Begin by making observations of the child while he is doing math problems. Take notes on the child's mathematical thinking, knowledge, behavior and dispositions. By documenting how he works, you can find out which problems he struggles with and which ones he can easily answer.
Reflect on the child's work and what math concepts he appears to solidly grasp. Reflection will allow you to come up with the best possible teaching approach catered to each specific child.
Create and administer an assessment exam before instruction. This way, you will be able to find out the child's skill level and determine what concepts you should be teaching. If you do not want to create your own assessment, you can find assessment exams at The Michigan Mathematics Leadership Academy.
Grade the assessment exam and determine what concepts the child does not fully grasp. Carefully go over the free response and word problems to make sure the child is able to accurately explain some of the theories and concepts he has been learning.
Administer the same assessment exam after instruction. The difference in the score will allow you to determine whether the child has made progress.
Continue to administer assessment exams before, during and after instruction on different math concepts and theories. This will allow you to determine whether the child has mastered the material before you begin to progress to the next section. This methodology will make sure the child has a solid foundation before moving on to more difficult material.