Start with a wrong answer.
Math class teachers care a lot about getting right answers. This is understandable. Right answers are nice, and in many cases, preferable to wrong ones. But learning a new concept doesn’t have the same stakes as building a rocket or performing a life-or-death medical procedure. When learning something new, it can be very helpful to explore wrong answers first. Before students can find a right answer, they can often contribute a wrong one and defend how they know it’s wrong.
What does it look like in Match My Dilation?
If students struggle with the challenges in Match My Dilation, you can always pre-teach a right answer for a related problem. But first, consider asking them how they know a wrong answer is wrong.
For example, on Challenge No. 3, telling students, "Hey—this is a wrong answer, but how do we know it’s wrong," may focus students on the property that all the angle measures in a scaled copy need to match the original.
The same question, –How do you know this is wrong?– may help students notice that the proportionality of the side lengths matters as well.
When students give a wrong answer and explain how they know it’s wrong, there are two likely outcomes. One, they’ll start to understand that wrong answers are valuable, not shameful. Two, they’ll experience realizations that may eventually help them find the right answer. Both of those outcomes are likely to invite more student thinking later!
Happy math-ing!
Dan & the Desmos Classroom Team
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Great advice from other teachers.
Springfield, MO
Take it slow. After teaching this for three periods, I skipped to slide 6 and then went back to slide 3, 4, and 5. I urged students to use the sketch tool to show their thinking that included numbers. A few students helped the rest of the class see the distances from the center. I paused and highlighted how to use the center of dilation.
Oakland, CA
Make sure to model the different ways to find the scale factor. Counting the sides and dividing. Counting up and over from the center of dilation. Using patty paper. Using rulers.
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