4, 0, 2, 3, 6, 9} / {−6, 3, 6, 9} / {−4, 0, 2, 6}) → {−4, 0, 2, 6}Prompt: Domain: all the inputs (first numbers). Range: all the outputs (second numbers).
2. The function f = {(8, 5), (−1, 8), (0, 7), (5, 8), (−3, 5), (6, 7)}. How many different values are in its range? → 3Prompt: The range is the set of outputs.

Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-9.