• 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 30 and 35. → 5Prompt: List the factors of the smaller number.
2. Find the LCM (lowest common multiple) of 11 and 9. → 99Prompt: List multiples of 11.
3. 60 = 2² × 3 × 5 and 150 = 2 × 3 × 5². Use these to find the GCF of 60 and 150. → 30Prompt: 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 27 pencils and 63 erasers. They make identical kits with nothing left over. What is the greatest number of kits they can make? → 9Prompt: The number of kits must divide both amounts.
2. 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.

• 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. A club has 18 stickers and 27 badges. They make identical kits with nothing left over. What is the greatest number of kits they can make? → 9Prompt: The number of kits must divide both amounts.
2. Which do you need: the GCF or the LCM? Find when two repeating app reminders next go off on the same day. (GCF / LCM) → LCMPrompt: 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.