Need help with correctness check mark on two slides

I am creating an activity for students to learn about the equations and graphs of polar functions. Students will be given a graph of a polar function, a hint about what form the equation should take, and then they play around and try to create an equation that matches the given graph.

I am trying to get the “correct” check mark to show, and I don’t quite know what is going wrong.
I have the math input boxes as “readOnly: true”. I also set up a number “a” in the graph component that will be defined to be 1 when the student enters the correct input (it is defined as 0 otherwise using a piecewise function).

To see that things are being computed correctly, I added a rectangular point to each graph at (-1,1) that shows the value of number “a”. In addition, I have a “Great job!” phrase show on the graph when students figure out the correct function. It all seems to be working correctly, but the check mark isn’t showing as correct.

The slides I am sharing here are the first few slides that start off with review of the basics (r=R is a circle, theta=K is a line through the origin at angle K radians). Students will have learned these two in the previous class, so I don’t provide hints for these. The answers are “r=7” for slide 2 and “theta=pi/3” for slide 3.

I have read through a couple of similar posts, but I am still not sure how what I have devised is not working.

I would appreciate any insights!

Since the student doesn’t truly interact with the graph, the correctness check will not appear. (Note I’ve made this same mistake.) I would have the CL for the math input reference the correctness variable a from the graph.
correct: correct=1

I did this for the second screen and started to do it for the third screen but will probably need a little more work since it is in terms of theta and not r.

Thank you so much! That makes total sense. In regards to getting the third slide working…

The third slide wasn’t working with the change because there is something going on with using the list I used to check the values. Desmos recognizes that everything is working numerically (hence the value of a would change to 1), but I am guessing that using the list interacts with the correctness checkmark in some way that doesn’t register. I changed the piecewise function for a to be separate restrictions of discrete checks, such as {f(g(pi/4),pi/4)=0}{f(g(7pi/6),pi/6)=0} and the correctness checkmark now works!

Thank you for your help–I really appreciate it!