# 3 + 2 = 5 Let me count the ways!

That we live in a print-rich environment is undisputed. Even in country areas one cannot travel far without being bombarded by print. In addition to road signs there is a plethora of billboards advertising the best places to sleep, eat, or play that can be found just ahead.

Environmental print is the genre with which many children first engage successfully with reading.  Ask any parent who’s detoured around fast food outlets, hidden shopping catalogues, or camouflaged cheaper brand names of identical products.

That we are immersed in mathematics in our daily lives is just as evident but doesn’t always receive the same recognition. I think this may in part be because people often think of mathematics as abstract algorithms and theorems that we (they try to get us to) learn in school; and that have no apparent application to our lives beyond the walls of the classroom.

However, even the examples mentioned above are just as rich in mathematics are they are in print. They include distances, and perhaps time, to the destination, cost of items, opening hours, and number of attractions. Anyone travelling a distance with young children will have answered questions such as “Are we there yet?”, “How much further?”, and “What time is it?

As I say in my statement about mathematics on my readilearn site,

“Mathematics is all around us. We use it every day for a huge range of purposes from deciding on the sequence in which we dress ourselves, to calculating how much time we have available for an activity.”

One of the resources suggests 25 ways for parents to keep their children thinking mathematically over the school holidays. I have shared these ideas previously in Counting on the holidays.

Recently I was at the gardens with my two grandchildren (G1 and G2, aged 6 and 4), their mother, and my Hub. The children consulted a map and signposted paths to follow the Children’s Trail which had various sculptures along the way. I am undecided about the value of distracting children from the trees and plants, as if the vegetation itself would not be interesting enough. However, the children enjoyed locating the sculptures in the sequence numbered on the map, and reading the accompanying information. They were engaged in purposeful reading and mathematical thinking in context: real life learning!

Pandas on the Children’s Trail © Norah Colvin 2016

As we headed back, G2 made a comment that showed she was engaged in mathematical thinking of her own. She observed that there were two children and three adults, which made five of us all together.

“That’s right,” I confirmed. “There are five’. I thought for a little while, then added, “And do you know what? As well as two children and three adults, there are two boys and three girls.” The children looked at the group and confirmed that I was right. They laughed – a different interpretation.

This gave me an idea for a thinking game: how many other arrangements of three and two could there be?  I wondered if the children would like to play along. I had never attempted this before and had no idea if there’d be more, or if we had already exhausted all options.

I looked at the group. I noticed our shoes: three had closed shoes and two had open shoes. I thought about our names: three shared one surname, two another. Then we were on. Everyone was thinking of ways we could be arranged into groups of two and three.

Sometimes we sorted according to different characteristics, as in the previous examples. Others times we used a simple yes or no sorting, such as two have hats with brims and three don’t have hats with brims. This is the easiest sorting to do, and the first that children learn.

G2 made many suggestions of this type of sorting for one and four.  One has the characteristic, the others don’t. This was age appropriate for her, and it was great to see her joining in confidently and contributing to the discussion. G1 was able to engage in the more complex thinking required for the groupings of three and two.

I was amazed at the number of different combinations we came up with, and that each of us was combined with others in many different ways.

These are some of the ways we arranged ourselves into groups of two and three (not physically, just in our discussion).

This seemingly mundane activity has potential for developing thinking and learning by encouraging:

• thinking about things in new and different ways
• looking for similarities and differences
• observing detail
• sorting according to different characteristics – which is important to both maths and science (think animal and plant classification)
• having fun with maths
• having fun with family

But wait, there’s more: When we left for home, two went in one car and three in the other!

I think this would be a great activity to do with young children learning about number. It may be a challenge for teachers in Australia where children wear uniforms to school but I’m already thinking of how it could be done with toys or illustrations. It’s not quite the same as doing it with the children themselves, but it could be fun. What do you think?

You won’t be surprised to discover that I have prepared a readilearn resource for sorting as well!