• Quick retrieval from earlier learning (Solve equations with x on both sides). Students answer on mini whiteboards.
• Show answers together and note who needs support in the main task.

1. Solve: −5x + 9 = x + 15 → x = -1Prompt: Add 5x to both sides so the x-term stays positive.
2. Ben solved 3x − 9 = 2x − 3 by adding 2x to both sides. Explain the mistake by finding the correct value of x. → x = 6Prompt: To remove 2x from the right, you must SUBTRACT 2x.
3. Solve: −3x + 10 = 2x − 15 → x = 5Prompt: Add 3x to both sides so the x-term stays positive.

• Show a "think of a number" puzzle and ask the class to work out the starting number.
• Share the objective: When are two plans equal? Equations from real comparisons. Read the success criteria together.

• Work through the example out loud, saying why you do each step, not just what you do.
• Example: Gym A charges $33 to join plus $3 per visit. Gym B charges $6 to join plus $6 per visit. For how many visits do they cost the same?
• Step 1: 33 − 6 = 6n − 3n
• Step 2: 27 = 3n
• Step 3: n = 9
• Answer: 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. Gym A charges $25 to join plus $4 per visit. Gym B charges $0 to join plus $9 per visit. For how many visits do they cost the same? → 5Prompt: Write each cost for n visits/films and set them equal.
2. Priya has $4 and saves $4 a week. Ines has nothing yet and saves $5 a week. After how many weeks will they have the same amount? → 4Prompt: Write each person's total after w weeks and set them equal.

• 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. Candle A is 24 cm tall and burns 5 cm per hour. Candle B is 12 cm tall and burns 2 cm per hour. After how many hours are they the same height? → 4Prompt: Write each candle's height after h hours and set them equal.
2. Sofia has $10 and saves $6 a week. Grace has nothing yet and saves $7 a week. After how many weeks will they have the same amount? → 10Prompt: Write each person's total after w weeks and set them equal.

Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-8.