• 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: −3x − 8 = 4x − 1 → x = -1Prompt: Add 3x to both sides so the x-term stays positive.
2. Ben solved 5x + 1 = 4x − 4 by adding 4x to both sides. Explain the mistake by finding the correct value of x. → x = -5Prompt: To remove 4x from the right, you must SUBTRACT 4x.
3. Solve: −4x − 11 = x + 24 → x = -7Prompt: Add 4x 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 $52 to join plus $5 per visit. Gym B charges $4 to join plus $9 per visit. For how many visits do they cost the same? → 12Prompt: Write each cost for n visits/films and set them equal.
2. Nia has $8 and saves $2 a week. Zoe has nothing yet and saves $4 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 38 cm tall and burns 2 cm per hour. Candle B is 35 cm tall and burns 1 cm per hour. After how many hours are they the same height? → 3Prompt: Write each candle's height after h hours and set them equal.
2. Omar has $6 and saves $5 a week. Zoe has nothing yet and saves $6 a week. After how many weeks will they have the same amount? → 6Prompt: 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.