6 vs 6

Okay mathematicians, welcome back! It is time to get your eyeballs ready to do some deep investigation into 2 collections 6 versus 6.

So you will need some paper and a pencil. So first of all, what do you notice about these two collections of 6 that's different?

Can you see something that's different? Great, can you write it down? Take a note of it or draw a picture of what you notice is different between the two collections. Yeah, and if you thought of one thing that's different, can you now think of another thing that's different between these two collections of six?

And you can write that one down too or draw a picture. Yeah, you're right. 'cause mathematicians represent ideas in lots of different ways. Okay, I now have a different question for you. What's something that you notice it's the same?

Yeah. Okay, so if you've got one thing that's the same, can you think of a second thing that's the same?

Yeah, and write that down too or draw it. Okay shall we talk together, so we spoke to some young mathematicians, too and these are some ideas that they came up with. So one of the things they noticed that's different is that one of the collections shows that 6 is a doubles fact. You know 2 threes.

But the other collection shows that 6 in that representation shows a shrinking pattern where 6 is 3 and 2 and 1 more.

Yeah, I'd like the backwards count 3, 2, 1. Uh-hum. And actually, what we probably should do mathematicians before we go any further is, we could maybe use a table to organize ideas so that it doesn't end up quite messy. So let's draw a table. And yeah, you're right mathematicians often use tables to help them organize information and ideas. So it's easier to read and also share with other people, Okay!

What about some things that are the same? Here are some ideas we had. One, both collections had 6 dots and the other is that both of them showed that there's one column of 3 inside of 6. Can you see that? Yeah, the blue column on the, like staircase, shrinking pattern or shrinking representation of 6 and then a blue column and also a green column on the other representation of 6 that shows 6 is double 3.

Okay! Yeah, we also notice that too about being the same that both collections show 6 is 2 threes. Yes, and in one the staircase representation we see 3 as one column of 3 in the blue and the triangle. The triangle in the green.

And yes, you could have had the triangle at the top and then instead of a column you could have had a row of 3 down the bottom and in the other one we can see the 2 threes. It's also easier to explain. Yes, you're right, but the 2 threes are different. Yeah, so one of the three's.

One of the collections, one that looks like 6 on a dice pattern has the 2 threes as two columns of three and the other one has three like a triangle and three as a row or a column. depending on how you're looking at it. Yeah, yes, and another thing that we thought of is that 6 when you look at this version of 6, can also show that it's 3 twos, 2 at the top, 2 in the middle and 2 down the bottom.

Okay, I have something else for you to wonder about then. When we look at this collection, these two collections, which collection best shows at 6 can be made by doubling 3 in your opinion. Can you point to it?

Yeah, we thought that one too because it's got 2 Um, 2 columns and they have an equal number in each column in 3 rows of 2. That's it. Yeah, yeah, it's an array where there's equal rows and equal columns. Okay, which collection best shows that 6 has 3 inside of it?

That inside the bigger number of 6 that we can see 3. Can you point to it? Oh, there's some debate! We agree.

This one shows a chunk of 3. And so does this one. Okay so in that case they tie. Okay. Which collection best shows that 6 can be partitioned into three smaller parts, or three smaller chunks. Uh-huh debate again. Some people are saying this one because of the idea of 3, 2, 1 or 1, 2, 3 if you're reading it from the top, down. And other people are saying this one 'cause you can read it from the top down and say Uh- 2,4,6. Yeah.

Okay, um what about which collection best shows that 6 is one less than 7. Oh neither, I agree with you in this case. Neither of them are very good at saying or showing to us that 6 is one less than 7. So mathematicians over to you!

Can you draw for us a representation of 6 that shows 6 is one less than 7? Okay! We look forward to seeing the results.