*This is a collaborative guest post
From a young age, children are introduced to the concept of division. Whether they are sharing sweets with their friends or grouping their toys, children will need to do some simple divisions at some point.
Sharing their favorite treats is perhaps the easiest way to explain the concept of division to younger kids. After all, sweets are something they love, and they are more likely to pay attention once sweets are involved!
It is one thing to explain the concept of division to children, and it is quite another to have them make sense of the symbols. Here, long division worksheets will come in handy.
Teaching division in terms of sharing and grouping
Your child will be taught about division in terms of grouping and sharing. For example, the teacher will instruct them to share a certain amount between a specified number of people, or to group an amount into equal pairs. It is important that children understand the difference between both instructions.
When Nathan has 6 cookies and is asked to share it equally among his 3 friends, Nathan will need to share out the cookies one at a time until everyone has equal amounts. That is; 6 ÷ 3 gives 2 cookies each. 6 ÷ 3 = 2.
Grouping has a slightly different dynamic than sharing. When Nathan has 6 cookies and intends to store them away in bags, how many bags of cookies will he end up with? Nathan will get his answer by filling each bag with a cookie one at a time, until the every bag has equal number of cookies. This time, we end up with 3 bags containing 2 cookies each, and the answer here is not the number of cookies each bag contains, but the number of bags in total.
That is; 6 ÷ 2 = 3. As children come along in their learning, they will come to see and understand how division is the opposite of multiplication.
Teaching division with arrays
Arrays are a wonderful way of teaching younger kids the relationship between multiplication and division. An array doesn’t work with sharing or grouping. Rather, objects are arranged in rows and columns, and children can see how division and multiplication can be interpreted from the arrangement.
For example; 3 groups of 2 represents the calculation 3 x 2 = 6.
Similarly, 2 groups of 3 represents the calculation 2 x 3 = 6.
Also, 6 split into 3 equal shares of 2 represents the equation 6 ÷ 3 = 2.
6 split into 2 equal shares of 3 represents the equation 6 ÷ 2 = 3.
Although these representations and strategies for introducing your child to multiplication and division might seem very technical and unnecessary for young learners who are just starting out with math, it is important that children understand the structure of the equations they are solving. Rather than simply giving children division problems such as 6 ÷ 3 to solve, it helps if they are able to attach representations to these equations.
As shown above, putting equations in concrete representations help children understand better the link between division and multiplication, and helps them see how division problems can be solved in more than one way.