Generalizations in Math

Do you help your students make generalizations in math?

Years ago when I taught third grade, we did a lot of work on  making generalizations based on the addition or multiplication of two numbers. 

Generalizations are where students tell about the pattern they see in the relationship of a certain group of numbers.  It’s a pattern than is always true.  We probably teach this all the time without realizing it.  For instance, having first graders look at a 100s chart and generalize that going up or down is adding or subtracting 10.

Our class has been doing a lot of counting patterns lately.  I started my summer reading a bit early and decided to try a few routines out with this year’s class.  I really like the counting routines and look forward to using them at the beginning of the year next year.

One thing I have added is making generalizations.  We’ve done a ton of counting forward or backward by 10.  On Thursday, we counted forward by 5 starting at 83 or something like that.  It was interesting to see which students could break apart 5 into 2 + 3 and which students counted on.  Some needed a bit more help.

After our counting routine, we made some generalizations about counting by 5s.  We just did this orally, through a discussion.  We also revisited counting by 10s and made some generalizations about counting by 10s, again, just orally.

With our little bit of time on Friday, we reviewed the generalizations we had made and wrote them down.  These generalizations, are for the most part, their language.  It’s great to see how their brains are working!

I’m realizing that it helps students articulate their ideas and be able to find the mathematical language.  Some were partway there.  For instance, one of my girls said, when referring to counting by 10s, that the tens place changes by one.  Well . . . kinda.  She’s on the right track, but didn’t have the right vocabulary.

I really hope it helps my lower kiddos who aren’t seeing the number patterns yet.