One of the biggest challenges in creating multiple versions of a geometry test or quiz is how to have different figures on each version of the assessment. For a proof or for questions about a figure, most images are static. While there are ways to randomize the actual image in a problem, it is usually easier to use the same image but randomize the labels and values of angles or segments. You can download a large question bank with several problems like this.
Consider the image below. We would typically have information like , , and with a series of questions about the other angles.
If we want this randomized, there are a couple of approaches. First, randomizing the angle measures is fairly straightforward. We can even put those dynamic values onto the figure. Second, randomizing the labels for the points and angles can further modify the figure.
Start by creating an unlabeled graphic in whatever editor you prefer. I generally use Geogebra, remove the labels from the figure, and either export it or copy and paste into Paint and save it.
I am going to start by modifying the original semi-dynamic problem that used the first image.
The values for ang1, ang2, etc. are from simple algorithms definitions. We can keep those for now, but much of that will changes as we consider dynamic labels.
Create a new algorithm definition for letters: list(“A”,”B”,”C”,”D”,”E”,”F”,”G”,”H”,”J”,”K”,”L”). That is 11 letters. We need four, preferably sequential. Thus, next definition is index: range(1,8). The highest value of 8 will start with H and go through L. Now, four more definitions: A: choose(index + 0, letters), B: choose(index + 1, letters), C: choose(index + 2, letters), and D: choose(index + 3, letters). Great! There are four randomized labels! Placing them is another issue . . .
Randomizing the angle numbers is more problematic. Generally, it is good form to keep them numerically sequenced from one side of the figure and go around to the other. That really leaves us with only two good options: the one in the original figure or going the other way. There are probably many other ways to do this than the one I am proposing here, but this should be pretty clear once you see it.
The value for aindex will simple pick the first or second text value for each of the angle labels. It is best to keep thinking of the angles and points as they are numbered and labeled in the original figure. What they are called in the problem will change.
is no longer static text, so it needs to be changed in the equation editor. Insert the variables A, B, C, and D with overbars and the parallel symbol.
Next, this is what it will look like for the measure of angle 1. Do the same for angle 2 (using a2t and ang2).
Let’s setup the answers, and then we can deal with the more compicated process of labelling the blank figure. The answers, from some simple geometry calculations are:
On to the figure . . . Insert Graph, Cartesian, and clear the current values for its setup.
On the function tab, choose New Picture and select the unlabeled image you created.
You will then need to add another new function: New, Text Box . . . ten times! We will do it once for each label. In the text field, use the names of the algorithm definitions. Thus, the first one will be A, and then we change the Left x and Top y values to try to place it where the A label is on the original figure. Using Apply will update the full graph in the question and can help you get the labels located properly. Then, repeat for each of the other three point labels and the angle numbers. I also change the font for the angle numbers to Arial and red for clarity.
The final question should have all of the labels properly placed. Click the randomize icon a few times and verify that all of the information, especially the answers, is correct. It is much better to find any errors now rather than have a frustrated student come at you!