So what do children specifically need to know about place value?

The following six elements are all inter-related and are learnt together as a child makes sense of numbers, but these elements are worth considering separately. If a child is struggling with place value it is likely to be a misconception or error in one of these. There is an article to follow which identifies the most suitable models and images to teach these aspects of place value.

**Base-10 structure**

Our Hindu-Arabic system uses symbols for the numbers 1 to 9 and then a place value system with a place holder of 0. Using these ten symbols we are able to represent large numbers just by their value in different positions. Simple and efficient to us as adults – if you want to see what it is like for children to understand, try counting or calculating in base-5…! Teaching how our numbers go from 9 to 10 is almost impossible without the use of models to represent them.

**Zero**

Children need to recognize 0 as a label for an empty set, or nothing, as well as a place holder for numbers in our base-10 structure. It is the latter that is obviously the more difficult to understand, and it makes the use of structured apparatus to represent numbers so important. It becomes a particular issue when multiplying by 10 or 100, with zeroes magically ‘added’ to a number. This needs breaking down and modeling with 2-digit numbers and apparatus so they can see the effect on each digit when numbers are 10 or 100 times bigger.

**The digits 1-9**

Counting to 10 and getting to know the value of each of the numbers is the first step to getting a feel for larger numbers. If a child is having problems with sequencing or recognition it is often a skills issue related to the incorrect or inaccurate recital of counting words. Young children could have an unstable knowledge of numbers to 10 (Broadbent Maths users - read Early Counting Experiences). If this isn’t addressed then recognizing the value of these in larger numbers makes comparing and ordering of numbers an issue for some children.

**Position of digits**

The place or position of a digit in a number shows the value it represents, which, once understood, makes base-10 so much better than, say, base-2 for reading large numbers. This can still be tricky though, so highlighting every third digit back from the ones is helpful when distinguishing the number of hundreds, thousands and millions:

**3**49 is 3 **hundred **and 49,

**1**28**3**49 is 128 **thousand** 3 **hundred** and 49

2**1**28**3**49 is 2 **million**, 128 **thousand**, 3 **hundred** and 49.

**Partitioning**

Using a developing understanding of the base-10 structure, partitioning involves separating out numbers so that the value of each digit can be seen, for example, 385 = 300 + 80 + 5. Confidence in doing this will be a pre-requisite to adding and subtracting larger numbers mentally and when using a written method. A step on is to partition in different ways, so 385 can also be shown as 300+70+15. This links well with exchange when learning to add and subtract.

It is worth pointing out the distinction that Thompson & Bramald (2002) make between quantity and column value of numbers.

** Quantity value** – being able to partition numbers e.g. 20 + 8

**– being able to say that 28 is 2 tens and 8 units**

*Column value*Quantity value is best used for the purposes of mental calculation, whereas column value is not needed until more formal written calculations are attempted.

**Exchange**

The principle of exchange is fundamental in mental and written calculations and is related to the value and position of each digit. Ten in any ‘place’ in a number can be exchanged for one in the next place to the left, so, for example, 10 hundreds can be exchanged for 1 thousand. Conversely, one in any ‘place’ can be exchanged for ten in the next place to the right, so for example, 1 hundred can be exchanged for 10 tens. The best way to understand this is to physically move base-10 material, exchanging 10 cubes for a 10-rod, for example.

**Links for current Broadbent Maths users**

Progression steps - number

Use the small steps of progression for number during your Place Value teaching.

Models and images - place value

Use the PV arrow cards and number generator to represent numbers.