Discovering patterns

       One of the most important skills that kids can learn in math is that our number system is FULL of patterns!  We are working this week on identifying and naming visual and kinesthetic patterns, extending the patterns, and creating our own patterns.  One activity that we are doing that is an extension of our pattern unit is recognizing a pattern when listing our facts that add up to 10.   The first thing we did was create towers of two different colors that equal ten.  Once they had a tower made, they colored it on a chart to record it.  They worked at this for quite awhile.  While a few students needed some encouragement to keep working at it, most of them were pretty persistent at finding a new way that they had not found.  At this point, their work was pretty random in how they were finding the facts.  The students were working independently at this point.

The next thing I asked them to do (during the next work session) was to see if they could figure out a way to organize their facts.  I didn't give them any direction other than "How could you organize your towers in a way that you could be sure you haven't missed any towers you could have made?"   For this part of the task they were able to cut apart the strips they colored so they could manipulate them.  My goal was that by arranging the towers they could see a visual pattern...Example:  One white block with 9 green blocks, 2 white blocks with 8 green blocks, etc.  If they could organize this visually into a pattern, we could then examine the addition sentences that go along with them and see a numerical pattern.  I loved seeing the lightbulbs coming on when they saw the numerical patterns in the addition sentences and didn't even need to look at their towers anymore to tell me the next addition sentence!  I also loved that they were able to tell me why they knew they were not missing any facts!

After they saw the visual pattern, they were able to see which facts they were still missing.

Learning the facts of 10 is so important!  Making it into a pattern is not only a good way to make sense of the facts, but this activity is also a good problem-solving activity because they have to take the random towers and organize them logically.  Then they have to verbally explain why their method will guarantee that they have not missed any of the facts.   Justifying their thinking is very important in all areas of learning, not just math!