Counting with understanding up to 20
A thinking mathematically targeted teaching opportunity focussed connecting the number words to items as they are counted
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, 2021
Watch Counting with understanding up to 20 video (6:49).
[Screen reads: you will need a pencil and some paper.]
Hello mathematicians, I hope you're having a really delightful day today. I wondered if you would help me do some counting today? You will? Thank you.
I have some pasta here, which is becoming one of my favourite bits of mathematical equipment and a cup.
[Screen shows a large piece of paper, a bowl of pasta and a cup.]
And I'm going to take a scoop of my pasta. Can you have a look in there? Can you see?
[Presenter scoops a handful of the pasta out using the cup.]
About how many pieces of pasta do you think I might have? What's your estimate? Can you write it down?
Okay, and can you read that number for me? Oh, I can hear lots of different ideas.
I'm gonna tip these out now and we should count them to work out how many we have. Are you ready to count with me?
[Presenter tips cup of pasta out onto paper.]
Okay, let's go. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 ,15, 16 and 17. I have 17 things here.
[Presenter pushes one piece of pasta at a time across from the pile on the right to the left using one-to-one correspondence from one through to 17. She then circles the pasta with her fingers.]
Let's try counting backwards. If I count them back into my cup.
So, can you remember how many we had? Yeah, 17. So I have 17, now I have 16, now I have 15, now I have 14, now 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 and zero.
[Presenter places cup on paper next to pasta and points finger to circle pasta to indicate that altogether there are 17 pieces of pasta. She then places one piece of pasta into the cup whilst counting down, using one-to-one correspondence. When all of the pieces of pasta are in the cup, the presenter shows her empty palm to indicate that there are no more pieces of pasta left.]
Nice counting mathematicians. Now that we counted it back into our cup, let's, let's count them again and see what happens.
[Presenter tips cup of pasta onto paper.]
I wonder if there's another way that we could count?
Last time we counted them all by ones.
[Presenter individually moves 3 pieces of pasta to the side then pushes them back into one pile.]
Oh, let's count by twos. But I think I only know my twos up until a few numbers and then I might get stuck, so, so let's try.
Ready? 2, 4, 6, 8, 10 and now I get a bit stuck in my head so I could keep counting but just keep counting using what I know about counting by ones. So, there's 10 here, 10, 11, 12, 13, 14, 15, 16, 17. 17 things.
[Screen shows the presenter moving groups of 2 pasta pieces from the large pile to an empty space to the left. As she moves them, she counts up by twos until she reaches the number 10. The presenter then uses one-to-one correspondence to count the rest of the 7 pieces of pasta.]
And you know what I was wondering, is if I spread these all out like this, how many things do I have? Yeah, 17 cause it doesn't matter if I spread them out, or if I clump them in close together. How many do I have? That's right. 17.
[Presenter spreads pile of pasta over the paper and circles the whole page with her hand. She then clumps them back together into one pile.]
So, what was the mathematics we were working on?
Today we were practicing counting with understanding.
So, this means that we can connect the number words to items as we're counting them, both forwards and backwards, and that once we've worked out how many, once we've quantified our collection, it doesn't matter if we spread it out or push it all back in together, we still trust that it's 17 or the quantity that we counted.
Nice work today little mathematicians!
[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.