Progression in learning place value

1. Progression in learning place value 1, 2, 3 4, 5, 6

2. Step 1: forming of equal groupings (no remainders.) Using things from the environment or structured apparatus, ask children to group objects. Group in threes to enable children to focus on grouping rather than counting. I have grouped my leaves, shells and bears into threes!

3. Step 2: forming equal groupings (with remainders) Ask children to group objects into threes again but this time introduce the idea that ‘remainders’ are objects which cannot be grouped. The remainders can be referred to as ‘units’. I have 2 groups of three and 2 units left over!

4. Step 3: successive groupings Next the concept of successive groupings can be introduced as shown below using base 3. Apples I can put three apples in each bag and three bags in each box!

5. Step 4: introduce a column structure When successive groupings are introduced we ignore position to start with. Once children understand the concept of grouping, we introduce recording and the idea of columns and movement right to left. We might also introduce different bases. The example below shows base 4.

6. Step 5: the principle of exchange The idea of exchange should be introduced gradually, preferably when children fully understand the concept of grouping in a variety of bases. Again this should be done practically using concrete materials. Children should be encouraged to decompose their groupings to establish the idea that they are composed of individual units. The units can then be regrouped. I can exchange 1 box of apples for 3 bags of apples and three bags of apples for 9 apples! Apples