The constructions in geometry unit is our last for the year. However, geometric constructions is typically a beginning of the year unit for most geometry teachers. Over the years, I experimented with placing this unit at the beginning and at the end of the year, but the end of the year is my favorite by far.
In May, when students are getting antsy and need a change, constructions are the perfect change of pace. Especially after our algebra-heavy circles unit, students need to do something different and hands-on. Continue reading for more information about my constructions in geometry unit.
Tools for Geometric Construction
Naturally, we begin the unit by identifying parts of a compass. Then, students spend time playing with the compasses and practice making circles. Most years, I give my students a worksheet that walks them through some basic constructions – not shapes, but simple tasks to complete with a compass. This was very helpful for the start of our constructions unit.
Constructing Equilateral Triangles
The first geometric construction we complete is an equilateral triangle. For this construction, I have students start out by constructing two full circles instead of arcs. Students quickly realize that (a) they have two options to complete their equilateral triangle, and that (b) they don’t need full circles.
Constructing Perpendicular Bisectors
In the same class, we cover perpendicular bisectors. For this one, I tell students to start by constructing two semicircles from either endpoint. At first, students continue to construct arcs that reach the other endpoint, but with practice they realize that their arcs only need to extend past the midpoint.
Basic Geometry Constructions: Angle Bisectors
The next day, we construct angle bisectors. Just like all of the interactive notebook pages for this unit, students have step-by-step instructions on the front cover of their booklet, and diagrams that correspond to each step. The front cover is a helpful reference for students. Inside the booklet, there are up to six spaces to practice each construction. I always tell students not to glue these pages into their interactive notebooks until they complete the constructions.
Perpendicular Lines Geometric Constructions Practice
On the same day, we construct perpendicular lines. The last angle bisector students construct is for a 180º angle. Some of them notice that the bisectors create 90º angles right away. This helps me explain to students that they are following the same procedure for perpendicular lines. I teach students to use the same procedure regardless of where the point they are constructing the line through lies.
It has been very helpful to pair similar constructions together in the same class period. It does not take all 42 minutes for students to learn a single construction. And even though it may take students over half the period to get the first construction down, they master the second one much faster because it’s very similar.
Constructing Polygons Inscribed in Circles
My favorite constructions to teach are the polygons inscribed in circles. Surprisingly, it’s pretty easy to teach all 3 constructions in one day. We start with the square, and then move on to regular hexagons and equilateral triangles.
For regular hexagons, I do not teach the traditional method of measuring to the radius, and repeatedly constructing arcs all around. One year, a student showed me an alternate method.
Instead of the usual method, we start by constructing a diameter, and then measuring to the radius, and constructing one large arc from an endpoint of the diameter. Then, we repeat the large arc from the other endpoint, thus creating the 6 intersection points we need to complete the hexagon. Need a visual? Check out this video!
Tangent Lines Constructions in Geometry
My least favorite constructions to teach? That would be the lines tangent to a circle. Having two very different procedures depending on whether the line is on the circle or not is frustrating – for students and myself. The step-by-step interactive notebook page comes in very handy on these constructions.
Additional Geometric Construction in Mathematics
Since this unit is at the end of the year, how much time we have directly impacts how many constructions we learn about. The other constructions not previously mentioned, like copying a line segment; copying an angle; and parallel lines; may be skipped. By this point in the year, we are beginning to prepare for our state exam. Since these constructions are not represented on past exams, I often skip over these.
Additional Tips for Practicing Geometric Constructions
Since I teach using a geometry interactive notebook, I have to teach students to clear their desks to practice constructions. Interactive notebooks require several supplies, and when practicing constructions, students need a flat surface, free of anything that could disrupt their movements.
Normally, students know that they should not glue anything into their notebooks until we complete the lesson. But for this unit in particular, it’s imperative that I remind them of this habit.
Is your constructions in geometry unit coming up? The full interactive notebook constructions unit is now available if you would like to save yourself loads of time. Each page includes step-by-step instructions with diagrams, and a geometric constructions worksheet inside the foldable. (And soon each page will also include geometric construction videos!)
Want to hear more about the constructions in geometry unit? Be sure to check out the companion video on my YouTube channel!
