Does anyone know a good resource for learning about straightedge and compass constructions besides "The Elements?" I tutor geometry to middle-schoolers and high-schoolers and thought that including construction problems might give them better intuition for the subject. I know most of the constructions in book 1 of The Elements, but would appreciate it if anyone could point me in the direction of a book or other resource that has interesting construction problems, hopefully graded by difficulty.
For compass and straightedge construction (personally, I still learn best by manually doing what I'm learning), see, e.g.,:
The following isn't a recommendation regarding pencil and paper geometric constructions, or resources that involve literal use of compass and ruler, but I've found that software like geogebra is extremely helpful when learning and/or teaching geometry, and is useful and appealing to pre-teens, all the way up to post-secondary students (and their teachers and tutors!)
Given that today's children and teens typically have developed facility with and attraction to computer applications, it is appealing to even the most resistant students!
The software helps students readily construct and manipulate geometric objects, as well as better understand, through immediate visualization, how changes in certain parameters affect resulting geometric constructions.
You'll find many applications, teaching lessons, tips, and such at geogebra.org (linked above, where you can download the software, and find links to curriculum, downloads, teaching tips, and discussion boards, etc.).
Note: Geogebra is free and well-supported software available for download to anyone and everyone.
One additional helpful package, very user friendly, (there's a minimal expense, but a lot of support) is the Geometer's SketchPad (see resources available at Dynamic Geometry).
Note that, more for yourself, there is a fair amount on such constructions in the hyperbolic plane. There is a good deal of unfamiliar stuff to learn, but the one simple statement is this: an angle is constructible in the hyperbolic plane if and only if it is constructible in the Euclidean plane. Here an angle is between two lines, or between a line and a circle that meets it, or two circles that meet. Who knew?
You might want to look at publisher's websites, places that publish school material. There is one near me (at least it was), Key Curriculum Press. Maybe they have something at the correct level and pacing.
HERE is a construction problem i solved on MSE. It could easily be in Euclid, which I have never read.