Counting with understanding (up to 12)

Hello there, little mathematicians! I was wondering if you'd help me quantify something? So, inside my lovely little cup here, I have some of these cubes and what I wondered is? How many do I have? When you look at that, about how many do you think there are? Ah, that's your estimate. Okay, should we tip them out and get started to see?

Oh, do you know I thought there would be more. What about you? Okay, well, let's count them to check shall we? And you know what I might do is, 'cause sometimes, when I count, I get caught on the ones that I've counted and that I haven't counted yet, so, I might use this piece of paper actually, just to help me, as I keep track of the count. So, so far, I've counted zero so now count with me, ready?

1, that's right you say the words, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. Let's count backwards and we'll put them back into our cup. So how many do we have here altogether? 12! And as we take one away, which is the same as counting back, we now have 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 and zero.

Ah, okay, let's try counting again but we're not going to use the cards this time to help us. So let's take them out and let's, ah, that's a really good suggestion, we don't have to count by ones, we could count by twos. Let's try that. Ready? 2, 4, 6, 8, 10. Sometimes I get stuck at 10 but do you remember how many we had in our collection? 12. So 10 and 2 more, 12.

Let's try to count back. We'll count back by ones this time. Ready? So there's 12, now 11, now 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, and none, zero. Do you know, I noticed something as we were counting, I think.

Let's try this one more time, ready? How else could we count this time? Ah, I like this thinking. Actually, you're thinking I could just make a collection of five. Like this on a dice pattern. That's one five and, another five. I'll move these closer together so that you can see them. Yes? So one five, two fives and two more and we call that twelve. Mm-hmm! One ten and two. There's one ten and two more and we call that twelve. But I wasthinking about something, you know, I don't think it matters in my collection if I have twelve things and I put them all in really close together and stack them up so they look really small. I still have twelve in my collection.

Mm-hmm, even if I spread them out I still have twelve things. Yeah, even if, I changed one of my cubes for a marker. How many do I have now? That's right! I still have twelve things, because I just changed one block for one marker. Okay, what about though what if I changed one cube for one snowman? How many do I have here now? That's right. I still have twelve things. What if I bunch them all up, really close together, and hide some of them under my snowman? Yes, even though you can't see them all, I still have 12 because I haven't taken any away, or added new ones. I just swapped one for one. What if, okay, what if, I change out one block for one pony? You're right! I still have 12 things! Nice thinking and counting today mathematicians!

So let's talk about the mathematics, mathematicians. Today we practiced counting with understanding, so that means that when we count, we can connect the counting words to the items as we count them, that we can count both forwards and backwards, and that we trust the final quantity that we've, once we've counted it. So even when we spread things out or we join them together, or we swap one thing for another thing. Once we've established, or worked out, something like it's 12, we can trust that it's still 12, and we don't have to keep having to recount it. Very nice work!

Looking forward to next time we get to be mathematicians together! Have a great day!