This warm-up is likely to invite lots of student responses. We omitted numbers here so calculation wouldn’t be a barrier. The question also encourages intuition and “eyeballing,” which is one of the cornerstones of geometric reasoning.
What do you do now that you have invited all of those responses? How do you celebrate those responses while also developing them toward the mathematical goals of this unit?
All of us are smarter than any one of us.
To accomplish the learning goals of this lesson, students will need to decompose complex shapes into more familiar ones. Consider asking your students to use the sketch tool to demonstrate how they saw which one had the greater area.
You can use the snapshot tool and share different sketches with the class, inviting other students to interpret the reasoning behind the sketch: “How do you think your classmate was thinking about the area here?”
Consider also asking your students questions like, “How are these sketches the same? How are they different?” Here is one example we’ve seen from students.
By celebrating the thinking in those sketches, you’re celebrating your students and the brilliance they bring to your class. By inviting your students to compare, contrast, and interpret those sketches, you’re helping students develop their thinking into ideas that are greater than the sum of their parts.
Have fun with this one!
Dan & the Desmos Classroom Team
PS. Please give us feedback on the last lesson.
Use the feedback form or just click your answer below then click "Submit" on the form!
How likely is it that you would recommend this lesson to a friend or colleague?
.png?width=1200&height=120&upscale=true&name=DM_Logo_6-A1%20(1).png "DM_Logo_6-A1 (1)"){kind=logo}
