I just got back last night after flying to Vancouver (well, Richmond actually) for the New Teachers’ Conference hosted by the BC Association of Teachers of Mathematics (BCAMT). Although the turnout for the conference was down a bit this year, it was still a great conference with lots of great math ideas being shared.
I was happy to be able to present a workshop there that I have done numerous times, one for primary teachers that I call “Big Ideas for Little People: Important Things to Know About Numbers After Counting”. Here in Canada (and also in the US) we tend to move children very quickly from counting to adding, but there is so much more for children to explore about numbers!
We want children to develop ‘number sense’, rather like common sense but regarding their understanding of numbers. This is something that develops over time as children have the opportunity to think about numbers in many ways. This, of course, means that we need to set up situations for children to do that kind of exploring and thinking so they can develop their number sense.
One of the components of number sense is understanding the ways numbers are related to each other, and in this workshop I talk about four particular number relationships that are very important for children to develop:
- whole-part-part relationships;
- anchors to 5 and 10;
- one more/one less (and two more/two less);
- and visual relationships (where children can look at a patterned arrangement of items are recognize at a glance what the number is — such as recognizing 5 spots on a dice as being 5).
The really wonderful thing about this these relationship is that not only do we want children to develop an understanding about these relationship for the basic numbers 1 to 10, but we want to help them learn over time that all of the relationships are applicable at every place value of the base 10 number system. So what children come to understand early in their primary years can be “rolled up” to tens, hundreds, thousands, etc. and also “rolled down” to tenths, hundredths, thousandths, etc., and in these extensions we see the great power of the relationships.
There is so much to say about this (several hours worth, actually, thus the workshop!) but hopefully this gives you a tiny glimpse into some important number relationships for children to think about.