Pre-work – Draw it out

Which of these can you draw fulfilling these conditions?

You can start from any point but you are not allowed to lift the pen while drawing.
Each edge (or line) should be drawn only once. So, you can’t go over any edge again.

Are you able to find a way for each of them? In case you don’t, why do you think that’s happening?

What students worked out7

Student 282020-12-02
I was able to do it for the 2nd, 3rd 4th, and 6th figures. I can see some relation with triangles, like if in the first figure you draw a diagonal of the rectangle then we can draw for it as well.
Student 242020-12-02
I too agree with Student 28 that it is possible for figures 2, 3, 4 and 6 but my rationale is, if we could unwrap it it could be made continuous without and dangling segments
Student 242020-12-02
It’s like a circuit so if at every point one and out is there than that circuit can be a circuit of no repetition.
Student 432020-12-02
I was also able to do it with 2nd,3rd,4th, and 6th figures.
Student 422020-12-02
I was able to draw figures 2,3,4 and 6 with the given conditions. Two things that can help in drawing each figure were:
1) draw the outermost framework first.
2) start from that point, from which maximum number of lines are diverging.
Following these two rules I was able to draw it very easily.
Student 292020-12-02
I agree with Student 28 that figures 2, 3, 4 and 6 are possible.
Student 192020-12-02
I could do figures 2, 3, 4, and 6! What worked for me was figuring out a point in each figure that had the most no. of lines passing through it and starting from there. A natural outer path developed itself because of it.