# Ten-frame filler

A thinking mathematically context for practise focussed on developing understanding of combinations to ten and the flexibility of numbers

## 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
• MAE-CSQ-01
• MAE-CSQ-02

• MAO-WM-01
• MA1-CSQ-01

You will need:

## Watch

Watch Ten-frame filler video (4:40).

Fill the most ten-frames on the game board.

### Transcript of Ten-frame filler video

[A title over a navy-blue background: Playing with tessellations. Below the title is text: Dianne Siemon and Paul Tabart. Small font text in the lower left-hand corner reads: NSW Mathematics Strategy Professional Learning team (NSWMS PL team). In the lower right-hand corner is the red waratah of the NSW Government logo.

A title on a white background reads: You will need.

• 2 players (or 2 teams of players)
• One game board
• 2 different coloured markers or pens
• Zero - 9 dice or a spinner

On the right side is an image of a game board with Title: 10-Frame Filler Game. The game board is 16 tables with 5 rows and 2 columns.]

### Michelle

So, for this game, you'll need 2 players or two teams of players, one game board, it looks like this and two different coloured markers or pens. You'll also need a dice or a spinner.

[Text over a blue background: Let’s play!]

### Michelle

Alright mathematicians, let's play.

[On the left side is a game board, on the right is a dice and a pen.]

### Michelle

Hello mathematicians. And hello, Barbara.

### Barbara

Hi, Michelle. Hi, mathematicians.

### Michelle

So, I've got a new game for us to play today. This game we can find in a book from Di Siemon and her colleagues, called "Teaching Mathematics from Foundation to Middle Years". And this particular game was developed by Di Siemon and her colleague, Paul Tabart. And it's called Ten-frame Filler. And let's play.

OK.

### Michelle

And we can learn as we play. So, would you please roll the zero to 9 dice?

[Barbara picks up the dice and rolls it.]

### Michelle

Oh, and you have a 7.

Seven.

### Michelle

So, the aim of this game, Babs, is to fill in the ten-frames. But as you're filling in 7, try to do it in one manoeuvre.

OK.

### Michelle

So, let's have a look at the structure of a ten-frame. What do you know about what's happening over here in this column?

### Barbara

One, I know that's 5.

Yeah. Because?

### Barbara

Well, there are 2 columns of 5 in a ten-frame.

### Michelle

So, what you might start doing is visualising if - for me, if I was you, I'd be like, "Well, I need one 5 and then two more".

Yeah.

### Michelle

You know, and whether you scoop across this way or this way, you know, the choice is yours. But just try to sweep it through in one movement.

### Barbara

OK.

[In the first frame, Barbara highlights in pink the entire left column along with 2 rows of the right column.]

### Michelle

Yeah. Nice. And I can see that that's 7.

### Barbara

Yep. And we can...

### Michelle

And I can see you're gonna change colour for me too, which is nice. I'll be in blue. Thanks.

[A dashboard comes up with colour options and Barbara selects blue.]

There you go.

### Michelle

And I'm gonna roll the dice.

[Michelle picks up the dice and rolls it.]

### Michelle

Oh, and I got a 4. So, there's 3 left here, I can't go there.

### Barbara

'Cause not enough space for you.

### Michelle

'Cause there's not enough space. So, I'm gonna just do 4. I can do it on any ten-frame, actually, if I want to.

### Barbara

OK. We don't need to go in order?

### Michelle

No, we don't have to go in order. And what I know about 4, is it's one less than 5.

Yep.

### Michelle

So, I can do a sweep and just leave one space in one column.

[In the last frame of the first row, Michelle highlights in blue 4 rows of the right column.]

Great.

### Michelle

And I will go back to pink for you, and you may roll.

[Text over a blue background: A little while later…

On the game board, the first 2 frames have pink highlights with initials BK above them. The 2 last frames of the first row have blue highlights with the last one having initials MT above it. The next row have pink highlights, except for the second frame which has blue highlights.

On the right, the dice show 9.]

Oh, 9.

Oh, a 9.

OK.

### Michelle

What are you thinking?

### Barbara

I just know I need to leave one behind. I'm just wondering which one I should leave behind. I'll leave that one there.

### Michelle

Well, I hope I roll a 3 or a 2.

### Barbara

Or a one. 2. Here you go.

