• Quick retrieval from earlier learning (Greatest common factor of two or three numbers; Least common multiple of two or three numbers). Students answer on mini whiteboards.
• Show answers together and note who needs support in the main task.

1. Find the GCF (highest common factor) of 18 and 63. → 9Prompt: List the factors of the smaller number.
2. Find the LCM (lowest common multiple) of 6 and 2. → 6Prompt: List multiples of 6.
3. 96 = 2⁵ × 3 and 144 = 2⁴ × 3². Use these to find the GCF of 96 and 144. → 48Prompt: Take each prime that appears in BOTH factorisations.

• Show a number in the news or a price tag and ask what each digit is worth.
• Share the objective: Choose GCF or LCM to solve a problem. Read the success criteria together.

• Work through the example out loud, saying why you do each step, not just what you do.
• Example: A club has 27 red tulips and 45 yellow tulips. They make identical kits with nothing left over. What is the greatest number of kits they can make?
• Step 1: GCF of 27 and 45 = 9
• Step 2: 9 kits, each with 3 red tulips and 5 yellow tulips.
• 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. A club has 6 red tulips and 21 yellow tulips. They make identical kits with nothing left over. What is the greatest number of kits they can make? → 3Prompt: The number of kits must divide both amounts.
2. Two lighthouse lights flash together. One flashes every 15 seconds, the other every 20 seconds. After how many seconds will they next be together? → 60Prompt: The time must be a multiple of both numbers.

• 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. Two runners start together on a track. One completes a lap every 9 seconds, the other every 12 seconds. After how many seconds will they next be together? → 36Prompt: The time must be a multiple of both numbers.
2. Which do you need: the GCF or the LCM? Tile a rectangular floor with the largest possible square tiles. (GCF / LCM) → GCFPrompt: Splitting into the largest equal groups → a factor of both numbers.

Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-6.