# Data toss – Stage 1

A thinking mathematically context for practise resource focussed on collecting and representing data

Adapted from Gervasoni, A. (2015). Extending Mathematical Understanding: Intervention, Ballarat Heritage Services Publishing

## 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
• MA1-DATA-01
• MA1-DATA-02

## Collect resources

You will need:

• small object (block, rubber, peg or a small soft toy)

• chalk or stick

• pencil or whiteboard marker

• paper or mini whiteboard.

## Watch

Watch the Data toss part 1 video (5:33).

Hit the target and record your results.

This video was created with Wendy from Hermidale PS, Cheryl from Hornsby Heights PS and Rachel from Albury North PS.

### Transcript of Data toss part 1

[Text over a blue background: Data toss 1. Adapted from Number Target by Ann Gervasoni. Small font text at the bottom of the screen reads: NSW Mathematics Strategy Professional Learning team (NSWMS PL team). In the bottom right-hand corner of the screen is the red waratah of the NSW Government.]

### Speaker

Let's play data toss.

[Text on a white background: You will need…

· small object (block, rubber, peg, a small soft toy)

· chalk or stick

· pencil or whiteboard marker

· paper or mini whiteboard

Below, are three images. The first shows four small items: a 50- cent coin, a yellow button, a purple cube, and an echidna-shaped pencil eraser. The second image shows a piece of white chalk and small stick. The third image shows a small whiteboard, a whiteboard marker, a pencil and a yellow piece of paper.]

### Speaker

You will need an object to toss. This can be a block, a rubber, a peg, a toy, or anything that will fit in the palm of your hand. It might be good if you do something that doesn't roll. You will also need some chalk or a stick to draw your target. We need to record our scores and we can use this by using our pencil and paper or a whiteboard and marker. We can play this game inside or outside. If you are using chalk, I suggest you play it outside on the cement. You could even use your stick to draw your target in the dirt. If you are playing inside, draw your target on a piece of paper.

[Over a blue background, text: Let’s play!

Outside, a dirt driveway. The speaker moves a ladder aside.]

### Speaker

I am playing my data toss game in the dirt today. You can join me if you like. Before we begin, we need to set up that game. We need to mark the starting line.

[On the left of the frame, the speaker uses a stick to mark a line in the dirt. She places the stick over the line.]

### Speaker

I'll use that stick to help us see that.

[From the line, she takes two large steps towards the right of frame.]

### Speaker

Then we need to take two large steps and this is where we are going to mark our target.

[She takes a step back. She places her palm flat on the ground. She uses a stick to draw a circle around her hand. She writes “100” in the centre of the circle.]

### Speaker

If you are drawing like me, what you need to do is take two steps, draw a circle around your hand and put 100 in it.

[She draws a larger circle around the original circle. Within this circle, she writes “50”.]

### Speaker

Draw a larger circle around that, put 50.

[She draws a third, larger circle around the second circle. Within this circle, she writes “30”.]

### Speaker

Another larger circle. Put 30 and...

[She draws a fourth, larger circle around the third circle. Within this circle she writes “20”.]

### Speaker

on the outside put 20. Now, might get a bit hard to see. So I found some string. I'll just pop that on it. Then we can clearly see our circles.

[She gathers a bundle of lengths of blue string. She places the string on the ground, to mark the circles that she has drawn.]

### Speaker

You can use whatever you've got at home or you might be able to see yours in the dirt. OK, our target. Nearly ready? I need a recording sheet. Could write it in the dirt, could get a bit hard.

[The speaker places a whiteboard beside the line she marked on the left of the frame.]

### Speaker

So I have a whiteboard here and my pen, ready. And lastly, I need my object.

[The speaker shows the green, echidna-shaped eraser to the camera.]

### Speaker

We have Eddie the Echidna, helping us out today. So we are going to toss our object 20 times and report our score. Are you all set up and ready? Let's begin.

[The speaker stands behind the starting line. She tosses the echidna at the target. It bounces a little, and lands on the line which separates the 30 and the 20 circle.]

### Speaker

Oh! That one should be there at 20.

[The speaker writes on the whiteboard. She tosses the echidna again. It bounces past the target. She writes on the whiteboard.]

### Speaker

Didn't land in my target, so I get zero. Zero.

[She continues to throw the echidna and record her score on the whiteboard.]

### Speaker

OK, last one.

