Lockdown Day 83 – Division
Numeracy and Arithmetic
We have in previous posts explored counting and the child’s introduction to mathematical operations of addition, multiplication and subtraction. Today’s post looks at the final (and most ‘disliked) mathematical operation.
Division involves breaking a number up into an equal number of parts. This concept builds on a child’s previous knowledge of addition, subtraction, and multiplication. As with any such concept, it is important to build an early concrete understanding of this concept to facilitate future, more abstract, learning. As with all operations, it is important to realise that children unknowingly use these concepts in their everyday living. The most effective learning comes from the concrete illustration of these problems in real-life situations that children can relate to, not from paper and pencil tasks.
Division allows us to divide or share numbers to find an answer. Please ensure that you know the correct terminology for division – this will allow you to use the terminology with the children in your day to day speaking, which will take the ‘fear’ out of meeting the words later on.
- The number that is being divided is called the DIVIDEND.
- The number that the dividend is being divided by is called the DIVISOR.
- The answer to the operation is called the QUOTIENT.
Let’s take an example. Say you have 10 apples. 10 is the dividend. You want to divide or share these 10 apples between 2 children. 2 is the divisor. At the end of the division process each child will have 5 apples. The answer to a division problem is the equal amount that each ‘child’ receives. 5 is the quotient.
INTRODUCING DIVISION TO YOUNG CHILDREN
Present division as a way to SHARE.
- Decide on the divisor – how many people are you going to share amongst?
- Give the child a dividend (the number of items to be shared) that is equally divisible by the divisor. I.e. If your divisor is 3, your dividend will need to be a number that is equally divisible by 3.
- Ask the child to count the dividend 
- Tell the child that the divisor is 3 (i.e. they will be sharing the 12 objects equally between the three people)
- Once the dividend has been equally shared (one for you, one for you and one for you), ask the child to count what each person received. The child will notice that each person received 4 objects. They each received an EQUAL amount. The amount that each person equally received is the quotient.
- State the equation: 12 divided by 3 equals 4.
Present division as a way to DIVIDE items into SMALLER, EQUAL GROUPS.
- Give the child a quantity of objects and ask the child to count how many objects there are in total (dividend). In this example we will use 12 beans.
- Ask the child to divide the 12 beans into equal groups of 6.
- Reiterate that the dividend was 12 and ask the child how to identify the divisor. How many equal groups are there? (2)
- State the equation and ask the child to complete it: 12 divided by two equals… (6).
- Keep the same 12 beans and push them all together again. Now ask the child to divide the dividend into equal groups of 4 and repeat the above steps.
- You can repeat this process with all the divisors of 12. This will allow the child to realise that the same dividend can be divided equally among differing divisors.
INTRODUCING THE CONCEPT OF A REMAINDER
Once the child has had a fair amount of experience with equations that divide equally, you may wish to throw the child a curve ball! Do not do this too soon though.
- Give the child 10 small biscuits and ask the child to share these equally between three people.
- The child will dish the biscuits out (one for you, one for you and one for you) until each person has three biscuits.
- They will be left with the dilemma of having one biscuit remain!
- Discuss whether it would be fair to give this biscuit to Person A. This would mean that person A has 4 biscuits whereas the other two persons only have 3 biscuits. Is this equal?
- The only fair way to resolve this dilemma is that each person gets 3 biscuits and that 1 biscuit ‘remains’ in the packet.
Whilst many children will learn multiplication and division tables by rote during the course of their schooling, a large majority of children end up finding word problems challenging.
Again, there are concrete ‘fun’ strategies that we can use in these early stages that allow children to understand that division operations can take different forms.
When faced with a word problem, the child needs to figure out how to set the problem up themselves instead of being given numbers in a problem already set up for them. A change in wording can easily change the equation.
As an example, let’s use a dividend of 20.
- First problem: If you have 20 sweets and you put them into boxes that each need to contain 4 sweets, how many boxes will you fill?
This requires the child to divide 20 by 4 to get a quotient of 5 for the answer.
- Second problem: If you have 20 sweets and you need to put an equal amount of sweets into 10 boxes, how many sweets will be in each box?
This requires the child to divide 20 by 10 to get a quotient of 2 for the answer.
- Third problem: If you have 20 sweets and you need to put an equal number of sweets into 6 boxes, how many sweets will be left over?
This requires that child divide 20 by 6. The quotient will be 3, and there will be two sweets remaining.
A good foundation with these early division concepts will stand the child in very good stead when faced with more abstract division equations on paper later on. The understanding of division is also most important as a foundation for fractions and decimals in later years.
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