Okay, this is tri triangles according to sides and angles. Um, this is where we're going to combine the information to form the full name of the triangle. You're going to have the children build as many different triangles as they can and then we can name them.
Um, I'm going to show you two in this presentation, but you would follow the same pattern and keep going. Um, with the children's triangles, you're going to need the geometry box of sticks, the geometry plane, paper slips and pencils, and geometry nomenclature books E1 and E2 as reference. But again, you are doing this presentation not with the booklets, but with the triangles you make from the box of six with the children.
Okay, this is presentation by sides and angles. This is where we combine the information for the full name of the triangle. Have the children build as many different triangles as they can and then we can name them.
Let's say I have this triangle. If I were considering the sides of the triangle, what type of triangle is this? Yes, absolutely.
It is an isosles triangle. You are correct. So, I have a little label for isosles.
Oh, forgot to write triangle. Let me do that. Isoses triangle.
Okay. But what if I were looking at the angles? What if I were looking at the angles?
H I have my handy me measurer. This is a right angle. This is a right angle.
H. This one is not. This one is not.
This one is not. But what is the rule for right angle triangles? All it takes is one.
So this is also it's an isosles triangle. It's also a right angle triangle. H.
Well, we could call it just an isosles triangle or we could call it just a right angle triangle, but we'd like to call it by its full name, its full triangle name, kind of like you have a first, middle, and last name. Triangles have a full triangle name. So, this would be called a right angled isosles triangle.
That would be its full name. So I'm going to do this right angled isosles triangle and put it together so that we have its full name. Shall we do another one?
Of course. Let's move this over to the side and we'll get another triangle. [Music] Hm.
All right, let's look at this one. If I named this according to its sides, what would it be called? This side is different.
This side is different. This side is different. When all three sides are different, we call it a scaline triangle.
Yes. Let's look at the angles. Get out my handy measurer.
Are there any right angles? No, no, no, no, no. They're all less than right angles.
So, we say that it is an acute angled triangle. So, what would its full name be? It would be an acute angled scaline triangle.
Eric, could we please use your triangle for the next one? You would continue with the children naming the triangles, measuring the angles, naming by sides, measuring the angles, naming by angles so that the children are naming them by their full name by both sides and angles. Okay.
After a little time, when they've had time to work with this, we're going to bring them back together and tell a little story. This is presentation chart of triangles. So, you're going to start off by gathering your children and you'll start with a little story something like this.
Last night I was thinking about triangles as I often do and I was wondering how many different types of triangles there are. I couldn't quite figure it out. So, I thought maybe if I made a chart and put my data in it, um, I would be able to know I could help keep track and organize all of these triangles that are dancing around in my head.
You want to try it? Let's see. I know that there are three different ways to have triangles according to sides, right?
Let me do those first. So, I'm going to make a little chart with the three ways of note not noting how we organize triangles by sides at the top. So, I have my graph paper, but I also have my ruler.
And I'm going to do it like this. So say 5 6 7 8 Okay. Mhm.
Okay. And I'm going to go down two down to here. Open this.
Okay. So what are my three types of triangles according to sides? I have equilateral and I have isoselles and I have scaline.
Okay. All right. So I have those according to sides.
Now what about according to angles? Well, there's three different ways we can classify according to angles, right? All right.
So I'm going to draw down. Let's see. 1 2 3 4 5 6 8 9 didn't have quite enough to do 10, so I'll leave it at seven.
And then I'll Try that on this side. Okay. Okay.
All right. And I'm going to come over here a little bit and going to add these cells this way. And I'll start here.
Come down. It's okay. I got a little overzealous with my my line.
I can erase that. Okay. So now if we're labeling according to angles, we have right angled and we have obtuse angled and we have acute angled.
Okay, let me just finish putting in my division lines here. Okay. Oops.
Got to remember to hold the ruler. There we go. Okay, so we can see our chart.
Now comes the fun part. Can we make an acute angled equilateral triangle? This is a note for you, not for the children.
The children can verify with the box of sticks if they want to. they might have done enough work with them to know that you can make an acute angled equilateral triangle. So yes, you can.
I'm going to draw a little equilateral triangle here and I'll show you how mathematicians show that a drawing is equilateral. So I'm going to put in my triangle and I'm going to draw one line on each of the legs. And that tells me and anyone who looks at my chart that all of the legs are equal in this picture.
Okay. Um what about isosesles? Can we make an acute angled isosles triangle?
Yes, we could. So let's make a triangle and we would show one line here, one line here and two lines here. That means that these legs are the same and this one is different.
Okay. What about scaline? Could we make an acute angled scaline triangle?
Yes, we can. What do you think we're going to draw on these legs? Right.
We'll draw one line here, two lines here, and three lines here. Because all three legs in a scaline triangle are different lengths. We'll fill out the whole chart.
We're going to decorate it, make it beautiful, make it lovely. We can give it a title. We can call it types of triangles and we'll write that in length right here.
Types of triangles. All right. So, let's get working and finish our chart.
So, these are some end notes for you. Uh making charts like this is an excellent tool for children to start organizing information, learning how to present data in tables and classifying their information differently. It gives another varied way to explain how they came to an answer.
Please note that when I when I was building triangles according to sides or building triangles according to angles, I altered the triangles by as few factors as I could to give the clearest impression. Let me show you. So when I had an equilateral triangle, they were all the same color.
When I wanted to show the isosles in the same presentation, I only changed one stick. I kept these the same color that I did with the equilateral. Then when it came time to change it to a scaline, I maintained the yellow and the black and changed this one.
Same things with angles. I have the brown sticks. So here I use the unpainted wooden one for the hypotenuse to make a right angle.
I used two brown and a green. So for the isoselles, so two brown and a green. Um and that was acute angled.
And then for obtuse angled, I kept the brown and the green and added this one to make an obtuse angle. Here I learned this trick from Andrea Fleiner who learned it from Ba Gratzini and this helps to maintain a very clear visual impression for the children. Please ensure that your illustrations reflect that and that you're using colors of sticks that are actually exist in the box.
You already know this from our introduction, but just a tiny reminder, you must use an unpainted stick to make a right angled triangle. Okay. Um that's why I have my corresponding unpainted stick for the um isosles triangle here um that I showed you.
But just to make sure you can see as clearly as possible that that is unpainted wood. All right, those are notes to wrap up um triangles according to sides and angles.