[She tosses again. It doesn’t land on the target. She writes down her score. She shows the white board to the camera. It features 4 columns of 5 rows of scores: 20, 0, 20, 0, 0, 0, 20, 20, 0, 0, 0, 0, 0, 30, 0, 20, 0, 0, 30, 0.]

### Speaker

These are my scores that I scored off using Eddie the Echidna. OK, I played my game. Let's head inside now to take a look at my data.

[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

• Draw a starting line (using chalk or a stick if outside) to show where you need to stand.

• Take 2 large steps forward then start to draw the target or use the resource sheet if inside.

• Toss your object 20 times, aiming for the target and record the score each time on a piece of paper or whiteboard.

## Watch

Watch the Data toss part 2 video (6:05).

Explore ways to represent and organise data toss scores.

### Transcript of Data toss part 2

[The whiteboard from the previous video lays flat on a white surface. Beside it, is a marker pen and a blank sheet of paper.]

### Speaker

With so many scores, it might be easier to put this in a table. I think a tally table would be a good choice, so we can see things clearly. We can draw one up.

[The speaker draws a table. In a single column, the speaker writes the word “Score”, then the numbers, “0”, “20”, “30”, “50”, “100” beneath it. The speaker then draws a large box around the text, then separates each row with a horizontal line. The column of numbers under the text “Score”, sits on the left side of the table. The speaker then draws a vertical line to the right of the column. The speaker then writes the word “Tally” at the top of the second column.]

We have our scores that we could possibly have tossed and we have our tally. Let's transfer our data from our tosses into our table.

[The speaker tallies the results from the whiteboard into the table, one by one. She crosses out each score on the whiteboard as she tallies it. The results are: zero was scored 13 times, 20 was scored 5 times, and 30 was scored 2 times. 50 and 100 were not scored.]

Now that we've transferred our data from our tosses into the table, let's have a look at our table more closely.

[The speaker moves the whiteboard out of the way and positions the tally table in the centre of the frame.]

I wonder how I can make it easier to look at the data, instead of having to count the tally all the time.

[The speaker draws a vertical line to the right of the Tally column. At the top of the third column, she writes “Frequency”. She draws a vertical line to the right of this column.]

We can do this by making another column. We call this the frequency column. It will help us tell how often we tossed that score.

[The speaker writes the frequency of each score as a decimal number: 13, 5, 2, 0, 0.]

Let's take some time to have a look at our data that we have now gathered. Which score did I toss the most? That is very easy to see on my table.

[The speaker points to the first row of tallied scores.]

13 times I tossed zero. Which score did I toss the least?

[The speaker points to the final two rows of the table, where the cells in the “Tally” column are empty.]

Good looking, I did not toss a 50 or a 100, so therefore, 50 and 100 were the scores that I tossed the least. Did you notice anything else from the data gathered? Yes, I did toss 20 more times than I tossed 30, and yes, there is a large gap between the number of times I've tossed 20 or 30, compared to how many times I tossed zero. I wonder what the total point scored would be. Let's use our table to find out that.

[At the top of the final column of the table, the speaker writes, “Points”. In the cells below, she writes the number of points gained from each score as a decimal: 0, 100, 60, 0, and 0.]

We're going to find the points for each score. Zero, I tossed 13 times, so 13 lots of zero is zero. 20, I tossed five times, so, five lots of 20, or five lots of two tens is ten tens, 100. 30, I tossed twice, two lots 30, or two lots of three tens is six tens, which is 60. 50, I tossed zero times, zero points, same with a 100.

[Beneath the table, the speaker writes, “Total Points”.]

My total points, adding all of these points together, zero plus 100, plus 60, plus zero, plus zero, so 100 plus 60, or ten tens and six tens, is 16 ten, which is renamed to 160.

[Beside “Total Points”, the speaker writes, “160”.]

My total points from this game of Data Toss is 160. As a mathematician, I take the time to reflect on my data. I wonder how I could improve it? I wonder what I could do to improve my total points? How can I increase my scores every time I toss?

[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

• Create a table, with 4 columns and 6 rows. Across the top row include the headings, score, tally, frequency and points.
• Record your scores as tally marks then write the total of each score in the next column.

• Have a look at your table, which score did you toss the most? Which score did you toss the least? What else did you notice about your data?

• Add together the points for each score in the fourth column.

• Combine all of the points that you scored.

• Play the game a few times, recording your scores. Think about how you can improve your score each time?

## Discuss

• How could I improve the total number of points?

• What is the highest possible score you could get?

• If you could change the scores in the target to help you get closer to 100, what would you change them to?