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Squares on the Coordinate Grid

21 Sep

I’ve written before about Squares on the Coordinate Grid, an Illustrative Mathematics task using coordinate geometry.

CCSS-M G-GPE.B.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

How do you provide opportunities for your students to practice I can look for and make use of structure?

SMP7 #LL2LU Gough-Wilson

How do you draw a square with an area of 2 on the coordinate grid?

It helped some students to start by thinking about what 2 square units looks like, which was easier to see in a non-special rectangle.

1 2015-03-16 09.28.06.jpg

What’s true about the side length of a square with an area of 2?

2 2015-03-16 09.48.23.jpg

How could we arrange 2 square units into a square?

3 2015-03-16 09.41.51.jpg

How do you know the figure is a square? Is it enough for all four sides to be square root of 2?

4 Screen Shot 2015-03-20 at 2.14.53 PM.png

CC made his thinking visible by reflecting on his learning after class:

5 Screen Shot 2016-09-20 at 1.18.28 PM.png

6 Screen Shot 2016-09-20 at 1.39.10 PM.png

“Now drawing the square root of two exactly on paper is nearly impossible unless you know how to use right triangles.”

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Posted by on September 21, 2016 in Coordinate Geometry, Geometry

 

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