I Can Guess Your Secret Number with Magic Boxes

This is the magic box activity.

Here's how it works...

Ask a student to pick a secret number from 1-31. Alternately, they can pick the day they were born...I was born on the 11th, for example.

Next, ask the student if their number appears in each of the boxes (Orange, Yellow, Blue, Green, Pink) My number, 11, appears in Orange, Yellow and Green.

Add up the first number in each box that was identified as containing the number...1 + 2 + 8 = 11

Reveal the secret number to the student to gasps of shock and awe!

So, How Does It Work?

The boxes are built on the idea of Base 2 or Binary counting. Think about each number in the box being created by combining only the numbers 1, 2, 4, 8 & 16.  For example - 7 is constructed with 4 and 2 and 1 or 4+2+1 = 7

This is also binary code - or how a computer stores numbers using a series of 1's and 0's.  Think about it like a series of switches that are either on or off.  

• For 7, the switches would read ON, ON, ON, OFF, OFF or 11100 (111 actually). 
• 14 would read OFF, ON, ON, ON or 0111. 
• Here is a table showing the numbers from 1 -16. To create a number greater than 31 would require another column with the heading 32.

Want to learn more - explore the website Exploding Dots. I am just learning about the possibilities. I was fortunate to attend an mini-workshop put on by our Board's Math Team. I'm most keen to see how students will react when we explore this strategy for solving math problems. 

I sure wish I would have known about it in Grade 9. See how easy it is to combine like terms using dots and chart paper.) 

(3x2 + 2x + 1) + (4x2 + 3x + 2)