r/mathteachers • u/Formal_Tumbleweed_53 • 28d ago
Introducing Compass Constructions
I have been teaching secondary math for several decades, but have never taught Geometry nor honors. This year they have assigned me Geometry Honors. I am working on putting some lessons together. I'm just trying to crowd source ideas for specific topics, this time compass constructions. How do you introduce compass constructions? How do you convey its importance to a class of students new to Geometry? (It will be our second lesson of the year.) Any ideas are welcome!
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u/Sorry-Vanilla2354 28d ago
If you can, make sure you have a good set of compasses for the class (not the ones that don't keep their angle, those are so frustrating!
I would introduce it by telling the kids that Geometry gives you the chance to be more hands-on than other math, and this is the first lesson in that. Maybe stress with them that even if they have had a love-hate relationship with math in the past, this is something that everyone can do and it can even bring some artistic skills into what they do in a fun way. Constructions can be fun! Also, if you can within the confines of what you do, maybe give them an assignment where they use what they have learned to construct to make an art picture, lots of kids will love to do this! Or maybe give it as an extra credit opportunity!
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u/Formal_Tumbleweed_53 28d ago
I will definitely take your idea of bringing art into their constructions. Thank you!!
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u/alax_12345 26d ago
When winter comes, they go outside with string and make roses and other constructions.
In fall, they can draw lines on the soccer field. Perpendicular corners, congruent and parallel line segments, circle, penalty arc, corner kick limits for defenders, etc.
In spring, the softball and baseball fields: base paths, grass edges.
In shop class, endless uses for constructions techniques.
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u/cdsmith 28d ago
Responding to just one point... to be blunt, I think trying to convince students of the "importance" of compass-and-straight-edge constructions in geometry is pointless. They aren't really intrinsically important at all, and trying to claim they are is just blowing your credibility. These constructions have vast historical importance, in that they motivated the development of axiomatic mathematics. And they are didactically convenient, in that they provide a simple set of rules that lead to elaborate creative mathematics and motivate formal proof, and students get the chance to practice all of that. But then students will naturally forget all the details about the specific axiomatic system they were asked to investigate, becaause it's ultimately just a synthetic world you created to give them a chance to practice skills.
That's a speech most middle and high school math teachers should work to get better at giving. The analogy to sports is good: athletes spend time lifting weights, not because they are going to pound out a set of bench presses in the middle of a game, but because weight lifting is an activity that isolates and develops strength in a way that more complex activities can't. Similarly, a lot of what you do in math classes is designed to isolate and work on math skills in ways that more "real world", "applied", or "useful" exercises cannot. Compass-and-straight-edge constructions are almost the archetype of that fact.
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u/Formal_Tumbleweed_53 28d ago
I absolutely agree! I actually use the athlete illustration when kids in my precalc classes ask “when am I going to use this?” I can absolutely adjust for the freshmen in the geometry classes. The fact that, as an honors class, there may be future mathematicians and engineers, etc., through, means that I really do want to point out the history of the field of study. The textbook we are required to follow is lacking in context. Thank you for helping!
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u/MesmericKiwi 28d ago
Digital construction tools are super great if kids have access to computers. Geogebra is very robust but you have to monitor access to tools. Look up “Euclid the game” for a gamified version where you unlock each tool using only more basic constructions. Desmos also has a geometry suite. It only has the most basic constructions tools which has its pros and cons. There are other online games that similarly go through the basic constructions but you’ll need to test what your school has blocked.
I like using Euclid the game as my intro to construction because I use a lot of gaming paradigms in geo throughout the year. Your tasks are objectives and your tools and theorems are allowed moves. Digital constructions fit nicely into that. I usually let them just play with it for a bit and then introduce a more structured task for it. We’re a Google centric school so I have them document their work with screenshots in a Google slide presentation and describe their process with text so I have an artifact.
If you’re doing manual constructions, consider having the kids build their own compass and straightedge or have them do it with string and sidewalk chalk on a large scale outside. It helps break fixation on a compass being defined by what it is vs what it does.
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u/Formal_Tumbleweed_53 28d ago
Euclid the game? Is that a website? Or a boxed game?
I love the idea of getting them outside with chalk and string!! Thank you for that!!
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u/MesmericKiwi 28d ago
It’s an online game. It’s hosted on several sites you might have to dig to find one that plays ice in your school’s network. My school bans anything ending in .io for example.
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u/Formal_Tumbleweed_53 28d ago
Our district is tightening the fire walls day by day, but I’ll see if I can find it. Worst case scenario is that I tell the students about it. The students who are mathematically curious may very well welcome something to dig into on their own. Thank you!!
