Today was another great, math-filled day!
We began the day by “circling up” and introducing ourselves to the whole groups. We each shared something fun that we will or have done this summer. We’ve got beach lovers, roller-coaster riders, Disney-goers, and animal caretakers. Yay for summer!
We were paired up with a colleague from a different district and we compared our work on the homework problems–variations on the “kayak problem” and the “tennis trophy problem” about evens and odds. We discussed the variety of valid interpretations for the problems based on the wording and based on what we know from the “real world” about kayaking and tennis tournaments.
Then Andrew launched the “Days of Christmas problem” and we set off on problem-solving. Triangular numbers! Square numbers! Gauss! Searching for patterns in tables and numbers! Making triangles and squares with counters! Generating expressions and conjectures!
Pam shared a great resource: MDC (mathematics design collaborative) through the SAS website. (for members only, but it’s free, so join!)
After breaking for lunch, we watched a video of 3rd graders solving the handshake problem. We made posters presenting how ideas related to expressions and equations play out at each of our grade levels, and then we displayed these posters in order to look for themes and alignment. (pictures below)
Fran and Andrea led a discussion about low-demand tasks and high-demand tasks and the importance of providing balanced opportunities for students to practice all types of mathematical thinking.
We concluded with Andrew’s presentation of Unit 3: Subtraction as the Art of Unadding. (Note: Spell check does not like the word ‘unadding.”)
Homework for tomorrow (Wednesday):
Work on the Library Problem
Work on the problems about temperatures (p. 3.19 #15 and #16)
Read Principles to Action: 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.