These Place Value professional learning resources are designed to deepen YOUR understanding of the levels of understanding that children go through as they develop THEIR understanding of place value, firstly additively then multiplicatively.
Children develop their understanding of additive place value in Years 1 and 2, when the focus of their learning is on additive thinking about Addition, Subtraction and Place Value. Even Multiplication and Division is additive in Years 1 and 2, as children skip count!
In Year 1, children begin to investigate standard and non-standard place value of teen numbers, then two-digit numbers. Standard place value is simply naming the values of each digit, for example, 24 = 2 tens and 4 ones. Non-standard place value means describing numbers using place values but not in a way that can be recorded in a place value chart, for example, 24 = 1 tn and 14 ones, 24 = 24 ones.
Children also investigate related place value concepts of friends of 10, 20 and any decade, and partitioning single, teen and two-digit numbers. They can then apply their understanding to add and subtract single-digit numbers bridging to 10, then to 20 and then to any decade.
In Year 2, children extend their understanding as they begin to investigate standard and non-standard place value of three-digit numbers, partitioning three-digit and tens numbers, and friends of 100. They can then apply their understanding to add and subtract tens numbers, before putting it all together to add and subtract two-digit numbers.
After this, there is really nothing else to understand about additive place value – so called because we are adding the values of the digits to make the value of the number. Children simply apply their understanding to investigate place value concepts of four-digit numbers in Year 3, place value concepts of five-digit numbers and decimals to tenths and hundredths in Year 4, place value concepts of whole numbers and decimals of any size in Years 5 and 6.
Developing this additive understanding during Years 1 and 2 frees children to focus their learning in Years 3 to 6 on thinking multiplicatively about Place Value, Multiplication and Division and Fractions.
In Year 3, children begin to investigate multiplicative place value of whole numbers – identifying that we are multiplying by 10 to get the value of the places on the left, and dividing by 10 to get the value of the places on the right. This understanding is vital to explining why the value of the column to the right of the ones column is tenths.
In Year 4, children extend their investigation of multiplicative place value of whole numbers to include decimals, explaining that when we divide 1 by 10, we get a tenth, which is the value of the column on the right of the ones column.
This understanding is extended to whole numbers and decimals of any size in Year 5 and 6.