Dice collection – Early Stage 1
A thinking mathematically targeted teaching opportunity focussed on subitising dice patterns and quantifying collections
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, 2021
You will need:
- paper to write on
- pen or marker
- someone to talk to.
Watch Dice collection Early Stage 1 part 1 video (1:53).
[Text over a blue background: Dice collection (Early Stage 1). In the lower right-hand corner of the screen is the waratah of the NSW Government logo. Small font text in the lower left-hand corner of the screen reads: NSW Mathematics Strategy Professional Learning team (NSWMS PL team).]
Hello mathematicians? Today we are going to be looking at and talking about a dice collection.
[text over a white background: You will need…
- something to write on
- something to write with
- Someone to talk to.
Three images on screen depict: a person holding a blank sheet of paper; pens and pencils in a pencil holder; an illustration of two people facing each other.]
For this task, you will need something to write on, something to write with, and someone to talk to that you can share your mathematical thinking with.
[A colourful background with white, zig-zagging lines.]
I have something that I would like to show you under this colourful piece of paper and I want you to think about what you see and what you notice. I would like you to use what you have chosen to write on to record your thinking. You can use pictures, numbers or words to record what you notice. Are you ready? Great! Here it is.
[16 blue and green dice are arranged in a 4 by 4 square. There are 8 green dice and 8 blue dice. All of the green dice have their 2 side facing upward and all of the blue dice have their 4 side facing upward. There are 4 blue dice in the middle of the square. The dice at each of the corners are also blue. The remaining dice are all green. All of the green dice are in pairs, along the outer side of the square. They are all arranged so that, within each pair, the dice form a mirror image of each other, based on the placement of the two dots.]
Write or draw one thing that you notice about this collection of dice. Have you written down one thing? Great! Now keep looking and write something else that you notice. I'm hearing some counting going on. Wonderful. Write that down too. When you have lots of ideas, talk to someone, if you can, about what you noticed about this dice collection.
[Text on a blue background: Over to you mathematicians…]
Over to you, 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]
- What do you notice about this dice collection?
- Write down all of your ideas.
- If you can, talk to someone, to share what you noticed about this dice collection.
Watch Dice collection Early Stage 1 part 2 video (3:15).
[On a white surface, 16 blue and green dice are arranged in a 4 by 4 grid. All of the green dice have their 2-face showing, and all of the bleu dice have their 4-face showing. The first row is arranged in the colour pattern, blue, green, green, blue, and the number pattern, 4, 2, 2, 4. The second row is arranged in the colour pattern, green, blue, blue, green, and the number pattern, 2, 4, 4, 2. The third row is arranged the same as the second row. The fourth row is arranged the same as the first row.]
Let's talk about some of the things you might have noticed about this dice collection. I'm going to record our thinking on my whiteboard here. Did you count how many dice you can see altogether?
Let's check by counting.
[The speaker points to each of the dice as she counts aloud.]
One, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16. That's right. There are sixteen dice in our collection.
[Beside the dice, the speaker writes “16 dice”.]
Now, I can see that our dice collection is made up of rows.
[The speaker points to the 4 dice along the top of the grid. She then points to each of the three rows below.]
This is a row, this is another row, another row, and another row. It is made up of four rows.
[On the whiteboard, the speaker writes “4 rows”.]
And in each row there are how many dice? That's right. There are four dice, can you see that? There are four dice in this row, four dice in the second row, four dice in the third row, and four dice in the fourth row.
[The speaker writes “4 dice in each row”.]
So I'm going to write four dice in each row.
What else did you notice? Yes, there are dots on our dice. Maybe let's look closely at that now. So I can see some dice that look like this in our collection.
[Beneath the grid, the speaker draws a square. She then draws a dot inside each of the four corners of the square.]
That have a dot in this corner, a dot in that corner, a dot in that corner, and a dot in that corner. By looking and thinking, how many dots can you see here on this dice? Yes, that was quick. Great, subitising!
[Beside the drawing, the speaker writes “4 dots”.]
Dice that look like this have four dots.
How many dice with four dots can you see in our collection?
That's right, there are eight of them.
[The speaker points to all of the dice with their 4-face showing as she counts aloud.]
One, two, three, four, five, six, seven, eight.
[Beside the text “4 dots”, the speaker draws an arrow, and writes “8 dice”.
Below the drawing of the dice, the speaker draws another box. She draws one dot in the upper left-hand corner, and one dot in the lower right-hand corner.]
And what about dice that look like this? That have a dot here, and a dot here, how many dots can you see on dice like this?
[Beside the drawing, the speaker writes “2 dots”, then draws an arrow.]
That's right, these dice have two dots. Now, have a look at our collection. And how many of those can you see there?
[The speaker points to each of the dice that have their 2-face showing.]
That's right, there are eight of them as well. Two here, two here, two here, and two here. And eight dice altogether.
[Beside the second arrow, the speaker writes “8 dice”.
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]
Think about the ideas that were shared about the first dice collection. Use those ideas as a starting point to help you to look at this dice collection.
What do you notice?
What else do you notice?
What is the same about the two dice collections?
What is different about the two dice collections?