Counting game (by ones)
Counting game (by ones) is a thinking mathematically context for practise resource focused on counting forwards and backwards by ones using ten-frame structures to reach a target number.
Syllabus
Syllabus outcomes and content descriptors from Mathematics K–10 Syllabus (2022) © NSW Education Standards Authority (NESA) for and on behalf of the Crown in right of the State of New South Wales, 2024.
Outcomes
- MAO-WM-01
- MAE-RWN-01
- MAE-RWN-02
- MAE-CSQ-01
- MAE-CSQ-02
- MAO-WM-01
- MA1-RWN-01
- MA1-RWN-02
Collect resources
You will need:
- 24 items (for example, pasta pieces, counters, pegs, pencils or blocks)
- pencils or markers
- something to write on.
Counting game (by ones)
Watch Counting game (by ones) video (3:39).
Michelle
Alright, I'm here with one of my favourite mathematicians today, Hi Sam.
Sam
Hi Michelle.
Michelle
How are you going?
Sam
Good.
Michelle
Are you ready to play one of our favourite games, the counting game?
Sam
Yeah.
Michelle
Do you remember how to play?
Sam
Yeah, but sometimes you lose track so maybe if we use some of these counters it might be easier.
[Screen shows a white piece paper in a landscape orientation and a yellow bucket with green counters inside. Sam picks up the bucket and then puts in back down.]
Michelle
That's an excellent idea.
Sam
We could also use a ten-frame.
Michelle
Great.
We... our target is going to be 24 today so how many ten-frames would we need?
Sam
Probably 2 then we could just put some on the side.
Michelle
That makes sense because 2 10s is equivalent to 20, isn't it?
Michelle
Oh yeah, I can see the big rectangle and then you partition that into 2 skinny rectangles.
[Sam draws a rectangle on one side of the paper with one long vertical line down the centre.]
Michelle
And then one, 2, 3, 4 lines in the middle will make 5 boxes on each side.
[Sam draws 4 evenly spaced shorter horizontal lines, creating 10 boxes inside the original rectangle.]
Michelle
You've got some knowledge about the structure of 10 frames.
[Sam draws a second ten frame on the other side of the paper.]
Michelle
Yeah, I like how you counted to check, so if there's five on this side, what do we know about this side?
Sam
That there will still be 5 because it is symmetrical.
Michelle
Nice, alright, so let's play. Would you like to start, or shall I start?
Sam
I'll start.
Michelle
OK?
Sam
So, let's go one, 2, 3.
[Sam places 3 counters in a box each in the right-hand ten-frame, starting with the bottom box in the far-right column and moving up the boxes vertically.]
Michelle
Ok, I think it's a good idea to get counters. I'm going to say 4.
[Michelle then places one counter in next box on the ten-frame.]
Sam
5, 6.
[Sam then places 2 more counters, one in the top right box and one in the bottom box in the next column.]
Michelle
7,8, 9.
[Michelle then places 3 counters in the next boxes on the ten-frame.]
Sam
10, 11 12.
[Sam then places 3 counters on the ten-frames, one in the last box on the right-hand ten-frame and 2 more in a new column of the left-hand ten-frame.]
Michelle
13, 13.
[Michelle places one counter in the next box on the ten-frame.]
Sam
14.
[Sam places one counter in the next box on the ten-frame.]
Michelle
15 and 16.
[Michelle places one counter in the next box above, and the other counter in a new column on the ten-frame.]
Sam
17.
[Sam places one counter in the next box on the ten-frame.]
Michelle
18.
[Michelle places one counter in the next box on the ten-frame.]
Sam
19.
[Sam places one counter in the next box on the ten-frame.]
Michelle
20. 21.
[Michelle places one counter in the last box on the second ten-frame and another counter outside the ten-frame.]
Sam
22,23 and 24
[Sam places 3 more counters outside the ten-frame making a total of 24.]
Michelle
Congratulations. Do you want to play again? Maybe you could play best out of three? But do you want to play going backwards this time?
Sam
Yeah, we could go backwards, forwards, backwards.
Michelle
Yeah, that's a great idea.
So, would you like to start, or will I start?
Sam
I'll start.
[Sam then removes 3 counters and places them into the bucket.]
Sam
24, 23, 22.
Michelle
OK.
[Michelle stops and collects the 3 counters from the bucket and puts them back in the same location next to the ten-frame.]
Michelle
Oh, hold on, I saw what happened there. So, we had twenty-four to start with.
So, at 24 and then you took away so we had 23, 22, 21. It’s always tricky in the backward count? That's why the structure can really help us, yeah. You do it this time.
[Michelle then removes the 3 counters again demonstrating the correct count aloud. Michelle then puts the counters back in place for Sam to try.]
Sam
23, 22, 21.
[Sam removes the 3 counters again and places them into the bucket.]
Michelle
Yeah, nice. So sometimes Sam, I like to like take it away and then say the number so I don't get stuck. So now there's 20, 19 and 18 and I can just double check, I do a quick scan in my head because this ten-frame is full and there's 2 missing here, so it was full it would be 2 10’s and there is 2 missing, so there's one 10 and 8 and we just recall that, we rename that 18. Alright, your go mister. I'm determined to win.
[Michelle demonstrates removing the counter before saying the number and then puts the counter back. She then removes one counter from the top left box and one from the next box underneath. Michelle circles the full ten-frame on the right with her finger and then points to the 2 empty boxes in the left ten-frame. Michelle places the 2 counters into the bucket.]
Sam
17.
[Sam removes one counter from the ten-frame and places it into the bucket.
Screen reads – Over to you!]
[End of transcript]
Instructions
- Use 24 as a target number.
- Take in turns to count on by saying the next 1, 2 or 3 number words in the sequence, placing the items into a central pile as they are counted.
- Players collect a point if they say the target number.
- A new target number is chosen and players play again.
- Try playing forward and backward.
- Use 24 as a target number.
- Take in turns to count on by saying the next 1, 2 or 3 number words in the sequence, placing the items into a central pile as they are counted.
- Players collect a point if they say the target number.
- A new target number is chosen and players play again.
- Try playing forward and backward.
An example of the game with target number 24
Player A: 1, 2, 3...
Player B: 4...
Player A: 5, 6...
Player B: 7, 8, 9…
Player A: 10, 11, 12...
Player B: 13…
Player A: 14...
Player B: 15, 16...
Player A: 17...
Player B: 18...
Player A: 19...
Player B: 20, 21...
Player B: 22, 23, 24!
Play again, starting at 24 and counting backwards to zero.
Other ways to play
Select a different target number and a starting number. For example, you might start at 35 and try to get to 51.
- Count in multiples. For example, you can start at 0 and aim for 85, counting by fives.
Reflection
What would happen if I had said....instead of ...? (identify a point time, when playing the game, to ask this question)
How could we change the game to make it more/less challenging?
What did you notice about playing the game by counting backwards? Did it make your brain work harder or was it less difficult?
Did you work out a way to play this game so that you didn’t lose? What was your strategy? Did it work?