# Pinch a ten

A thinking mathematically context for practise focussed on reasoning and counting to work out how many

## Syllabus

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

• MAO-WM-01
• MAE-RWN-01
• MAE-RWN-02

## Collect resources

You will need:

• small bag of dried beans or counters

• piece of paper

• pencils or markers

• something to write on.

## Watch

Watch Pinch a 10 video (4:54).

Pinch from a collection to try and create 10.

### Transcript of Pinch a 10 video

[On a wooden table is a table with headings less than 10, 10 and more than 10. On the left side of the table is a bowls of coloured plastic chips.]

### Speaker

Welcome back, mathematicians. We're here to play a game today, I learnt from Marilyn Burns called Pinch a Ten. To do this, we have a table that we're going to use to record our moves. We need some counters or you could use some dried beans or pasta at home. And in case I need some support in determining how many I have, I also have this…

[The speaker holds up a paper with a drawing of 2 hands.]

### Speaker

…tracing of my hands and one of my other little mathematician friends did to help me with play this game. So what I do is…

[She places her hand into the bowl.]

### Speaker

…I stick my head into my counters and I pinch what I think will be about 10.

[She picks up a handful of chips.]

### Speaker

So for me at the moment, to work out how many I have…

[She puts the chips down.]

### Speaker

…I know a couple of structures that I can use and I know some things about 10. So for example, one of the things I know about 10 is that when I have 5 of something and five or something…

[She picks up the paper and holds up her hands against the drawings.]

### Speaker

…it always combines to make 10 of something.

[She put the paper down.]

### Speaker

But I know that 5 can also look like this.

[She sets up 4 chips around 1 chip. She leaves 3 chips on the side.]

### Speaker

And because I can't make 5 fives on a dice pattern, I know that I must have less than 10. And in fact, I know this is 5…

[She points to the arranged set. Then to the remaining chips.]

### Speaker

…6, 7, 8.

[She points to each chip.]

### Speaker

Or I could count them all, one, 2, 3, 4, 5, 6, 7, 8. The important thing is that we work with the students to get them reasoning as well as counting to work out how many.

[She picks up the chips.]

### Speaker

So in my first attempt, I had less than 10.

[She places the chips in the first row of the column Less than 10.]

### Speaker

So I'll put that there to say I had less than 10.

[She picks up a handful of chips.]

### Speaker

OK. I think I have 10 this time. So let's see. I definitely feel like I have more than I had before.

[She puts the chips down.]

### Speaker

So, this time I might show you my strategy…

[She holds up the hand drawings.]

### Speaker

…that Holly and Sam showed me, and that is that I know that I have 10 fingers. And so what I can do is…

[She places a chip over each finger on the drawings.]

### Speaker

…just move each counter onto the tip of one of my fingers. And because there's 2 empty spaces, I know that I still have less than 10. In actual fact, I have 2 left and that means I still have 8 exactly like I had last time…

[She picks up the chips.]

### Speaker

…even though it felt like it was a bit more. I could also prove it's 8 because I could pick up both of these stacks…

[She picks up the chips on the table and places it against the other chips.]

### Speaker

…really carefully. And if I lay them like this, you can see that they're the exact same height. So I can use direct comparison to say they're both 8 and 8 is less than 10.

[She places both stacks under column Less than 10.]

### Speaker

OK. Let's try this one.

[She picks up a handful of chips.]

### Speaker

OK. So let's check these once again.

[She sets up 4 chips around 1 chip. She leaves the rest on the side.]

### Speaker

I'm gonna try my fives strategy and again, I have 8 and again I have less than 10.

[She picks up the chips.]

### Speaker

I almost grabbed another few, but I didn't. So next time I need to see if I can estimate a little bit closer.

[She places the chips under column Less than 10. She picks up a handful of chips.]

### Speaker

Let's try. So maybe this time I'll just grab an extra one and see what happens. It does feel fuller and I might use this strategy again.

[She gets the hand drawings.]

### Speaker

So I know I have 10 fingers. And so if I have one counter for each fingertip, that means that I'll have 10.

[She places a chip over each finger on the drawings.]

### Speaker

If I can't fill them all in, I'll have less than 10. And if I have too many, I'll have some counters left over from the other side. And things are looking good. Since all of my fingers are covered and I have 10 fingers, I must have exactly 10 counters.

[She picks up the chips.]

### Speaker

OK. So in my fourth attempt…

[She places the chips under column 10.]

### Speaker

…I managed to pinch a 10.

[She picks up a handful of chips, and arranges them like dice patterns 5 and 4.]

### Speaker

Oh, no. And I was one away. And I know I'm one away because if this were a 5 also I would have a counter here.

[She points at empty spot in the middle of the 4 chips.]

### Speaker

Like this.

[She places a chip in the empty spot.]

### Speaker

It doesn't.

[She places the chip back.]

### Speaker

And so it's one less than 10, which is 9.

[She picks up the chips.]

### Speaker

So I'm pretty good at getting less than 10.

Just not so great at making ten or getting too many. Let's see what happens this time.

[She places the chips under column Less than 10.]

### Speaker

OK. I'm just going to get a big bunch.

[She picks up a handful of chips.]

### Speaker

This time and see what happens. So, I know.

[She arranges them into the dice pattern 5.]

### Speaker

Well, I'm going to use my fives strategy because I know two 5 makes 10. And this time I think I have too many.

[She picks up the chips.]

### Speaker

So let's have a look on my fingers to check.

[She gets the hand drawings.]

### Speaker

If I move this over.

[She places a chip over each finger on the drawings.]

### Speaker

So I know I have ten fingers. If I can put one counter for each finger, that would be exactly 10. But in this case, I have these two 2 over.

[She drops 2 coins on the table.]

### Speaker

So on my sixth attempt.

[She picks up the chips.]

### Speaker

Of playing pinch a 10, I got more than 10.

[She places the chips under column More than 10.]

### Speaker

Over to you, little mathematicians.

[Over a grey background, the red waratah of the NSW Government logo appears amongst red, white and blue circles. Text: Copyright State of New South Wales (Department of Education), 2021.]

[End of transcript]

## Instructions

• Take a pinch of dried beans or counters and determine how many you have in your collection. Is it:

• less than 10

• 10

• more than 10.

• Complete the chart.

• Use what you know about numbers and counting to help you decide whether you have more than 10, less than 10, or exactly 10.

• Play again 5 more times.

## Reflection

• How did you work out how many you pinched?