Dynamic Addition

Dynamic Addition in Montessori means exchanging or carrying on numbers during an addition sum. This process as with all Montessori concepts starts with the concrete material in this case the Golden Beads and then moves to abstract materials using simply pen and paper and no manipulatives. In between there are various other materials that can be used to aid this process such as the stamp game, and the small or large bead frame.

Nuh has been able to perform quite large addition sums since his was about 5 using this method, and moved to abstract at about 6. However I have found that he constantly needs refreshing on these concepts otherwise he forgets. I think that this is because Montessori Maths uses a spiral approach to teaching and not true mastery. It is something that I am thinking deeply about at the moment any way. This is a piece of work completed with the manipulatives notice how he is not carrying the numbers on by writing them on the sheet. This is because he can simply count how many units, ten bars, hundred squares and thousand cubes he has by changing them out for each other as required.

We use the stamp game paper for Dynamic addition sums, as it is easy and is colour coded if you need that, Nuh does not I have used black and white versions and he can perform the sums the same. He definitely has a solid grasp of place value, even if he does not recognise that term for it. It is important I feel to note that when beginning carrying forward or dynamic addition you start with the Golden bead material then slowly move to abstract using smaller sums than in the thousands. So you might start by using sums that only include 10's and units, alternatively you can start by only exchanging one column at a time, so the units. When this is accomplished with ease you can then add in exchanging of the 10 column, then 100. The point is to start slow and build up, don't just go straight in with a full exchange of all three columns.

Moving towards Abstraction 

The stamp game uses coloured wooden squares with a value printed on them, instead of counting out beads to make your addend you simply count out the number of tiles you need to each column. In the example below, Nuh has two addends 3456 and 1235, he needs to find the total obviously. It is good practise to use a ruler between the two addends, however we used the lid of the box and a clipboard to differentiate.

When both addends are laid out it is time to put them together, just like you do with the golden beads.  You can then count each column starting with the units and make the necessary exchanges:

Notice how the units column has more than 10, Nuh counted up to 10 then moved the 10 tiles to one side, he then put them back in the box and retrieved a 10 blue tile.

Now all the exchanging is complete, in this instance just one exchange, he can write his answer on the paper.








Abstraction 

In the picture below he completed this work without manipulatives, so he has written the number that he is carrying forward in each column. He has a solid grasp of the fact that once you have more than 10 in any column you must carry forward.