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[Text over a navy-blue background: bunches of balloons. (Early Stage 1). From resolve. 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.]

Speaker

Bunches of balloons from reSolve.

[Text over a white background: You will need…

· pen and paper

· 18 balloons (these could be made out of play dough or you can use rocks, paper clips or leaves).

An image below shows 18 small, colourful balls of play dough and two pens.]

Speaker

For this activity, you will need pen and paper and 18 balloons. These could be made out of play dough or you could use rocks, paper clips or leaves.

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

Speaker

Let's play.

[The group of 18 small, colourful and an orange marker pen each rest on a separate piece of paper. The edges of the paper have been taped together.]

Speaker

Hey, there mathematicians. Today you're going to help me solve a problem using my little balloons down here. Can you see them down on my page? Just by looking and noticing, do you know how many balloons we're going to be using today? It's a bit tricky, isn't it? Maybe I could arrange them in a different way that's easier for you to find the total. Let me see.

[The speaker arranges the balloons into 2 rows of 5.]

Speaker

I know that my brain really likes the number ten, so I think I might start with a ten-frame. Which I'm gonna put them up here.

OK. Now I know that this is a ten-frame because I can see five in the top row and five in the bottom row. And we know that five and five is ten. Now, make a second ten-frame.

[The speaker arranges the remaining balloons into one row of 5 and one row of 3.]

Speaker

OK. There. Is it easier to use this structure to work out how many balloons that we're using today? I can see a full ten-frame, and I can also see a second ten-frame, but this one has two empty spaces. And I know that eight is two less than ten, so we must be working with 18 balloons today. Alright, mathematicians. Our job is to think about how we can use these 18 balloons and put them into equal bunches. And that just means equal groups. What we're trying to discover is how many balloons can we put into each bunch so that each bunch has the same number of balloons. And because we know the total number of balloons, which is 18, but we don't yet know how many bunches we'll have or how many balloons will be in each bunch, we're going to use a strategy called trial and error. I think to begin with, I might make groups of three. Going to put my bunches with three balloons in each.

[The speaker arranges 3 balloons into a bunch. She arranges them into a triangle, with 2 on the top row and one, positioned between them on the bottom row.]

Speaker

And I think this is a good spatial pattern that I can use to show that each of my bunches will have three because we know that two and one more is three. So as you can see, I have one three.

[The speaker arranges 3 more balloons into a bunch, in the same formation as the previous bunch. As she points to the 2 bunches, she knocks a balloon with her finger.]

Speaker

Now I have two, oops, it rolled... I have two threes.

[The speaker arranges a third bunch of 3 balloons, then a fourth bunch.]

Speaker

Now I have three threes.

OK. Now, mathematicians, I have four threes.

[The speaker arranges a fifth bunch of 3 balloons. She then arranges the 3 remaining balloons into a bunch.]

Speaker

My plate is a little bit sticky. Now I have five threes and look, now I have six threes. So we had 18 balloons in total and we've put them into six bunches, six groups, and inside of each bunch or group is three balloons. So we have equal groups.

[The speaker places a third piece of paper, and a purple pen, below the other 2 pieces of paper in front of her.]

Speaker

And mathematicians, we know that as well as using concrete materials like my balloons down here, we can also draw a picture to represent our thinking. Now, I'd like to do this in two different ways today.

[Using the orange marker pen, the speaker draws a horizontal line across the piece of paper on the right of screen.]

Speaker

So I'm going to roughly find the halfway point of my page and draw a line across. OK. I'm going to start with the equal groups of three that we found here. Now, going to start with this group here.

[Above the horizontal line, the speaker draws three small balloons, each with a string attached. Beneath the balloons, she writes “1 three”. She circles the bunch of balloons that she has just drawn with the purple marker pen. With the orange marker pen, she draws a tick above the first group of playdough balloons.]

Speaker

One balloon, two balloons... three balloons. I have 1 three. And to help you see that and keep track of all of our groups, I'm going to circle it using this purple Texta, 1 three. And I can tick off that I've done this group.

[The speaker points to a second bunch of playdough balloons. She draws three more balloons, which all have curved strings. Using the purple pen, she draws a large circle around both of the bunches of balloons she has drawn. She crosses out the text “1 three”. Beneath the second bunch of balloons, she writes, “2 threes”. She draws a tick above the second bunch of playdough balls.]

Speaker

Now, let's do this group of three down here. Here's one balloon, two balloons... three balloons. I know mathematicians, if you look, I don't have 1 three now. Now I have 2 threes. So we can record that like this, 2 threes, OK. Tick that one off.

[The speaker points to a third bunch of playdough balls. On the other sheet of paper, she draws a third bunch of three balloons. She crosses out the text, “2 threes”, then draws a large purple circle around the 3 bunches of balloons. She then writes, “3 threes”. She repeats the process for the remaining 3 bunches of balloons.]

Speaker

Now, let's do this group over here.

One balloon, two balloons, three balloons. And if you look, we don't have 1 three, and now we don't have 2 threes, but instead we have 3 threes. And I can record that underneath as well. 3 threes. OK. Now, let's do this one over here. We've got one balloon, two balloons, three balloons. Now, we don't have 3 threes anymore. And cross that one off. Now we have 4 threes. And I can record that underneath as well. OK. Now let's do this group over here. One balloon, two balloons, three balloons. And as you can see, we don't just have 4 threes now. Now we have 5 threes. Let's write that underneath, 5 threes. And lastly, we have our last group to draw in.

