Mathematical imagination warm up 1

Hello there, young mathematicians, welcome back! Today to warm up our brains, we're going to look at this big blue rectangle here and I also have this smaller orange rectangle. And what I'm wondering is, can you use your mathematical imagination and imagine how many of these smaller rectangles would it take to fill this larger rectangle?

Can you now pick up your pencils and your book and draw a picture to show me how many orange or smaller rectangles you think it would take to fill the big blue rectangle? Over to you mathematicians!

Welcome back young mathematicians. How did you go with your drawing? Can you show me what yours looks like?

I see there's a few different ways of thinking, isn't there? This is what mine looks like.

So this is my big blue rectangle that's representing this rectangle. And I think four of the orange ones will fit onto the blue one.

So one here, a second one here, a third one here, and a fourth one here. Some of you are thinking the same thing.

Should we check to see? Okay. Say here's our smaller rectangle. Let's put it over the top of our big one.

Oh yeah, and now as I'm visualising. I think this rectangle here, if I use my fingers, I think that would definitely fit up the top.

Are you seeing that too? Let's check. So I only have one rectangle, so I can't just lay them out, so what I might do is very carefully, mark this place with my finger. I'm pretty confident that fits there and actually, what I imagine is it's going to be the same on this side 'cause this looks like it's about half way and if I fold my piece of paper over...

I can check. Yes. Look at that. So now what I see...is that this would take up the same space on this side 'cause they're halves, look, if I move this over.

Oh, and you think I should fold it this way to prove too? That's good thinking. Let's do that. Fold it the other way in half, and now let's look.

Yeah, look. 1, 2, 3, 4. 4 small rectangles, cover the area of my bigger rectangle.

A bit like what I imagined in my mind and what I drew in my picture. Nice warming up of your mathematical imaginations, little mathematicians!

I wonder what would happen now if my rectangle was only this size? About how many of these rectangles do you think I would need to cover all of my paper?

Over to you mathematicians to think about it and draw a picture. Okay!