• Quick retrieval from earlier learning (Functions: definition and comparison). Students answer on mini whiteboards.
• Show answers together and note who needs support in the main task.

1. Is this relation a function? {(2, 2), (9, −8), (8, 5), (−5, 0)} (Yes / No) → YesPrompt: A function gives exactly one output for each input.
2. Function A: y = 6x. Function B is shown by the table x: 0, 1, 2, 3 → y: 5, 8.5, 12, 15.5. Which has the greater rate of change? (A / B / They are equal) → APrompt: The rate of change of A is the coefficient of x.
3. Is the function y = 5/x linear or non-linear? (Linear / Non-linear) → Non-linearPrompt: A linear function can be written as y = mx + b.

• Show a "think of a number" puzzle and ask the class to work out the starting number.
• Share the objective: Decide whether a relation is a function. Read the success criteria together.

• Work through the example out loud, saying why you do each step, not just what you do.
• Example: Is this relation a function? {(−1, 7), (7, −3), (−3, 5), (−3, 1), (4, 2)}
• Step 1: x = −3 has two different outputs: not a function.
• Step 2: No
• Answer: No
• 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. Is this relation a function? {(−2, 6), (−2, 5), (−3, 6), (8, 1), (−5, 2)} (Yes / No) → NoPrompt: In a function, each input (x) has exactly one output (y).
2. Which set of ordered pairs is a function? ({(5, 0), (−3, −1), (2, 0), (−3, −2)} / {(2, −4), (0, 4), (6, −2), (0, 3)} / {(1, 7), (−2, 4), (3, 3), (0, 1)} / {(3, −4), (1, 5), (−1, 0), (−1, −1)}) → {(1, 7), (−2, 4), (3, 3), (0, 1)}Prompt: Check the first coordinates in each set.

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

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