Checkerboard Border

From Dan Meyer’s bloghttp://blog.mrmeyer.com/?p=17257&utm_source=feedburner&utm_medium=email&utm_campaign=Feed%3A+dydan1+%28dy%2Fdan+posts+%2B+lessons%29

Connecting Patterns & Functions.2

• I'm going to show you a picture for only a few seconds

• I want to know how many blue squares you see. Just a guess.

• Don't over think it. • Go from the gut.• You will have 5 seconds.

Let’s Talk About ItLet’s Talk About It• Think-pair-share your guess.

• Write down a number of blue tiles you know is too high and a number you know is too low.

Examine the PatternExamine the Pattern

The handout has the four earliest iterations of the pattern.

Count and/or construct each one.

Write down and share a fast way to figure out the number of blue tiles in the twentieth iteration of the pattern.

Let’s CheckLet’s Check

100th Version100th Version• The huge square is the 100th version of the

pattern. How many squares are in it?

• Let’s mathematize the situation.• If you can turn this sentence into variables,

then a computer can handle any problem of this sort instantly and we'll be done with them forever.

100th Version100th Version• We will record all the mathematizations on

the board.

• Find how 2 of the mathematizations are connected.

How did you do?How did you do?

Millionth VersionMillionth Version• One version of this pattern has one million

blue tiles. • Tell me everything about that version of the

pattern.

Millionth VersionMillionth Version• Find the number of white tiles in the huge

square. • What numbers of blue tiles you'll never ever

see.