Having watched Ioan sharing in to equal groups, Finny begged me for his own ‘sharing’ tray. So, I challenged him to look at dividing by 2.
- Tuff tray
- Bath crayons
First, Finny read the information given.
Dory has 12 shells
He set the 12 shells out in two lines, the way Dory does, then started drawing around his groups of 2, as if they were arrays.
He had a go filling in the number sentence underneath. “There are _ groups with _ shells in each group.”
Finny then used his grouped shells to fill in the sums. To do this he needed to know that: 12 shells shared between 2 is 6.
The ‘shared between‘ can be replaced by a ÷ symbol, because ‘shared between’ means divide by.
The ‘is‘ can be replaced by an = sign.
He also worked out that if he knew 12 ÷ 6 = 2, then he could also write 2 x 6 = 12.
Ioan talks more about the connection between ‘shared between‘ and the ÷ symbol in a post on ‘Making Equal Groups’.
Finny had a go at working the 2 x 6 = 12 practically, with some more shells. He set them out in arrays, then showed me it could also make 6 x 2 = 12. There is also a post on ‘Making Arrays’.
Dory has 16 shells
For _ x 2 = 16, Finny knew straight away that it was 8, so I asked him to show me how he knew.
Multiplication and division are inverse operations. Start with 8, then multiply it by 2 and we get 16. Now divide 16 by 2 and we get back to 8.
Dory has 20 shells
This time there was a number line, to show the equal groups, or ‘jumps’ of 2. Finny recognised that they were all even numbers. He counted up the jumps, to get 20 ÷ 2 = 10.
I asked Finny to show me 20 ÷ 2 = 10 using the shells. Then I asked if there was another way to work this out. He rearranged the shells to come up with 20 ÷ 10 = 2.
Finally, he demonstrated what 20 ÷ 10 = 2 would look like on his number line.
Before and after
DfES Outcomes for EYFS and National Curriculum (2013)
Numeracy Year 2 programme of study
Number – multiplication and division
- recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers
- calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs
- show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot
- solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts.