Constructions are an integral part of high school Geometry.
Teaching constructions well requires great assessments. You’ll also need a deep knowledge of the construction process, and you’ll want quality construction tools, mainly a compass. Tips for making great constructions are really helpful, as well as having excellent methods for demonstrating the step-by-step procedures.
In this article, we’re going to look specifically at assessments.
Great Assessment Tools
In order to have optimum student learning, begin with the end in mind!
In my department, we used three primary assessments for this unit: completing the constructions by hand, answering multiple choice questions about the constructions processes, and a cumulative project.
1. Having students complete the constructions by hand
This assessment is very straightforward and can be easily converted for online instruction…as long as students have the ability to upload their work!
We simply named the construction and provided the beginning element. For example, #1 might be “Construct the angle bisector.” and we’d provide an angle. (Kuta software’s Infinite Geometry has basic constructions questions.)
During instruction, I knew that I needed to emphasize what a true construction looks like compared to someone who just eyeballs it or even measures using a protractor or ruler.
So for instance, during warm ups and lesson wrap ups, I talked to them about the arc lines (made by the compass) that I’d be looking for when I graded their quizzes.
I told them that with constructions, we don’t erase these types of marks…they are the evidence that we are doing it correctly…just as showing work in solving an equation is evidence that you know what you’re doing in Algebra.
If you need a refresher on the basic constructions, click here.
2. Multiple choice questions about constructions
Here’s a quick, 2 minute video of me showing you a few of our multiple choice questions as well as going over a couple of the ways we ask questions. Click play!
I created Google forms mini assessments for each section of the constructions we teach.
The use of Google forms makes this type of assessment super quick to grade (it grades itself, lol). They’re perfect for assessing online–whether students are learning virtually or just using technology inside the classroom.
They also lend themselves well to higher level depth of knowledge questions.
One type of question asks, “What comes next?”
Another type is, “Which step is NOT a step in this construction?”
These questions involve a great deal of vocabulary. This knowledge helps you as you plan instruction.
On the second and following days of teaching a new construction, I would often use questioning similar to these as we reviewed the process;
I’d stop after the second or third step and ask everyone to think…where is the next place I need to put the compass? Point A? Point B?
Or, I’d ask them to think through how many times I’d have to adjust the compass in a particular construction…once? twice?
Or, will we use the compass or the straightedge in the next step?
Finally, I’d ask questions such as, “If I bisect this angle, when I’m finished, what do I have in the figure?” (The original angle has been cut, or bisected, into two smaller but congruent angles.)
Click here to see more examples of Constructions multiple choice questions for assessment.
3. Constructions Project
Our in-class project allows for student choice and is super simple to prepare.
We selected 6-8 geometric designs that could all be constructed entirely using the constructions that we taught, according to our state’s standards.
The majority of the designs had no instructions, while 2-3 of the most difficult ones did have step by step instructions.
A quick search of the web should provide you with lots of options.
We copied each design (usually four to a page) and then cut them apart so that each student could have a copy of it as they worked.
ProTip: We didn’t copy 30 of each design…instead, there were only 2-3 of the simplest ones, graduating up to the most difficult. In a class of 30 students, I’d have 40 or so copies.
That way, the last students to choose still had an option or two.
Our reasoning was that we didn’t want students to unnecessarily choose projects that were too easy just out of laziness (being honest here!).
And we didn’t want them copying each other!
Strategically, I always “randomly” (except it was anything but random) selected students who were having the most trouble with Geometry or constructions specifically…to choose first.
This way, they had all the options, and I could gently let them know which were more challenging and which were less challenging.
But I didn’t assign a specific one. I let them make the fully informed decision.😁
Interesting notes:
- I found that students really didn’t tend toward choosing the easiest anyway. Some did, of course, but most just picked the one they liked the look of the best.
- There was one design that appeared simple but actually required the greatest number of constructions…and came with no directions.
For that reason, I would sometimes allow a student to swap if I had watched them give true effort to the current choice and they were just really overwhelmed. In a semester, with 60-80 students, this might happen with one student.
I showed the class all of the options before letting anyone choose and told them to have a 1st choice but to have backups in mind in case their first choice was already gone!
Details of the assignment:
Students had to recreate the design completely by using constructions, although it could be scaled up or down.
They were reminded that this wasn’t an art project! No drawing or eyeballing.
They had to write out the steps for the design in order so that someone could use their steps without the image and re-create the design.
You’ll want to be very aware of where your students are in their understanding (through observation as well as the use of mini formative assessments, above) so that your interaction with them is appropriate to the level of help they need.
Two students may ask the same question, but you’ll be able to answer one with detailed assistance and the other with a question to get them going in the right track…in this way you’re differentiating for each student, according to his or her needs.
Then the students had to make a second image, also constructed but styled and “cleaned up.”
They added color to this one and could also add embellishments or details not in the original design.
The original (given) design, the constructed, the cleaned up version, and the steps were all put on a poster or large construction (haha) paper for the finished product.
Believe it or not, this was completed in class, using all of one class period (90 minutes) and 10-15 minutes in each of 2-3 additional days.
And there you have it! Constructions assessments in a nutshell.😂 Check out our other posts for teachers, here.
You’ve got this!