In December, I went to a conference that focused on strategies for teaching Common Core standards. One of my biggest takeaways was in regards to the activities that we need to try to integrate to make our lessons Common Core aligned. The biggest argument against these activities is that we don't have the time. What I learned in this conference is that the activities don't have to take an entire class period. You can plan the activity to take ten minutes or to take twenty. It's all up to you.
I applied this mindblowing idea to a lesson I taught in January on indirect measurement.
Part of the Do Now for the day was to sit with a partner. Another part was to practice converting height measurements into inches. We went over the Do Now questions as usual, then my next slide said to determine who was partner A and partner B, and to fill in the table given to students as part of their notes with the height of each partner in inches.
Students were asked to think of ways to answer the question "If partner A stands 64 inches from the mirror, how far from the mirror will partner B have to stand to be able to see partner A's eyes in the mirror?" Students didn't jump to using similar triangles right away. They weren't sure how to picture the arrangement, so we skipped to the first two examples, which had diagrams of similar situations. Once they had those examples under their belts, they were able to complete this problem with ease. Once they completed the problem, they came to the back of the classroom to see if they solved the problem correctly.
Here is how I had the activity set up:
I had the tape placed on the floor for partner A to know where to place his/her heels. This piece of tape is 8 tiles (the tiles in my classroom are 8 x 8") away from the mirror.
I placed the mirror on the floor and taped down two tape measures end to end. Partner A places his/her heels on the tape shown above, and partner B stands at the measurement their team found for him/her to stand away from the mirror. I told students to place their feet on each side of the measuring tape, with their heels lining up to their calculated measure.
Each team came to the back of the room one at a time, and tested the measurement they calculated to see if it was accurate. If it is accurate, then the students can see each other in the mirror. If the students couldn't see each others' eyes, they had to go back and recalculate. Some students thought it was the coolest thing, some students just asked "That's it?" (Honestly, I was surprised by the students that were excited at all.)
After students tested their calculations, they went back to their desks and worked on two more examples (from the Common Core Geometry Regents Exam). Overall, the lesson was a success, and the students and I enjoyed it much more than I thought we would.
You can get the Interactive Notebook Printout here.
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Thanks for posting this, especially with the details about speeding it up. When you teach reflections, do you reference this phenomenon of angle in=angle out (aka the Minimal Path problem)? There's a good explanation of why the angles are equal in Measurement by Paul Lockhart around page 150.
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