Dana’s Rectangle

Inspired by the work of the Navajo Math Circle, CAMI explores the area of rectangles and their borders, testing conjectures and making generalizations.

Eric started the meeting by talking about the Navajo Math Circles, which is a joint project of the Navajo Nation and mathematicians from Math Teachers Circle Network. A recent documentary tells the story. This meeting’s problem is from an article about the Navajo Math Circle (see Further Reading pdf link above) by Tatiana Shubin, whose video Grid Power was the subject of this past July’s CAMI meeting.

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Making and Testing Conjectures: The Diagonal Problem

Draw a rectangle on grid paper and draw a diagonal. Is there a way to predict the number of squares the diagonal will pass through?

I have been thinking about MP3 from the Common Core, specifically about how to get students to make conjectures, to test those conjectures and to refine their conjectures when it turned out they were not always true. I was also thinking about student perseverance and helping them not get too frustrated. I’ve done some activities like Marilyn Burns’ consecutive sums problem (see additional resources below), but I want something that feels messier and a little more unwieldy. Continue reading “Making and Testing Conjectures: The Diagonal Problem”