Counting with understanding up to 12
A thinking mathematically targeted teaching opportunity focussed on counting forwards and backwards while connecting language, symbols and quantities to trust the count
Syllabus outcomes and content descriptors from Mathematics K–10 Syllabus © NSW Education Standards Authority (NESA) for and on behalf of the Crown in right of the State of New South Wales, 2023
Watch Counting with understanding up to 12 video (6:49).
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?
[Michelle has a cup with assorted coloured cubes in it.]
When you look at that, about how many do you think there are?
[Michelle picks up the cup.]
Ah, that's your estimate. Okay, should we tip them out and get started to see?
[Michelle tips the cubes out of the cup.]
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.
[Michelle places down a A4 piece of paper and a sticky note with 0 written on it.]
So, so far, I've counted zero so now count with me, ready?
One, 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.
[Michelle places down a cube, as each cube is counted, the corresponding sticky note is placed on the paper.]
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.
[Michelle removes a cube at a time placing them back into the cup, as she does she removes the corresponding sticky note.]
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.
[Michelle tips the cubes out from the cup and gathers them in a pile on the right.]
Let's try that. Ready? 2, 4, 6, 8, 10.
[Michelle now places 2 cubes at a time on the paper.]
Sometimes I get stuck at 10 but do you remember how many we had in our collection?
[Michelle circles the 10 cubes with her finger.]
So, 10 and 2 more, 12.
[Michelle now places the last 2 cubes down.]
Let's try to count back.
We'll count back by ones this time. Ready?
[Michelle now places one cube at a time back into the cup, circling the group as she removes each one.]
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?
[Michelle tips the cubes back out of the cup.]
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 5.
Like this on a dice pattern.
[Michelle place 5 cubes to the left in a dice pattern.]
That's one 5 and, another 5. I'll move these closer together so that you can see them.
[Michelle now places another 5 cubes to the left in a dice pattern.]
So, one 5, 2 fives and 2 more and we call that 12.
[Michelle circles the 2 groups of 5 with her finger.]
Mm-hmm! One ten and 2. There's one ten and 2 more and we call that 12.
[Michelle now places the last 2 cubes under the 2 groups of fives and places a sticky note down with 12 and one 10 and 2 written on it.]
But I was thinking about something, you know, I don't think it matters in my collection if I have 12 things and I put them all in really close together and stack them up, so they look really small. I still have 12 in my collection.
[Michelle gathers the 12 cubes up into a small pile.]
Mm-hmm, even if I spread them out, I still have 12 things.
[Michelle now spreads the 12 cubes out across the A4 paper.]
Yeah, even if, I changed one of my cubes for a marker.
[Michelle removes one of the cube and replaces with a marker.]
How many do I have now?
That's right! I still have 12 things, because I just changed one block for one marker.
[Michelle now removes the marker and replaces with a cube.]
Okay, what about though what if I changed one cube for one snowman?
[Michelle removes one cube and replaces with a snowman.]
How many do I have here now?
[Michelle circles the group with her finger.]
That's right. I still have 12 things.
What if I bunch them all up, really close together, and hide some of them under my snowman?
[Michelle bunches the cubes up together hiding some of the cubes underneath the 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.
[Michelle now swaps back the cube and removes the snowman.]
What if, okay, what if, I change out one block for one pony?
[Michelle swaps out a cube for a toy 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!
[End of transcript]
Watch and follow along with the video and be ready to help count the items. You will be counting forwards and backwards.
You will be connecting the words that you say to the items as you count and them.