# PMI@UP 2017 Day 10

What a full two weeks!  And yet there always seems to be more to do.

We started the morning with the post-assessment and beliefs survey.  The analysis of that data will be shared later this summer.

We then spent some time refreshing the addition and subtraction of signed numbers, and representing that with joining and taking away piles of color-coded counters.  That discussion progressed into exploring the multiplication of signed numbers.  We found that when one or two of the factors are positive whole numbers, then we can rely on the “__ groups of size ___” model.  However, when both factors are negative we need to rely on logic and the distributive property in particular.  We ultimately had three explanations: one based on patterns, one based on the notion of the opposite, and one based on comparing the products 4×4 and the expanded form of (5+(-1))x(5+(-1)).

We then split into teams of 3 to do “Bungee Barbie” and started analyzing the data over lunch.  Here is the winning drop:  https://photos.app.goo.gl/TJO0BwptyT0slWrm2  .  After the drops, we debriefed on the mathematical thinking and topics that occurred within that task.

We then got into our “Kumbaya” circle and reflected on what we learned about mathematics, what we learned about teaching, and our commitments to how we can improve our own classrooms.  We then read “Hooray for Diffendoofer Day.”  The key take-away message: Teach your students to think and the tests will take care of themselves.

### Homework

Continue to give your students the best educational experiences possible.  Continue to learn how to make those experiences richer, and continue to seek out why of mathematics.