I am committed to adding in more number sense practice in all my classes this year. We are regularly doing number talks, brain teasers, estimations, strategy chats, and other quick but routine plugs for flexible thinking. But my main focus this year is going to be adding the clothesline. I have used clothesline math in algebra for the last few years, but mostly only once or twice when we introduce slope. This year I want to use it in all 6 classes both for specific content and as part of other warm ups (estimation, number talks, etc). I saw Chris Shore talk at TMC17 and made it my one thing. He does a great job explaining the underlying idea/structure and providing resources at the aforementioned link, but I’m going to try to capture student language/moves/misconceptions from specific activities this year. (If you want to read my very first clothesline attempt: Clothesline: Slopes)
Setting the Stage: The day before, we draw lots of intersecting lines, measured angles, and started making claims about angle relationships yesterday. Most (but not all) students were there and had at least some introduction to the words: vertical angles, linear pairs, traversal, alternate interior, alternative exterior, corresponding, and co-interior.
Style: Quick warm up/ try now when entering class.
How it went: Students were either handed one of the four cards (a, b,c ,d) and told to place on the clothesline with a best guess OR were asked to quickly sketch a number line and place a,b,c,d, on it at the tables. (Each table as a whiteboard stuck in the middle). Board placers joined their tables when they finished:
A minute after class started, I asked if any of the four students had a mathematical reason why they placed card where they did on the line.
Student B: My angle was smaller, and therefore closer to 180*.
Student C: But we don’t have degrees on it. Do we need a protractor? Continue reading “Clothesline Math: Geometry Style! Vertical and Linear Angle Relationships”