||Let's take stock of the PoW program in Philadelphia this year and think about how we should approach the end of this year and next year in order for SDP to get the most out of it. Brief summary of what we did and what we saw.
||Individually review a selection of submissions. Discuss as a group what you notice in the submissions.
||Topics for discussion:
- What do you notice about the math and strategies?
- What do you notice about the writing?
- What do you notice about the kids' orientation to the process?
- What's likely to be different about what you do with us in this format than what you do in the class?
||What do you know about how teachers are using this in the classroom?
|| Next steps:
- What are you already doing with your teachers as professional development?
- What's your focus for the end of the year? Next year?
- Where/how might we fit in? What can we do to enhance what we have?
||Overview NSDL Math Tools Workshop program: develop use of new online tools for mathematics; develop SDP teacher pedagogical content knowledge; develop local professional community and leadership in the context of local workshops and online courses.
||Let's do math: Balloon Booths.
||Discuss solutions. Benefits of the technology for this problem? Discussion.
||Responses to question posed in Balloon Booths: Last year a student playing this game in a different booth found that 3/2 made the diameter too small and 5/3 made the diameter too large. Recommend a strategy the student might use to find a fraction that will pop the balloon.
||Brainstorm - What is algebraic reasoning?
||Discuss in groups:
Describe the algebraic reasoning in this set of tasks.
What are natural algebraic questions that this game might lead one to ask?
||Share and wrap up
||Files to download:
Geometer's Sketchpad file
Excel "blank" file
Some algebra connections to consider:
- reasoning about the relationship between quantities: scale factor (variable), diameter, and nail width (unknown)
- reasoning about the relative effects of changing the numerator and changing the denominator, singly and jointly
- reasoning about numbers between two fractions can be thinking about inequalities and can lead to graphing solutions that are very nice:
e.g. 3/2 < y/x < 5/3
or y > 3x/2 and y < 5x/3.
Graph y = 3x/2 and y = 5x/3 on the same graph and you can get integer solutions for y and x by inspecting the area between the two. This shows the value of going ahead and representing things algebraically, even when it doesn't seem at first like it gives the kind of solvable equation one expects.