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.”
Easing the Hurry Syndrome 