## 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? 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. What’s true about the side length of a square with an area of 2? How could we arrange 2 square units into a square? How do you know the figure is a square? Is it enough for all four sides to be square root of 2? CC made his thinking visible by reflecting on his learning after class:  “Now drawing the square root of two exactly on paper is nearly impossible unless you know how to use right triangles.”