Those children really didn’t understand what I was asking. But children who draw 4 cherries and 3 baskets don’t understand the question. Most children come to school understanding some types of story problems and not understanding other types. That is because understanding word problems is the basis of all of elementary whole-number arithmetic.
For this problem, I have seen children draw 3 baskets, draw 4 cherries in each basket, and then miscount the cherries – maybe they count 11, or maybe 13. Miscounting is one thing – everyone makes minor mistakes. I would know that a child understood this problem if he or she: Probably the most important job for elementary school teachers (of math) is to help every child come to understand every type of story problem.
Pictures and diagrams are problem solving strategies that many students learn at the earliest stages of math development.
This is a good strategy as it is a way to communicate mathematical thinking.
There are two basic types of patterns: repeating and growing.
A repeating pattern has an identifiable core that repeats over and over, such as ABACABACABAC.
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.