Brushloads

Hi there mathematicians, we have a challenge for you today. It's called brush strokes and it comes from Enrich maths.

Now to do this it would be good if you had some cubes or something to help you visualize. So you might have had the cubes that you made and you could use them for multiple purposes including this task. You need five of them. Or you could use other cubes.

I'm using these ones today. So the challenge is when the painters come along to paint whatever it is that you construct, that for each face they need 1 brush load of paint. So the challenge is to arrange the cube so that they need the least amount of paint. So for example, if I arrange my cubes like this to be painted as a structure, but I'll lay it down so you can see it.

There would be five faces on this side that need painting. And then five faces on this side. Five faces on this side.

Five faces on this side and one for each of the top. Yes, so there will be 4 fives plus 2 ones. Yes, which is 20 plus 2, which is 22. So it would need 22 loads of paint. And we don't have to worry about the ones on the inside 'cause that's inside our construction.

Yes, now when I'm thinking about what's the most efficient structure that I could build a couple of rules apply.

I can't do any crazy things like this. They have to join, the faces have to join perfectly and I could think about things like - I'm laying them down for you to see. But if I make a structure like this and put it down. Now I might think about so I still have five faces on the front and five faces umm- this is tricky to pick up, underneath that need paint. So that's 2 fives? And then on the bottom now and then I'm going to go around the edges.

So under here there's 3, 4, 5, 6, 7, 8, 9, 10. Plus 10 ones and two fives is 10. And 10 more is 20. Oh, so this structure is more efficient than the first one.

And what I should do, mathematicians, very good pickup, is record my thinking. So the first one I'll draw it as a sideways tower. 5 and this one looks like this.

Okay, so over to you mathematicians to find the most efficient or and or the least efficient construction

Have fun!

Okay mathematicians, what's some of the maths here? Yes, so you really need to tap into your reasoning and problem solving skills with this task as you try to workout the smallest number of brush loads or some people are calling them brush strokes and the largest. You'll also be exploring ideas of surface area with different objects and this will really help you build your mathematical imaginations as you're trying to workout which services haven't been painted and need to be painted. Enjoy!