We began with the idea of the start and end value in the problems 6 – 2 and 6 + -2 because it was a burning question. We also discussed how to use the words greater than and less than when comparing numbers. We don’t want to use their location compared to zero but rather how far left and how far right they are. Marina gave insight that in calculus class she uses the idea more negative instead of less than when comparing negative numbers. We also had good discussion about having different ways of approaching problems and how to fit these into the time constraints of a classroom. We then watched the video about how uncomfortable it is to think:

http://www.realclearscience.com/video/2017/03/03/the_uncomfortable_effort_of_thinking.html

There was great discussion about how difficult it can be to take this time for ourselves and our own growth without constantly trying to figure how it can help our students. Teachers don’t always have this opportunity – even during in-service.

We talked a lot about positive and negative numbers and using the area model for multiplying fractions – we agreed that the model has its limitations for multiplying mixed numbers. We thought using the distributive property helped with that – for example – 4 1/2 x 2 1/3 – you could do 4 x 2 + 4 x 1/3 + 2 x 1/2 + 1/3 x 1/2 and use the area model for 1/2 times 1/3.

We watched a video on “My favorite No” – https://www.teachingchannel.org/videos/class-warm-up-routine

We also discussed the ideas that were evident in Ms. Flahive’s and Ms. Ramirez’s classrooms from Principles to Action. And then worked on coming up with rich problems for use in our classroom to set the tone for the new year. We will continue this idea tomorrow as some of us are ending the workshop then.

Homework:

Read the reference material on pages 11 and 13 of Block 3.

Read the message entitled “Upside Down Teaching” and in your notebook, complete respond to the discussion prompts for teachers at the end of the message (on p. 94). Try to make connections about what we’ve read about and discussed so far in PMI.

Thanks for a great day.