At the core of solving math problems is the necessity to have a deep foundation in number sense.We can't expect students to solve every problem with numbers. Most of the time they will move around in the steps as they refine their thinking and their solutions.Children need to experience how to deal with math problems on their own terms and in concrete ways before moving to the abstract.To differentiate, begin to encourage students to label their drawings.Remember that drawings do not need to be perfect; they just need to clearly show their thinking.You can tell the children that the trunk of the tree is the problem. Little branches grow from larger branches, and to calculate the final answer you only count the final number of little branches.You can always point out that a good way to check an answer is to re-read it and see if it actually makes sense. The guess and check problem solving techniques helps students to think logically, make predictions and use mathematical equations. Drawing a picture is the step between the visual and symbolic language of math.Only then can we see the results of their conceptual understanding of applying mathematics.When we tell elementary students to make a pattern, they often do not understand.A growing pattern repeats a mathematical process that makes the figure or number grow.Fibonacci numbers are a great example of growing patterns and are found throughout nature.