Our poem/riddle math books are complete! For the past few weeks we've been reading story problems in poetic form and learning how to determine the mathematical operation required to solve the problem. Then we've illustrated these problems to show and explain our mathematical thinking.
We are taking a break from story problems and are beginning a unit on Growing Patterns. This is another type of problem solving. Children are learning to build, extend, and describe growth pattens, which is an important aspect of developing algebraic thinking. Let me give you an example of this by describing what we did today:
I drew a caterpillar on the board made up of 3 circles. I then labeled the caterpillar 1 year old. I asked the children to count the circles, which of course they did easily. I said, "now I'll draw the same caterpillar one year later", and drew a 4 circle caterpillar and labeled this one 2 years old. I asked, "How many circles will there be when the caterpillar is 3?" and the children correctly said, "5!" We continued in this manner until the caterpillar was 5 years old (with 7 circles).
I posed this harder question - who could tell me how many circles would the caterpillar have when he is 10 years old? Most children could not make this leap. They could come up with the answer doing it year by year, but were unable to extend this pattern forward (they were not immediately able to see the rule and apply it).
I showed the children how to make a T-Graph and we entered the information we had worked on together. Then the students drew a T-Graph on their papers and worked at their desks until they were able to tell me the correct answer. Some used pictures (adding circles to caterpillars, year by year), and some did this with just numbers. It was fascinating to watch and listen as worked this problem out.
This is just the beginning! We will see where our mathematicians will take this...