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