Problem Solving Using Patterns

       We have been busy this week using our knowledge of repeating patterns to help us solve problems.  One of the problems I presented this week was adapted from a book called Introduction to Problem Solving by Susan O'Connell.  It is an EXCELLENT resource for problem solving!  The problem  involved them making an extended pattern and then looking for specific pieces of the pattern.  It was about a squirrel who was making piles of nuts for winter.   He placed the piles in the order of walnuts, acorns, pecans.  The question I presented the kids with was, "What kind of nuts would be in the 15th pile?"  The students were very quick to notice that the squirrel was using an ABC pattern in his piles.  They spent some time making the piles and took a bit of guidance to realize that they somehow needed to label their piles so they knew which was which.  Some students used a dry erase board to show their patterns and some chose to use blocks to show their patterns. 

      After solving this initial problem and discussing it, they really caught on to what we were doing and were able to answer a variety of questions about their patterns. Examples..."After making 20 piles of nuts, how many of those piles were pecans?"  The students are using manipulatives to solve these problems and then defending their answers by explaining to the class what they did.  The rest of the class gives feedback on if that was a good way to do it and if they think there was an easier way to solve the problem.

      We will work on many problems involving patterns throughout this week that I also adapted from the resource mentioned above.  With some problems we will include using a set schedule to figure out the pattern for which days the brother has to walk the dog, how many days in the month it will be the sister's turn to walk the dog, etc. 

Here are some pictures of the students working on the calendar problem.