• 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, 0), (2, 1), (2, 5), (−3, 9), (−2, −3)} (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), (1, 6), (0, −3), (1, 7)} / {(3, 7), (4, 4), (2, 4), (−1, 6)} / {(4, 3), (−4, 2), (−3, −3), (−4, −1)} / {(6, 0), (5, −3), (2, 7), (6, 2)}) → {(3, 7), (4, 4), (2, 4), (−1, 6)}Prompt: Check the first coordinates in each set.
3. Is this relation a function? {(3, −1), (−1, 2), (8, 8), (−2, 10), (−2, 7)} (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 = {(−2, 7), (1, −3), (−3, 6), (−4, −2)}. What is the range of R? ({−4, −3, −2, 1, 6, 7} / {−3, −2, 6} / {−4, −3, −2, 1} / {−3, −2, 6, 7}) → {−3, −2, 6, 7}Prompt: Domain: all the inputs (first numbers). Range: all the outputs (second numbers).
2. The function f = {(0, −3), (−5, −3), (9, 0), (−4, −1), (8, 0), (2, −1)}. 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 = {(0, 0), (−1, 7), (−3, 0), (−5, 6), (9, 6), (2, 7)}. How many different values are in its range? → 3Prompt: The range is the set of outputs.
2. R = {(8, 3), (1, 5), (7, 8), (−4, 9)}. What is the domain of R? ({−4, 1, 3, 5, 7, 8, 9} / {3, 5, 8, 9} / {−4, 1, 7, 8} / {−4, 1, 7}) → {−4, 1, 7, 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.