I designed this 3-Act Task to serve as an introduction to linear inequalities in two variables and systems of linear inequalities in two variables. A link to all lesson files may be found at the end of this page.
What do you notice?
What do you wonder?
What do you notice?
What do you wonder?
Define three lines to form a triangle, with the smallest area possible, that contains the four points. Justify how you know each coordinate lies within the triangle.
Extension:
How might you define 4 points such that you would need 4 inequalities to define the smallest possible region that contains them all? Would your method work to reliably require 5 inequalities for 5 points? n inequalities for n points?