Teacher notes

• Encourage students to see the difference in what the numbers mean in a “Sharing” problem and a “How many sets of ...?” problem.

In a “Sharing” problem they are finding “How many do each get when an amount is shared amongst a certain number groups?” The answer is the number of items in each group.                 

In a “How many sets of …?” problem they are finding “How many sets do we get when we divide an amount into sets of a certain size?” The answer is the number of sets.

• Both “Sharing” and “How many sets of …?” problems can be solved as multiplication problems where one factor is unknown. For example in a “Sharing” problem, 15 ÷ 3 = ? can be solved as 3 × ? = 15. In a “How many sets of …?” problem, 15 ÷ 3 = ? can be solved as ? × 3 = 15.      
• Students may need to use materials such as play money, at least to start with, to understand this strategy.
• Arrays are good for helping understanding. Students need to know the number in each row and are given the number of rows (number of sets).
• Student progress is often hindered because they don’t know their basic facts. It might be a good idea to check these again before starting this section.
• You could get students to work in groups for this Activity and share their ways of working out each answer. They could try and convince each other that their way is better.
• Students should understand that answers to both “Sharing” and “How many sets of …?” division problems can involve remainders. A remainder is produced when an amount cannot be shared equally or be put into sets with an equal number in each.
• To progress beyond using a number line to find the remainder, students need to be able to identify known multiplication and division facts that are close to the numbers in the problem. For example, 26 ÷ 5 is close to 25 ÷ 5 = 5 so 26 ÷ 5 = 5 with 1 left over.