Programming the Math Sheet

What it teaches

That images are data, and that precise instructions produce precise output. The screen of any device is a grid of tiny squares (pixels). Here you are the programmer: you write a list of symbols, and anyone who follows it to the letter gets exactly the same picture. Change one command and the picture changes; forget one colour command and a pixel stays blank.

What you'll need

• Squared paper, or draw a 5x5 grid on paper or a whiteboard.
• A pencil and one colour to fill in squares.
• A symbol legend: star = start square, arrows = move (up, down, left, right), filled square = colour this cell.

How to run it

1. 1

   Agree on the legend together: a star marks where the pen starts, each arrow slides the pen one square in that direction, and a filled-square command means colour the square the pen is on now.

2. 2

   One student is the programmer and writes a short list of commands. A second student is the computer and follows them exactly, one command at a time, never guessing what the picture should be.

3. 3

   The computer moves an imaginary pen across the grid. On every colour command they fill the current square; on every arrow they slide one square and colour nothing.

4. 4

   Compare the finished grid with the picture the programmer had in mind. Any wrong or missing square is a bug: find the command that caused it and fix the list.

5. 5

   Swap roles. Try a bigger picture, or hand your command list to someone who has not seen the drawing and check whether they can reproduce it exactly.

Talk about it

Ask the class: if a photo is millions of tiny coloured squares, what is the computer really storing? Just numbers. Every image, on every screen, is data that an instruction wrote down.