After discussing "perseverance" (from Mathematical Practice #1) and distributing the notebooks I told everyone to skip the first page (where we would put our Skills List) and draw a 4x4 set of dots where we would start working on the first problem of Dan Finkel's A Mathematician at Play (AMAP) #1 <https://mathforlove.com/2018/01/mathematician-at-play-puzzle-1/>. It is easy to demonstrate perseverance at this problem - keep drawing more polygons! Every hour a student solved the puzzle and every hour a student argued that 16 is the maximum number of sides due to the number of dots (Mathematical Practice #3). I asked students how we could extend the problem and they said we could try a 5x5 set of dots. I regret rushing on to a new problem in third hour. During the other hours I let the problem take up the whole time and many students were engaged up to the last minute, though no one was able to draw a 25-sided polygon!
We began with #14 from Martin Gardner's My Best Mathematical and Logic Puzzles: arrange 12 matches to form a polygon with area 4. It's another good opportunity for students to exercise creativity and one solution provides an opportunity to review area of triangles and the 3-4-5 right triangle.
We started the hour with one more example of finding the area of a grid square, then used whatever method we had adopted to prove the Pythagorean Theorem.
Here is the list of problems that students pasted in their notebooks:
The last day of the week students were introduced to vectors with the following set of problems (based on Exeter 2.22 (#10), 2.73 (#11), and 2.87-88 (#13-14)):
What I like about these selected Exeter problems is that they have both a rote procedural component (plot these points) and a conceptual component (what type of figure is this? / what do these figures have in common?). I believe Dan Meyer wrote somewhere (probably while expounding his headache-aspirin philosophy) that while carrying out a simple mechanical process, resources in the brain are freed up to think about that process.