Balancing numbers 1

[No sound. Hulk is placed on one side of the scale and four bears are placed on the other side. The scale does not move.]

[No sound for the beginning of the video. Hulk is placed on one side of the scale and eleven bears are placed on the other side. The scale makes a tiny wobble.]

So now I'm wondering how many more bears are needed to make the scale balance?

How many bears are equivalent in mass to the Hulk?

So write down in your notebooks, what's an estimate that you think is way too high? Write down an estimate that you think is too low, write down an estimate that you think is pretty reasonable.

Over to you mathematicians!

[No sound for the beginning of the video. Hulk is placed on one side of the scale and enough bears are placed on the other side to balance the scale.]

So was your estimate reasonable? Hmm, I see you thinking. So how many bears are needed to make the scale balance? In other words, how many bears are equivalent in mass to the Hulk? Hmm, let's have a look. I wonder how I could work out how many without having to count everything? I wonder if I can see something inside of this collection? Oh, there's three, and three, and four.

Oh, and that's making me think of three and three is six, and four more, and I can arrange them, uh-huh, into a ten frame, so I can use what I know about structures to work out how many by looking and thinking. And then I can see, look five, so one ten and five is fifteen.

Look, here's what I imagined in my brain. The rectangle around the outside, one long line down the middle and four internal lines and that makes ten. Yeah, and here's where I can see five on my dice pattern, look. Mm-hmm. Like three on a dice and two on a dice and that's five all together. One ten and five. Fifteen. Fifteen bears and one amazing Hulk. Mm-hmm.

Now I need to think about how I can record my findings as a mathematician. Here's one way. I could draw a picture. Hmm and it's quite lifelike because look I can see the bears and I can see the Hulk, I can see his really cool hair, but I could also draw it a bit more like a mathematician, where I just put the most important mathematical information.

Hmm, so over to you mathematicians. Create a drawing to represent the problem.

Some of the mathematics here. When both sides of the balance scale are level we can say they are equivalent. So 15 bears is equivalent to 1 Hulk. Hmm and when we're thinking about representing mathematical ideas, like this situation with the balance scale, we can represent ideas in different ways. You can, you can create drawings that are lifelike, hmm, like I did here. I can see they're bears and I can see the Hulk, or I can do drawings that are more mathematical, where we just put the most useful information in there. Yes, so you can also create drawings that just include the most important mathematical information to represent situations and ideas.

Until next time mathematicians.