Alright. Mathematicians, we don't have 5 threes anymore, we have 6 threes, and I can record that. 6 threes, just like that. 6 threes, we had 18 balloons in total and we found that we could put them in two equal groups if we had six equal groups of three.

[On a new sheet of paper, the playdough balloons are no longer arranged in bunches of 3, but have been pushed into the middle of the page.]

Speaker

Now, I've pushed all my balloons back into the middle, let's see if we can find a different way of having equal groups when we're using 18 balloons. Last time we had equal groups when we used three in each bunch, this time, let's try equal groups of five and see what happens.

[The speaker arranges 5 of the playdough balls into a bunch. She arranges them so that they look like the 5 face of a dice; 2 balls on top, one in the middle, then 2 more on the bottom. She arranges another bunch of 5, and then another. She has 3 balls of playdough remaining.]

Speaker

OK. Do you recognise this five from a dice? I thought it would be helpful for you. Hey, I've got one five. Now I have two fives.

They're a bit sticky, my play dough balloons. Now I have three fives and mathematicians, do you notice what we have left? I don't have enough balloons to have another five, I have these three leftovers. Three equal groups of five, but one group of three. So it doesn't quite work. Push them back to the middle. How about we try groups of four? Let's see if that will give us equal groups.

[The speaker arranges 4 playdough balls into a bunch. She then arranges another bunch of 4, then another, and then another. She has 2 balloons remaining.]

Speaker

OK. Got one four... two fours, three fours, they're like little dice balls aren't they? Four fours. But mathematicians, the same thing has happened, we have these two left over. We don't have enough to make another equal group of four. So four doesn't work for equal bunches either. How about this time we try equal groups of six? Let's see if our bunches of six we'll make equal groups. OK.

[She arranges the balloons into a bunch of 6.]

Speaker

Is my six dice pattern nice and easy for us to recognise? I have one six.

[She arranges 6 more balloons into a bunch.]

Speaker

Look, now I have two sixes.

[She arranges the remaining balloons into another bunch of 6.]

Speaker

And now, mathematicians, look, now I have three sixes. It's worked, we have equal groups again. OK, let's draw our picture of our equal groups of six balloons over here, just like we have at the top.

[On the sheet of paper on the right, the speaker draws a bunch of 6 balloons below the horizontal line. She draws a tick beside one of the bunches of playdough balls. Beneath the bunch of balloons that she has just drawn, she writes, “1 six”. She draws a purple circle around the bunch of balloons.]

Speaker

One, two, three, four, five and six. And let's tick off this one. I have 1 six. Then I can draw my circle around it to show that group, 1 six.

[The speaker draws another bunch of 6 balloons. She ticks off another bunch of playdough balls. She circles the 2 bunches of balloons that she has drawn, crosses out the text “1 six”, then writes “2 sixes”. She repeats this for the third bunch of balloons.]

Speaker

Alright, let's do this one over here. One, two, three, four, five, six. OK. Now, I don't just have 1 six anymore, so we can cross that out, now, I have 2 sixes... 2 sixes and tick that one off. And now let's draw these group here.

One, two, three, four, five and six. Tick that one off. And I don't have just 2 sixes anymore, now we have 3 sixes and we can record that underneath like that. So, mathematicians, you helped me to solve our problem in two different ways. We worked out that we could find equal groups or equal bunches for our 18 balloons when we put them into groups of three. And we also worked out that if we put our 18 balloons into equal bunches of six balloons in each bunch, then we had equal groups as well. So now it's over to you mathematicians to explore and see what other equal groupings you can find when you're using your 18 balloons.

[Text over blue background: What’s (some of) the mathematics?]

Speaker

Let's have a look at what some of the mathematics is in this activity.

[Text over a white background: What’s (some of) the mathematics? We explored ways that balloons can be shared into groups that all have the same size (equal groups). Below the text, are two images showing moments from the video. On the left, the playdough balls are arranged into 6 groups of 3. On the right, the playdough balls are arranged into 3 groups of 6.]

Speaker

We explored ways that balloons can be shared into groups that all have the same size, equal groups.

[Text: We used trial and error to share the balloons into equal groups.

· We shared the balloons into equal groups of three.

In an image below the text, the playdough balls have been arranged into 6 groups of 3.]

Speaker

We use trial and error to share the balloons into groups. We share the balloons into equal groups of three.

[Text: The group all have the same number of balloons. They are equal groups.]

Speaker

The groups all have the same number of balloons, they are equal groups.

[Text:

· Next we tried equal bunches of 4 but we discovered that we had 2 left over, so we knew we couldn’t share them equally suing fours.]

Below the text, is an image in which the playdough balls are divided into 4 groups of 4, and one group of 2.]

Speaker

Next, we tried equal bunches of four, but we discovered that we had two left over, so we knew we couldn't share them equally using fours.

[Text: The groups do not have the same number. They are not equal groups.]

Speaker

The groups do not have the same number, they are not equal groups.

[Text: We can record out thinking using pictures, numbers and words. An image below the text shows the playdough balls arranged into 3 groups of 6. The bunches of balloons, that the speaker has drawn, are on a piece of paper on the right. Above the line, there are 6 bunches of 3 balloons. Below the line, there are 3 bunches of 6 balloons.]

Speaker

We can record our thinking using pictures, numbers and words.

[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]