Dear {{custom.firstName}},

 

In the last unit, I offered some ideas for inviting lots of thinking from lots of different kinds of students. Perhaps now you have students sharing lots of their ideas with you. Great work!

 

Now what can you do with those ideas? How can you celebrate what students are offering and help them grow their sense of themselves as mathematicians while also helping them develop that knowledge?

Tell me about a different world.

When you ask a question and a student answers incorrectly, it's often helpful to realize that they're answering a different question correctly.

 

For example, in a large sample of students last year, only 12% correctly answered “Not enough information” on the following warm-up.

57% of them chose Tank A. We love celebrating students for the thinking they offer us here and also helping them develop it further. Consider telling students, “Tank A makes a lot of sense to me, too. Lots of times, the steeper slope means something is happening faster.”

 

Then consider drawing little boxes at the top of each y-axis and saying to your students, “But tell me about a different world where the shallower slope represents a tank that fills up faster than the steeper slope.”

If students aren’t sure, consider asking them for any two numbers, large or small. Write them in the blanks yourself. And just like that, they’ve created a different world, and you can ask them to tell you about it.

 

Happy math-ing!

 

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?

{{custom.npsHTML}}

Great advice from other teachers.

Chicago, IL

 

I spent time on the first few slides. I also went over how to compare the scales using equivalent fraction/slope. We did a lot of whole class.

 

Toronto, Ontario

 

I spent a comfortable two days on this making sure student thinking was shared and developed as needed. I think this activity is very important and the connection between the representations of equations and graphs is just beginning to take shape.

 

Chicago, IL

 

This lesson takes longer than you might expect.

 

Vancouver, WA

 

Warm-up was good, most students chose the steeper line.