Binary Flippy Do - How To

Today in AP Computer Science Principles we made the Analog Binary Calculator. We have been working up towards binary. I do not start them with the big explanation of This Is Binary.

Instead I do a series of puzzles as warm ups and exit tickets for the week or so before the actual lesson. That way by the time we get to full scale binary they have had some positive experiences and built their own understanding of how binary works.

(Why do I even do Binary? Here you go)

So for example I show them a picture of two light switches and point out they can either be on or off. Working with a partner they have to figure out how many numbers they can store using the light switches. What if we add a third switch, how many then? Without listing all the combinations can you predict how many numbers you could represent with 4 switches? This makes a great warm up activity.

The great thing about the flippy do is it is super easy to translate numbers back and forth. My stronger math kids pick up the number theory behind it quickly, while my weaker math students are successful so they will stick with it rather than tuning out.

If you also cover the full two's comp representation it is also an incredibly easy way to teach the steps.

Materials:

• Index cards - 4x6 or larger
• Markers
• Scissors 
• Rulers - helpful, but not necessary

Steps:

First you fold up the bottom 1/4, draw 8 columns, and cut the bottom flippy things like this:

Can you tell this is my white board?

Second, you label the powers of two. Then put 1's on the back of the flaps and zeros underneath as shown:

Then I have them do a few puzzles:

• How may ways can you represent 13? 3? 15?
• Count from 0 to 13. Any pattern with even/odd numbers?
• What is the largest number this can store?
• What is 01111111? 00111111? 00011111? - what is the pattern here?

The point here is, if I just tell them that there is only one way to make any base ten number in binary it goes in one ear and out the other. Snore.

If instead they are doing a puzzle, and after a few realize THEMSELVES that there is only one combo per number, they internalize that at a different level. They don't forget it.

After all this we do the algorithm to change from binary to base ten and back. The best part is when the kid in the back, the one that hates math, tells their neighbor "Hey, I actually get this".