Explorations and Games

Learning Goals:

  • Locate objects using a grid system
  • Make predictions related to patterns
  • Develop and apply reasoning skills to make and test math predictions

The Exploration:

Andrea wants to send secret messages to her friends. She creates a grid and fills it with the letters of the alphabet in order. She uses letters to identify the columns of the grid and numbers to identify the rows of the grid. Then she sends a message by using the positions of the letters and spaces in the grid.

To make it harder for people to decode her messages, she uses different sized grids for different messages, and sometimes she leaves some blank spaces at the beginning of the grid. For example, this is a grid that has a key of 8-3, because it has 8 columns and 3 blank spaces at the beginning:

An 8 by 4 grid with letters A-H across the top and numbers 1-4 down the left side. Grid boxes are filled by the alphabet from left to right, with the first three grid boxes left blank.

Using the grid above, the code H2 D1 G3 C2 can be decoded to spell the word “math” by using the grid coordinates to find each letter. This grid can even be used to spell out full sentences and phrases by using coordinates like B1 or G4 to represent spaces between words!

Try using this 8-3 grid to decode these two messages:

D4 B3 H3 F4 F1 E3 D1 F1 F2 H1 G1 A1 G3 C2 H1 B1 F1 B3 G1 H1
G3 E3 D4 B1 D1 H4 G1 D2 A2 A2 H1 E3 H1 A3 G3 A1 F2 H1 D4

Without seeing the particular grid Andrea uses, she can still send her friends secret messages that they can decode if they know how many columns are in the grid and how many blank spaces are at the beginning of the grid. We call this kind of information the key. So for the grid above, the key is 8-3, to represent 8 columns and 3 blank spaces before the alphabet starts. What the key doesn’t tell us is how many rows the grid will have, once we’ve filled it with the alphabet.
If the key is 6-2, the grid would have six columns and two blank spaces at the beginning.

Try encoding the message “this is secret” using the key 6-2 grid!

Questions and Prompts to Support your Child:

  • Tell me about how you are decoding messages – Left to right? Looking for patterns? Checking for any blank spaces first?
  • How is the thinking involved with encoding messages (listing out letter coordinates) similar to the thinking involved with decoding them? How is it different?

Extensions & Adaptations:

  • Can you decode the message E4 A2 D1 D4 A2 A5 D6 D3 A2 E4 E4 B1 C2 A2 E4 A1 D4 A4 D1 B3 using the key 5-1 grid?
  • Experiment with other grids to create and decode other secret messages – remember to include the two-digit key for your grid, so that others can do the decoding!

Adapted from: University of Waterloo – CEMC Problem of the Week Database