Base ten system and its respective materials provide an effective dynamic model for addition that allow children to recognize the importance of adding ones to ones, tens to tens and so on. This model also is used to demonstrate the processes involved in regrouping. The children learn that in the case of having 10 or more ones (10 or more tens etc.), as result of addition operation, is required that 10 ones (10 tens) be grouped to form a ten (a hundred) and the new formed group must be joined with the respective block. The use of such models is so important: they help children understand the procedures involved in addition and subtraction algorithms.
Here is the geometrical representation of the addition operation (Dynamic Model) for 38 + 16 .

Demonstration: Click on slider i and assign for it the value i = 0, then the 10 rectangles will be grouped in one block. Click on slider a, and slide its point to the left. Then the formed block will jump to the left joining the 4 blocks on the left side. The new situation of the 5 blocks and 4 rectangles resembles the sum of the given numbers (54). The simulation of the above model is a resemblance of the mental process for adding two 2-digit numbers.
_ Try to understand how the model is built.
_ Try to build your dynamic model for other cases of adding 2 two-digit numbers.