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Checkerboard Border From Dan Meyer’s blog http://blog.mrmeyer.com/?p=17257&utm_sour ce=feedburner&utm_medium=email&utm_cam paign=Feed%3A+dydan1+%28dy%2Fdan+posts+ %2B+lessons%29 Connecting Patterns & Functions.2

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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.

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Let’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.

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Examine 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.

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Let’s Check

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100 th Version The huge square is the 100 th 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.

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100 th Version We will record all the mathematizations on the board. Find how 2 of the mathematizations are connected.

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How did you do?

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Million th Version One version of this pattern has one million blue tiles. Tell me everything about that version of the pattern.

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Million th Version Find the number of white tiles in the huge square. What numbers of blue tiles you'll never ever see.

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