Coded hundred square
Stage 2 – A thinking mathematically targeted teaching opportunity focussed on investigating relationships between quantities and patterns on a hundred chart to solve problems
A task from NRICH Maths
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
You will need Coded hundred square game board (PDF 102 KB).
Watch Coded hundred square video (4:17).
[Text over a navy-blue background: Coded hundred square. From NRICH. 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.]
Welcome back mathematicians. Today we are going to have a look at a task from NRICH called coded hundred square.
[Text over a white background: You will need…
· Coded hundred square gameboard.
On the right of screen are images of two coded hundred square gameboards. One shows an empty 10 by 10 grid, with some coded squares below. The other, shows an array of coded square puzzle pieces. These are groups of squares, arranged into a variety of shapes. Each square contains a different pictorial code.]
You will need a coded hundred square gameboard. And you might like to take some time now just to cut out all of your puzzle pieces and also your gameboard. So, we're ready to go.
[Text on a blue background: Let’s play! Text is added to the previous slide:
· It starts with one and ends with one hundred.]
Let's play. Our task is to try and crack the coded hundred square. As you can see, this hundred square is written in code. And we also know that it starts with one and ends with 100.
To begin, what do you notice about the puzzle pieces that we have? You might like to pause here and record your thinking.
Noticing and wondering is one way mathematicians can start to think about and make sense of a problem. And I'm curious to hear what you may have noticed when looking into the puzzle pieces.
[Additional text on-screen: Some of the symbols are repeated. Three of the symbols are highlighted by a blue circle. Further text: Some boxes have just one symbol. Some boxes have two symbols. 1 box has three symbols. Some boxes with one symbol are highlighted. Some boxes with 2 symbols are highlighted. The box with 3 symbols is highlighted.]
A-ha, yeah, I noticed that too. Some of the symbols are repeated and also some of the boxes have just one symbol, some boxes have two symbols but only one box has three symbols.
[The additional text and circles, highlighting the various symbols, all disappear. Further text appears: We are starting to notice some really useful things.]
We're starting to notice some really useful things. And that's got me wondering if we can use what we already noticed so far to help us make sense of this code a little bit more.
[Further text: There are nine symbols that have only one ‘digit’ so we think these might be like the numbers 1-9. Yellow circles appear, highlighting all of the boxes with only one symbol.]
And what I'm thinking is, if we think about the symbols as digits, there are nine boxes that have only one symbol, and perhaps they might be like or... perhaps they represent the numbers one to nine in this code. What do you think?
[The additional text and yellow circles all disappear from screen.]
I wonder what else the digits in the code might be trying to tell us.
[Text: We can think of ‘10’ as a big rhombus and a small rhombus because:
· The big rhombus can be found going down as an entire column, like 1 in a hundreds charts does.
· If the big rhombus represents 1, then it makes sense that the small rhombus represents 1 ten.
Red circles appear over two of the squares; one with a single big rhombus, and one with a big rhombus and a small rhombus.]
And now that I look a little bit further into it, I can also see that perhaps we can think of ten as a big rhombus and a small rhombus, because the big rhombus can be found going down an entire column like one does in 100 chart. And also, if the big rhombus represents one, then it makes sense that the small rhombus represents 110.
[Slide change. Heading: Coded hundred square. From NRICH. On the right of screen, are the coded hundred square puzzle pieces. One, by one, three puzzle pieces appear on the left side of screen. The puzzle piece, identified as containing the number one, appears first. The puzzle piece, identified as containing the number 10, appears second. The puzzle piece, identified as having a sequence of singular codes, appears and connects with the first puzzle piece. A red cross appears over the pieces in the bank on the left of screen as they appear on the right.]
I think we might be ready to start building our coded hundred square and if we take what we've noticed so far and begin to arrange the puzzle pieces like this, do you think we might be able to crack the code? Are we on the right track? Do you think this will work?
[Text over a blue background: What’s (some of) the mathematics?]
What's some of the mathematics?
[Text over a white background: What’s (some of) the mathematics?
· We can notice relationships between quantities and patterns we see in a hundreds chart to help us solve problems.
Below, are 2 images of previous slides from the video. The first slide contains the coded hundred square puzzle pieces, where the codes representing the numbers one and 10 are circled. The second contains the bank of coded hundred puzzle pieces, where some of the pieces have been marked with a red cross, and also appear on the left side of the screen.]
We can notice relationships between quantities and patterns we see on a hundreds chart to help us solve problems.
[Text: Over to you… From NRICH.
· Can you build it up? How did you do it?
· Can you build it up in a different way?
· How man ways are there to build the coded hundred square.
An image on the right of screen contains the blank 10 by 10 grided square, as well as the coded hundred square puzzle pieces.]
Over to you mathematicians. Can you crack the code and build the coded hundred square? And if so, how did you do it? I'm also wondering if there is more than one way to build up the coded hundred square and are we able to find out how many possibilities there are of cracking this code? Over 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]
- This hundred square is written in code.
- It starts with one and ends with a hundred.
- Can you crack the code and build it up?
- How did you do it?
- Can you find another way to build it up?
- How many different ways are there to crack the code?
- Create your own coded hundred square puzzle.
- Share it with friends to see if they can break your code!