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

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