I am back on Unit 2 after a short excursion to Unit 3. I did this lesson today and it went pretty well overall. Students were pretty engaged through out trying their paths. One question I asked was for students to estimate how many different paths they did try. Then I connected it to how many possible paths there were.
Here are some other notes:
- I think you could have made the third problem with smaller numbers. Since the complexity was still the same, the biggest challenge was the mental math for students.
- I also think the 4th one threw some kids (they had a hard time knowing what the "cost" was of some of the lines). But overall it was a good challenge.
- Having colored pencils available or multiple copies was also good to help students organize their work.
If you are used to teaching math, this lesson might be a great opportunity to show multiple representations of a function. Students did tables to show patterns or did multiple examples.
Also, I personally didn't do a good enough job of stressing the "computationally hard" piece of the lesson. We talked about reasonable and unreasonable time, but the reflection questions at the end talked about a problem being computationally hard which students didn't understand. Next time I would emphasize the connection more.