• Quick retrieval from earlier learning (Solve systems by elimination; Solve systems by substitution). Students answer on mini whiteboards.
• Show answers together and note who needs support in the main task.

1. Solve: 3x + y = 23 and 5x − y = 25. Type the solution like (2, −3). → (6, 5)Prompt: The y-terms are opposites. Add the equations to eliminate y.
2. Solve the system: y = 2x + 12 and 5x − 3y = −34. Type the solution like (2, −3). → (−2, 8)Prompt: Substitute 2x + 12 for y in the second equation.
3. Solve: x + 2y = 4 and 3x − 4y = 2. Type the solution like (2, −3). → (2, 1)Prompt: Multiply the first equation by 3 so the x-terms match.

• Show a "think of a number" puzzle and ask the class to work out the starting number.
• Share the objective: Solve real problems with two equations. Read the success criteria together.

• Work through the example out loud, saying why you do each step, not just what you do.
• Example: At a museum, 5 adult and 5 child tickets cost $70. 4 adult and 2 child tickets cost $48. How much is one adult ticket? (Type the number only.)
• Step 1: c = 4
• Step 2: a = 10
• Answer: 10
• 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. At a museum, 3 adult and 5 child tickets cost $52. 3 adult and 3 child tickets cost $42. How much is one adult ticket? (Type the number only.) → 9Prompt: Let a = adult price and c = child price. Write one equation for each group of tickets.
2. In a basketball game, Mateo made 26 baskets, all 2-pointers or 3-pointers, scoring 70 points. How many 3-pointers did Mateo make? → 18Prompt: t + h = 26 and 2t + 3h = 70 (t = twos, h = threes).

• 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. In a basketball game, Amara made 28 baskets, all 2-pointers or 3-pointers, scoring 75 points. How many 3-pointers did Amara make? → 19Prompt: t + h = 28 and 2t + 3h = 75 (t = twos, h = threes).
2. At a museum, 5 adult and 4 child tickets cost $107. 5 adult and 2 child tickets cost $91. How much is one adult ticket? (Type the number only.) → 15Prompt: Let a = adult price and c = child price. Write one equation for each group of tickets.

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