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