[Michelle picks up the dice and rolls it.]

Lovely.

### Michelle

So, I am gonna choose 2 here, which means I get to claim this ten-frame, MT.

[In the first frame of the second row, Michelle highlights the first row and writes MT above it.]

### Barbara

OK.

[Barbara picks up the dice and rolls it.]

### Barbara

Oh, a one. Perfect.

[In the first frame of the third row, Barbara dots the first cell in the left column.]

### Barbara

There we go. BK.

[Text over a blue background: Over to you!

Text over a blue background: What's (some of) the mathematics?]

### Michelle

So, what's some of the mathematics?

[A title on a white background reads: What's (some of) the mathematics?
Text below reads: This game helps us think about smaller numbers hiding inside of 10. We saw that:]

### Michelle

This game helps us think about smaller numbers hiding inside of 10. So, we saw that…

[An image appears of a frame with a blue highlight that goes from the first row of the left column to the last row of the right column, and another blue highlight down the 4 rows of the right column. Text below reads: 10 is 6 and 4, 10 is 4 and 6.]

### Michelle

…inside of 10 we can see 6 and 4 or we can see 4 and 6.

[An image appears of a frame with a blue highlight that goes across the first rows of both columns, and a pink highlight that goes from the second row of the left column to the second row of the right column. Text below reads: 10 is 8 and 2, 10 is 2 and 8.]

### Michelle

We could also see that 10 is made up of eight and two or two and eight.

[An image appears of a frame with a pink highlight that goes from the first row of the left column to the last 2 rows of the right column, and another pink highlight down the 3 rows of the right column. Text below reads: 10 is 7 and 3, 10 is 3 and 7.]

### Michelle

And we could also see that 10 is made up of 7 and 3 and we can also see that 10 is made up of 3 and 7.

[Below the images, text appears that reads: (You might have noticed other things too about 10 that you can share with your friends, teachers and your families!)]

### Michelle

And you might have noticed other things too about 10 that you can share with your friends, teachers and your families.

[A title on a white background reads: What's (some of) the mathematics?
Text below reads: In this game it's important that we ‘sweep’ to collect the number that we rolled (rather than colouring in individual dots). We noticed that we could sweep numbers in different ways using different thinking.

At the bottom of the screen more text reads: The different ways of sweeping helped us use and talk about 6 in different ways and this is really important for building our number sense!]

### Michelle

We also noticed something else. And that is that in this game it's important that we sweep to collect the number that we rolled, rather than colouring in individual dots. So, we noticed that we could sweep numbers in different ways using different thinking.

[A game board appears in between the text.]

### Michelle

For example, we could sweep 6 like this…

[In the first frame, a pink highlight goes down the entire left column to the last rows of the right column.]

### Michelle

…by knowing that six is made up of 5 and one more, and also knowing, aha, the structure of a ten-frame.

[Under the first frame, Michelle writes: 5 and one.]

### Michelle

We could also sweep 6 by knowing that it's double 3.

[In the second frame, a pink highlight goes from the third row of left column up and across to the third row of the right column.

Under the frame, Michelle writes: 3 and 3, and Double 3.]

### Michelle

And we could also sweep 6 by knowing that it's 4 less than 10.

So, if we work out where the 4 is…

[On the third frame, a line appears down the side of the first 4 rows of the left column. A pink highlight does from the last row of the left column and up the right column.]

### Michelle

…the rest has to be six.

[Under the frame, Michelle writes: 4 less than 10.]

### Michelle

So the different ways of sweeping helped us use and talk about 6 in different ways. And this is really important for building our number sense. Alright mathematicians, back to you.

[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

• Roll the dice.

• Record the number that was rolled in one of the ten-frames in a single, sweeping movement.

• Take it in turns to roll the dice and fill in the ten-frames.

• A player can add their number to any ten-frame.

• If there is not enough space in any of the ten-frames, miss a turn.

• If you are the player who completes the ten-frame (for example, you roll a three and there is a ten-frame with 7 already filled in), you get the claim it by putting your initials on top of the ten-frame.

• The player with the most ten-frames at the end is the winner.

## Discuss

• Was there a strategy that helped you to win the game?
• What numbers do you think were the best to roll? Why?
• Have we found all the possible combinations to 10 using 2 numbers?
• What might happen if we had a third player? Would it make it easier or harder to win?