37 + 25 = ■ + ●

I've posted about Connecting Arithmetic to Algebra before. This slide, based on the book, is one of a number of useful ones from Kristin Gray's blog:

Today, before the main part of the maths lesson, we looked at an equation on the board. I asked them not to calculate it (although some couldn't resist of course);

37 + 25 = ■ + ●

I asked, "What do you notice?"

Aditi started us off by saying it was balanced. Brilliant! We'd done some work on balanced equations earlier in the year, so I was really pleased to hear this as the first thing.

There were some other good points, and then Justus said the two numbers could be instead:

38 + 25

We looked slowly at what he'd done. Justus said that you could always do this, take it from one addend and give it to the other. Most of the class agreed. 

That's going up on the Claims Board.

"What other pairs of numbers could we have?" I asked.

And then there were a flood of answers.

Alonso gave us:

-1 + 63

and then there were lots of sums with minus numbers in too!

James gave us:

-38 + 100

And Annie:

It's another reason to start a lot more writing in their maths journals next year. There is a lot of great thinking, and it's getting wiped out, rather than pondered over for a bit longer and looked back on. The class were evidently enjoying the freedom of the exploration and talk, but not everyone joined in the discussion. Writing would give more time for everyone to get their thoughts together and put them into words. In September...

On other occasions (like this), I've used Cuisenaire rods to help in representing the pattern. Today the ideas seemed to flow so well without this, but another time I might use them again for something like this.