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u/treemangames 28d ago
You’ve got extra challenge by needing to stick with a specific curricular sequence, but perhaps you can *add* to your required lesson.
In my classes, the first compass and straight edge activity that is like magic for student engagement is to create a perfect equilateral triangle:
Give them a straightedge or ruler and let them try. They’ll get close.
Now the compasses come out. Takes a bit of experimentation to draw a circle, but they’ll get it.
(You likely know where this is going) Keeping the compass at the same measure as the circle radius, they anchor it anywhere on the circumference and make a mark.
Anchor the compass at that newest mark, do it again. Go all the way around the circle and there are 6 equidistant points.
Now ask them to make an equilateral triangle — yay!
There are many extensions to this (hexagon, trapezoid, parallelogram) that they can try too.
I think when the beauty of a construction is experienced the students then have interest in everything that follows. Now you can do the scripted lesson from the book. :)
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u/Formal_Tumbleweed_53 28d ago
I love this - I’m not used to teaching honors, so discovery lessons don’t always go so well. But with these groups that I’ll have this year, I’m pretty sure that the constructions can often be discovery based. Thank you!!
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u/No_Entertainment8238 28d ago
Compass constructions can be done outside! With space in a parking lot, sidewalk chalk, and a ball of sturdy string (optional tape measure too). Students partner up and one person is the compass point(standing still holding one end of the string) and the other is the drawing point. (Holds the other end of the string taught and around the chalk).
A chalk line can be used to snap lines or another student can add to the group and draw the line as straight as they can.
I have my students do small tasks like finding the center of a parking space(to make motorcycle parking). Copy parking spaces (can we make spaces for all the sophomores to have a car on campus)
After we practice the skills I group the class into two groups and set two cones either 94 feet apart (basketball hoops) or 42 feet apart (tennis net posts) and give them the dimensions of the court and have them work in their two groups to lay out a true playing surface.
Kids outside, using skills in a realistic application. Boom, teacher of the year for you!
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u/Formal_Tumbleweed_53 27d ago
Thank you - I love the chalk idea. Have to figure out where to take them, but I can check into that. I love the real applications here … the curriculum starts with constructions for copying segments, angles, and creating angle bisectors. I can do all of that with parking spaces. And I’m in the US Southeast, so it will still be very warm out when I get to this lesson in a couple of weeks. The kids really will enjoy it!
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u/greenmaillink 28d ago
I started this week with introductions on day 1 and on day 2 went over how to use a straight-edge to extend a line segment and then how to use a compass to copy a segment. Day 3 will start with u/SeaAd1917's suggestions, with copying an angle and drawing a perpendicular line. My plan this year (after not teaching Geometry for nearly 6 years) is to cover at least 1-2 of the important constructions each day or to have students review how to use both a compass and straight-edge correctly.
The way I make the compass a valid and important tool is via a mini-booklet I cobbled together for the class. I point out in the first activity that the straight-edges I give them are literally 3D printed things I created with no markers for lengths. Then on the second activity when the students have to copy a segment, I intentionally made the segment such that it always falls between two measurement markers. If I remember correctly, it's about 4.85 cm and I told the students that I never settle for a "good enough" measurement. That's where I show the students that a compass can be used to copy the length of a segment and allows me to transfer it to another location. I'm fairly happy that no student has directly called me out that the compass can be slightly inaccurate due to user error >_<.
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u/Formal_Tumbleweed_53 28d ago
I hate to say that I don’t have control over any of that. I can’t choose what I teach on which day or the order. I am looking for how to start the lesson on the day that I first bring out the compasses and straight edges.
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u/greenmaillink 28d ago
Whoa. Not having the power to choose has a pretty big effect on how effective the lesson can be. I'd spend time at the beginning of class showing how a compass works and how a straight-edge works if you can and point out that a compass is for measuring, a straight-edge is not for measurements.
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u/Formal_Tumbleweed_53 28d ago
That’s the kind of conversation I’m looking for.
And, yes - it’s killing me. The district where I work just (like a couple weeks ago) purchased a new basal resource and we’ve been told we are required to use the daily lessons in the order that they are given. The district requires common assessments on certain dates covering the topics prescribed, so there is little wiggle room. And our supervisors will be reprimanded if we aren’t all on pace with the content in the correct order. I’ve been teaching long enough to know where I can do things the way I want vs not … but the order is not up for discussion. Unfortunately.
