This will be a quick post because I have a student-posed math problem that I need some time to reason through!
Today, students found the area and perimeter of squares that increase in side length by one each time. Students used a variety of models when building their squares from Minecraft carpets, to Geoboards to graph paper. Here is the completed activity sheet from their work: I then gave them a few minutes to talk to their tablemates about things they notice in their work. Here are the answers they shared as a class and I recorded on the board:
“An even dimension by even dimension = an even area”
“An odd dimension by odd dimension = an odd area”
“The perimeter goes up by 4 every time the square gets bigger”
“The areas are square numbers.”
“The areas go up by odd skip counting: +3, +5, +7…”
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