A Sense of Place
At Eversfield, we spend a lot of time helping children to understand how the number system works because it is fundamental in a child’s overall mathematical development. Right from the start, we encourage children to look for patterns in numbers, for instance noticing that the units digit never changes when we add or subtract a ten. When we encounter a child who needs to count on their fingers to do this, we know it means they have yet to see the pattern and are in need of our help. To be successful at the important skill of column addition and subtraction, children first need to grasp the basic concept of tens and units. Mrs Brown and 1SB have been focusing their attention on this in recent lessons.
For children at the beginning of Form 1, learning needs to be visual and it needs to be active and, ideally, it should also be fun. No surprise then that Mrs Brown started by telling the children to stand up and look under their chairs. Beneath everyone’s chair she had hidden a card. On the card some children had a little message about place value, such as the one Sarah had, which read ‘2 tens 4 ones’. Somewhere in the classroom was another child with a card on which the same number was represented as a diagram, and the children’s task was to find each other. For instance, Jack was very pleased and proud to find Sarah, and Leo was thrilled to discover that he matched with Freddie.
This accomplished, Mrs Brown set tasks for the children to tackle individually. Some children had Dienes pictures of tens and units in their Maths books, Dienes being the Hungarian mathematician and educationalist who invented the squares, sticks and cubes we use in our classrooms. The children had to match the Dienes picture with the relevant number. It seemed hard at first but, once they had started, everyone rose to the challenge and enjoyed what they were doing. Avaida quickly realised that, in order to make 13, she needed one ten and three units. Lincoln, finding the whole experience very exciting, was soon able to work with hundreds as well as tens and units.
Most of the numbers were straightforward but a few had been included specifically to test the children’s understanding. Olivia was initially puzzled when making the number 11, which required one ten and one unit. Two items only…it didn’t seem enough, but Mrs Brown was able to reassure her that she was absolutely right. Logan was intrigued by a diagram featuring a hundred square and a single unit but no tens. What could this be? After a discussion with Pippa, he matched the diagram with the number 101. This provided an ideal opportunity to see 0 in action as what we would call a place holder. If it wasn’t there, it would be easy to muddle with 11. In the past, I have seen children write 101 as 1001 because they would say to themselves ‘one hundred and one’ and haven’t yet grasped the concept of the hundreds column. In Mrs Brown’s lesson children had the opportunity to see practically how the number system works.
We also have some very useful equipment in school called Numicon which is, if anything, even more visual than Dienes. Some children used the Numicon to make teen numbers. Haaris counted very carefully from 10 to 15 and realised that a ten piece of Numicon together with a five would go together to make the number he needed. Meanwhile, Henry spotted that he needed the blue tens piece every time, and only the units changed.
Those children who completed the core task were able to practise their place value skills further using the iPads. The place value activity they used, which is freely available via the Topmarks website, is a little more abstract than Dienes but reinforces the fact that, for example, a 4 appearing in the tens column of a number does in fact have the value of 40.
To finish, Mrs Brown called the children together and used an interactive baseball game on the whiteboard to confirm what they had learnt. Haaris quickly identified 13, whist Liam was excited to match the diagram with the number 43.
After such a successful lesson, the children should now find it easier to apply their place value skills in other contexts, such as ordering numbers or suggesting where a number should fit on a number line. Hopefully, as they move through the school, the sound grasp of place value gained in Form 1 will help them to understand column addition and subtraction where carrying and borrowing is required.