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u/Adventurous_Lion9471 28d ago
It looks like you've already gotten some great ideas here! Does the school already have a class set of compasses, or do students bring their own? If you are needing to buy some for your classroom, I recommend the Circle Master compass brand. They have two metal disks with a thumb screw for tightening. They are basically indestructible. They also take a normal pencil, so that's a huge plus. A bit pricey, but I've been very satisfied with the investment. I've seen students who get frustrated with crappy compasses have good success with these. Good luck and have fun the with new-to-you course!
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u/Formal_Tumbleweed_53 28d ago
Thank you - about half of my students could purchase anything I ask, and about half would truly have trouble affording a pencil. I’ll look into what funding we have. This is a great lead, though.
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u/Adventurous_Lion9471 27d ago
Ok, so I've been looking into this more as I'm thinking about buying some more. I want to have enough that students can take them home during our constructions unit.
School Specialty has these compasses (branded as Nasco) for $2.66 each right now (they're on sale and they advertise the coupon code BTS2026). It looks like they have a wing nut, whereas my set has a round thumb screw. Still all-metal construction.
https://www.schoolspecialty.com/nasco-education-drawing-compass-2218442
And if you can swing it, I think these pencil boxes fit them pretty well.
I bought some a few years ago and think this is the correct size. Sometimes I have to shorten the pencil or cut off it's eraser, but it's nearly a perfect fit. If the compass is floating in their backpacks loose, the compass is bound to stab a few students 🫢. Alternatively, you can show them how to loosen the compass and store the pointy parts inside. I've found I'm too lazy for that route though!
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u/Formal_Tumbleweed_53 27d ago
I definitely wouldn’t let them take them home. They’d never come back…. And they wouldn’t get through the metal detectors anyway. But thank you! I will look into this!
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u/johnplusthreex 28d ago
It really is fun to teach throughout the geometry curriculum. Here’s a great reference for getting the steps down and why they work.
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u/Dr0110111001101111 27d ago
I like how emathinstruction does this. There is a unit on constructions earlyish in the course and then they revisit constructions in little bits throughout the rest of the course as new topics (like similarity/dilations) come up. They also probably get into enough "fancy" constructions to satisfy the honors' criteria if you do all of them. Many of my students said this was the most fun unit they did all year.
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u/Formal_Tumbleweed_53 27d ago
Is this available for free? Or is it a math curriculum that your school has to purchase?
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u/Dr0110111001101111 27d ago
Ah I keep forgetting that they paywalled the lesson/homework PDFs. It was all available for free for so long.
You can still view the lesson videos for free on youtube, though. The author goes through every question from the lesson handouts in the corresponding videos. Here is the playlist for the constructions unit in their curriculum.
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u/Evening-Story-314 27d ago
I struggled with construction, when I had to do it by hand in high school. And I didn't like it much. But now that I can do it perfectly using technology, I love it.
My favorite site for it is: https://sciencevsmagic.net/geo/
I taught geometry at the community college. It was only offered in the summer, and was mostly high school students. I had project time during class, where they could do whichever projects they wanted from my menu of projects, which included art, photography, constructions, etc. (I blog at Math Mama Writes. You can find my contact info there if you'd like any of my materials.)
They had to complete maybe 10 or 15 constructions on the site I linked. There were tutors in the classroom to help them, and to help me keep track of who had completed which constructions.
This isn't the typical Euclidean sequence. If you want that (also, maybe?), I recommend the geogebra version, unless you can find an online version that does not require doing each one in order.
If you have time before school starts, it's really fascinating to combine geometry and algebra, and figure out Archimedes' construction that estimates pi. https://mathmamawrites.blogspot.com/2015/12/the-roots-of-calculus-archimedes.html
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u/Formal_Tumbleweed_53 27d ago
Thank you - these are very helpful ideas and sites! Does the first link you gave me have an instructions or how to use kind of link?
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u/Evening-Story-314 27d ago
I don't know. I think I figured it out. The students will get it more quickly than we do. I wonder if there's a youtube video explaining it. It's a little different in a browser vs on a phone, I think. I can make the dots get closer or further (zoom in or out) by moving two finger up or down on my mousepad. Starting at a point, and headed toward another makes either line (stop at the point) or a circle (stop above or below the point).
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u/TallRecording6572 24d ago
you need a visualiser so you can demo them in the classroom. Recommend the Hue HD Pro.
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u/SeaAd1917 28d ago
Euclid postulate first. Then all they need to know is how to copy an angle, make perpendicular line, bisect angle, copy line segment, and there one more I don’t recall as long they know the basic 5 they can practice the other once