We began the day by reviewing some of the math homework from yesterday. Everyone shared the problems they had written by writing them on post-it notes and then sticking them to posters that had been put up around the room. It became clear that the most common subtraction problems involved comparing, with an unknown difference (Lucy has A apples. Julie has C apples. How many more apples does Julie have than Lucy?). Participants suggested that this might be because this is a fairly standard basic subtraction. In contrast, very few people wrote problems involving both addends being unknown. We discussed the ways in which this also is a useful skill. Participants noted how they need to check themselves and make sure that they are writing problems that demonstrate the full spectrum of subtraction. Elyse suggested that with advanced students, she might give them the reference sheet on the spectrum of subtraction, and ask the to write their own problems.

After the homework review, we did the sheet on comparing fractions. Participants grappled with relating the fractions to benchmark numbers, and thinking about whether one piece was being added or taken away, and also considering the size of the pieces.

Next, we started thinking about signed numbers.We discussed how to model positive and negative numbers in terms of the number line, and also using chips of different colors to represent positive/negative numbers. We used these models to think about adding and subtracting signed numbers. To make sense of subtracting signed numbers, we re-wrote the subtraction problems as addition problems.

After lunch, Nursen led a pedagogy discussion.

Homework:

Math Homework:

Block 2, page 36, #5 and #6. (Do not spend more than 30 minutes on these two problems together. If you haven’t gotten an answer by the end of 30 minutes, write down what you know, and some questions that would help you to continue before setting it aside.)

Pedagogy Homework:

Read Principles to Actions: Section titled “Build Procedural Fluency from Conceptual Understanding” (p. 42-48).

Also read: Webb, Bozwinkel, & Decker. Beneath the Tip of the Iceberg: Using Representations to Support Student Understanding.  MTMS, 2008.  (Handout from class today)

In your notebook:

• Identify a procedure or skill that you consider essential for students at your grade level to learn.
• Describe the conceptual understandings that support students’ learning of the procedure or skill.
• Write questions you have about the readings.
• List 2-4 ways that the math work you’ve been doing in PMI connect to these two readings.