math

## Angles

I know you’ve probably seen this activity floating around the math blogosphere already, but I think it’s a really good one! I’m glad I gave it a try.

I used masking tape to make angles all over a table, then I had my grade 3 students (6 of them) use sharpie markers to find angles. After, we came up with a definition for “angle”. They decided it is where two straight lines meet each other. I didn’t tell them that – they figured it out. Next, I showed them how to use a protractor, and they measured angles. We then compared the angles and “discovered” 3 different kinds: right angles (somebody knew that), bigger than 90, and smaller than 90.

I gave them the vocabulary words – right, obtuse and acute. Then I gave them three pieces of paper with those words on top, and asked them to sort some pattern blocks.

Some of them had to go on two pieces of paper because they had two kinds of angles. Oh, and did you know there’s more than one way to make a triangle? This was surprising news! Again they used protractors, this time to justify their sorting.

Usually, I feel like, “Angles: check.” And I move on. But I feel like these activities really made sense to everyone, and they really learned something new (grade 3 is the first official place learning about angles takes place.) In fact, a week has past, and the tape is still in place. In their own “free” time, the students are still talking about their learning, and explaining to curious grade 2s what the tape is doing on the desk. Anybody who has taught for any length of time can testify to how hard it is for kids to leave tape on their desks alone!

I’ve spent a lot of time on Number Sense, but geometry is important too. I’ve got some interesting things to tell you about spatial sense as well, but I’ll save that for later.

## Fractions

Found this on Twitter the other day, and decided to give it a try.  We are “finished” with some learning about adding and subtracting and unitizing and counting.  We need to move on – both for my sanity and because there are other things that need to be covered in the curriculum.  We will circle back to this in the new year, and we’ll keep practicing when we do a daily Number Talk at the beginning of our day.

I’d decided to move on the geometry, mostly because I’m a sucker for all the Christmas tie-ins.  I love making 3D shapes into ornaments and decorations! But then this fun fraction activity popped into my life, and I thought it would make a nice transition from Number Sense into Geometry.

On day 1, a shortened math period due to irrelevant circumstances, everybody cut out their pieces.  (As an aside, I know that cutting isn’t math, but we have some fine motor issues, and it’s really good to for us to cut as often as possible.  Also, I have a life to live and it’s takes 20 kids 15 minutes to cut these out so I let them!)  I started by holding up the “whole” and one of the fourths, and then asked the recommended question:  What do you see?

They named a bunch of stuff, unrelated to math:  I see white and yellow, I see a fried egg.  Then they moved on:  I see a small square and a large square; they both have 4 sides, and 4 corners; they are the same but different.  Then I let them go play with their shapes.  We came back and talked about what we saw:  the different shapes in different sizes, teh same shape in different colours, etc.  Then we had lunch.

On the second day, I asked them if they could use the paper to show half.  I was interested in their understanding of half, and also, would they see that you could make half of all the shapes, not just the whole.  While I walked around and talked to different groups, I was so glad that I know that I should ask them to explain their thinking.  Some of them had very unexpected answers that showed partial or complete understanding in a different way than I was originally thinking.

All of these came with justifications for how it shows half. One is half yellow (front) and half white (back), one has purple lines dividing it into sections – half the sections are yellow and half are white, and one uses the purple “lines” to divide a design in half.

We talked about symmetry, which I hadn’t intended to do, but it naturally fit.  I really thought I could do this activity and move on to fourths and thirds.  It was clear we weren’t ready.  Luckily I am SO organized (haha) I was able to grab this book off my shelf:

It’s about a brother and sister who do not want to share fairly, but an unspecified adult (mom?  dad?  babysitter??) tells them to share.  They each get half of the pizza, the dessert, the juice.  Then I sent everyone back to show half again.

We had better results, and each came with a really good justification.  Then, just to make sure we all understood that each shape could be divided in half, I sent everyone to fold each piece in  half.  Which they did.