This year in geometry I started teaching constructions by having students fill out a foldable using instructional videos as a reference.

By doing this, I made several mistakes. Students saw constructions as an annoying set of steps to memorize and repeat. Most students (as well as the Khan Academy) completely missed the point of using geometric relationships and logical reasoning as a tool to create complex, accurate drawings.

Next year I plan to re- sequence the lessons to support understanding first:

- I will allow a few DAYS for students time to play with the compass first. To notice, to wonder.
- I will create an environment for them to talk to each other using the vocabulary we just learned to communicate and try to create this
- I will make sure patty paper is available at all times.
- I will assign this project during the first few days of school to motivate students to get proficient using a compass:
- I need straight edges without measurements on them so that students have a reason to use a compass instead of a ruler.
- I will not immediately provide steps to make constructions. I will challenge students to complete a few basic constructions by hand to teach the intent of constructions
- We will play Euclid, the Game!
- I plan to still use a foldable for constructions next year, but I’ll have students complete each set of instructions as they conclude how to draw it themselves.
- I will buy 10 dry erase compasses to encourage student collaborations using my big white boards.
- We will incorporate constructions as we move toward transformations. for example: when students figure out how to construct a perpendicular bisector, they should also use it to construct a reflection:

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I love this and am so glad I read it. I provided a “construction instruction” foldable at the end, and was planning on providing it at the beginning next year. So happy to have read your post, because now I will not. Fawn also mentioned letting the students discover the constructions by themselves as well! As they discovered, I had them write the steps down in the notebooks. I did include the steps (from mathopenref) in the foldable just in case their steps weren’t very clear or someone was absent. I felt that it was ok to provide the steps at the end. I also had them write down the page in their notebook where THEY had hand written their own steps as well. Still not sure what I will do with the steps as they are rather detailed. But I do think it is good to have as a reference in their notebooks. Hmmm. Still thinking on that one as well.

I also love your emphasis on vocab as I decided to do that more with constructions next year as well. I would also love to include Geogebra more, but not sure where that fits in.

I agree that I want to invest more time in geogebra too. It seems like I could easily end up spending much more time on constructions than I did this year. I want to be able to find a balance because there are so many other aspect to geometry that I want to make sure students have time to work on as well.

Agreed. I also felt that the by hand constructions were very limiting, especially when we got to triangle centers. They constructed the center to ONE triangle, thus just one TYPE of triangle. With Geogebra, this would be dynamic so they could see when the center can be outside of the triangle, and other cool things. So maybe I’ll do by hand for the first part of the unit, then introduce Geogebra for the triangle centers next year. Love talking about this with you! It’s really helping me. THANK YOU.

Thanks for a great post. I teach 7th grade math and constructions were one of the hardest concepts for my students to grasp last year (doesn’t help that many couldn’t use their cheap compasses very well). You have given my lots of food for thought. Thank God I don’t get to that for several months. It was painful last year!

Lisa – thanks for sharing this. My plan was to do some basic constructions by hand first, and then use the iPads and Euclid the Game as a ‘reward’. I usually introduce constructions by talking about how the ancient Greeks played a game of constructions, (but that may of dubious value, depending on whether the kids care about what the ancient Greeks did or not) and why constructions actually ‘work’. I am glad you mentioned patty paper, because my original intention was to incorporate that, and I had actually forgotten!

I have been using unmarked straight edges since I started teaching these; it’s fun to get the kids to see them as a beautiful tool despite their lack of markings. They still try to measure things other ways, but this makes it more challenging.

As far as the triangle centers go, with a large class, I have in the past assigned each group a different type of triangle and had them share the results – usually in the interest of time.

The project looks fabulous – please share results!

These are awesome ideas. I am lucky to have a school year start a couple of weeks after you and can use your ideas. I started with a day on the DG resources for a straight edge and compass for two days and it made a difference. However, I am finding it difficult to get out of the mode of direct teaching the different constructions. One of my challenges with the topic has to do with the fact that I feel like I am giving them some of the building blocks for geometry and asking them to trust me that it works. For me for constructions, I would prefer to give a deductive foundation and not an inductive one, but most of the constructions require an inductive approach with the knowledge they have. This conflict for me causes the angst I have on the topic. Building Geometry intuition is not an easy endeavor. Thank you for giving some great ideas on how to do it.

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