I decided to make today the final day of thinking problems that are not explicitly targeted at specific outcomes from the program of studies.

I gave my first class the probability and Sudoku problems I gave my second class yesterday, and their progress was much the same.

I gave my afternoon class the following problem:

A heart is constructed by attaching two white semi-circles to the hypotenuse of an isosceles right triangle whose equal sides measure cm. The new ﬁgure is then mounted onto a rectangular piece of red construction paper as shown below. (The dashed line, the side measurement and the right angle symbol will not actually be on the ﬁnished card.)

You are going to write your valentine a message in red ink on the white region of the card.

Determine the total amount of area available for your special valentine greeting.

(I got this problem from the Centre for Education in Mathematics and Computing at the University of Waterloo.)

I was expecting this to be a quick problem, however it ended up taking about of the class. As usual, it started off very slowly with a lot of standing around with little engagement. Eventually one student student asked about formulas (hypotenuse, I think). I responded that they could google any formula they needed.

Eventually, with a little prompting from me, all groups were successful in solving this problem.

**Observations / Reflection**

- In my first class, students persisted on unsolved problems even after a second one was put up. I take this as a good sign of engagement.
- I realized that in my zeal to not give answers, I was reducing my engagement with students too much. Today I engaged more, asking questions about their solutions.
- Talking with students is important for relationship building, which I've always thought to be important, but today was a reminder that it's still important in this style of teaching
- Even when students are doing correct math and using appropriate problem solving approaches, they have
**a lot**of difficulty verbalizing their approaches. When I ask them to verbalize, it gives them practice and helps them learn how to do it (with some prompting and coaching from me, of course). - I was especially impressed by one student who googled the Pure Math 30 diploma formula sheet and correctly used the cosine law to solve for the hypotenuse of the triangle

Tomorrow I will start the Linear Relations unit, leveraging questions from the MathWorks 12 textbook and workbook.