Place Value - Reading and Writing Numbers
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- The first digit (M) tells us we have 1000, so nice and easy so far.
- The next digit appears to be a C, which is 100, However it precedes a digit of larger value (M=1000) so we need to know that these digits go together and actually mean C(100) less than M(1000) so 900. So we now have 1000+900=1900.
- The next digit is L(50) and does not precede a larger digit so we have 50, totaling 1950 so far.
- The next digit I(1) precedes a large digit V(5) so this again tells us that these go together and we have I(1) less than V(5) so 4. We now have a total of 1954.
Before attempting any of the tasks below, children should be confident recognising and writing the numerals 0 to 9. If they still need more practice with this, please see my post 'Early Years Counting - techniques to help kids really understand numbers'. It would also help if they already have some understanding of place value and how the number system works.
Discuss skip counting and encourage the child to think about how it is easy to "count up in" 10s. Then ask them to start putting the objects into piles of 10. Once they have more than 10 piles, talk about how it is getting difficult to keep track again and encourage them to think about how they could organise the piles into rows of 10.
Talk to the children about how many are in each pile and how many are in each row. They should relatively easily be able to see that there are 100 in each row, so if they have 3 complete rows they know they have 300.
A simple task like this gets children thinking in the same way as our number system, without having to teach them anything!
You can play a game based on this with children by getting them to act as the monsters. Each child can only remember a single digit number to keep count and they can pretend to get angry if they are asked to remember more than 9. Once you get to 10 and the first monster starts to get angry, you.will need another monster to help. You can discuss how you could get this second monster to also count to 9 but then you could only count up to 18 in total. However, if the second monster counts how many times that first monster has got angry (counted to 10) then you can count all the way to 99 with just two monsters.
Using an abacus is a great tool for making the transition from objects such a Dienes blocks. Dienes blocks help children to visually understand the relative size of each digit as the strips of 10 are the same as 10 units stacked together. However, children need to be able to understand that when we read and write numbers, it is purely the position of each digit that tells us what it is representing. For example, in the number 25, children need to understand that the 2 actually represents more than the 5.
When using an abacus, we use the second row to count how many times we have counted to 10 on the first row, thus one ball on the second row represents 10 on the first row even though the balls are the same size. This will really help children to understand that each digit is worth ten times more than the digit to its right even though they are written in the same way.
You first need to make sure that children are aware that they must always align the arrows and demonstrate how to make the number up. The act of assembling the numbers will help children to make the link between the size of the number and the position it ends up in within the larger number. For example, the 300 has the same value as the 3 in the made up number. It is also a great task for helping children to appreciate the parts of a number, e.g. 364 being made up of 300 and 60 and 4. Arrow cards can also be used when moving on to numbers that contain zeros.
Children need to understand that we start with a ones column and then build on that, moving to the left each time we need larger numbers. We only move as many digits to the left as we need but we need to keep all of the digits to the right.
For example, in the number 102, we have had to move to the left twice to account for the one hundred. However, we need something in the tens position to show that the one is two places to the left. As we have no tens, we need a zero. However, for the number 12, we do not need anything in the front (012) as we have only had to move to the left once (for the tens) so do not need a hundreds column at all.
If children can understand this they will more easily be able to understand how the numbers work after the decimal point. They will be able to understand why the zero in 1.03 has significance whilst the zero in 1.30 does not.
If you try introducing zeros too soon to a young child who is just starting to learn about the number system, it can be more detrimental than helpful. They will start getting confused and adding or removing zeros when they shouldn't, meaning that they start focusing on the digits again rather than the positions. However, if the child has had a lot of practical experience investigating the number system and how place value works it will be much easier. I would therefore strongly advise leaving out numbers that contain zeros until the child has a very strong grasp of place value.
However, he is capable of writing double digit numbers correctly - when asked to write 54, he wrote 54 rather than 504. This suggests that he, like many children, defaults to writing numbers purely from repetition and recognition rather than understanding of place value. He is currently aware of all double digit numbers and can correctly read and write most that were asked for up to 99. However, he currently has no awareness that a third digit represent hundreds, even when it is not followed by two zeros. For example, when asked to read the number 243, his reply was
This is just one case study, and at five years old the child is only just beginning the learning process - he would not be expected to have a true grasp of place value at this stage. However, I have seen examples of this lack of understanding of place value time and time again, and even in much older learners. For these children, many areas of maths are therefore much more difficult, including the use of written methods for addition/subtraction, and simple rounding and estimating. However, if we were to help all young children really understand our number system and make sure that they learn numbers through understanding place value rather than recognition then their mathematical futures would be much brighter.