Bridging the Gap, Day 7—Mathematician MeetUp

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SWBAT—Students will be able to. We start every lesson with this ritual to center and focus students so they know their goals, maps and measurements. (italics will just be practiced, not spotlighted). 

4.MD.5—Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint <rvw; build twd. polygon>, and understand concepts of angle measurement (as degrees of a 360 circle). <caternary curve ==> polygons ==>angles as degrees ==> measure angles>

4.MD.6—Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. <caternary curve toward polygons, measure angles> (+4.NBT.3—Use place value understanding to round multi-digit whole numbers to any place.) (2d circle on board, measured, 3D slices measured...) 

4.IE.6b—Measure and estimate the weight, length and angle of objects <guesstimate string length, weights, then angles as they take form; measure to verify, signal to check in

4.IE.6e—Construct and interpret graphs from measurements. <graph angles:number of weights>

Standards for Mathematical Practice—Posted & Reviewed to empower mathematicians.

4.IE.6a—inference vs. observation and understand that scientists' explanations come partly from what they observe and partly from how they interpret their observation. <are we inferring? observing?>

4.IE.6c—Formulate and justify predictions based on cause-and-effect relationships. 

  1. 5m: Total Recall: (AoC 76, Whiteboard) Quick group graphing rope characteristics and history <how might we organize and why?> from Morning Meeting. (4.IE.6e, 4.SLS.1, 4.SLS.1b, 4.SLS.1d, 4.SLS.2; Whiteboard)
  2. 5m: Powers of Observation: (twizzlers, caternary curve string, image of cables on overhead, whiteboard, Journals). <Compare/Contrast (C/C) cables/twizzlers/string (Venn Diagram), groups diagram in journals, quick Share + Jot  (4.IE.6a, 4.IE.6e; WB, Journal)
  3. Slicing the pie—Rulers to protractors. All angles of a polygon should add up to 360*, is it obtuse or acute? Guess it then measure it. Explore with caternary curve. Is this a polygon? No. It's a curve. What's the key difference?
  4. 30m: Caternary curve: (15 minutes, string tied with knots and paperclips, weights, protractors, rulers, journals, instructions/AoC 76-79) <partners, large + small groups>  (4.MD.5, 4.MD.6, 4.IE.6a, 4.IE.6b; WB, Journal, A/V)
    1. 5m: Guesstimate length; graph guesses, test, quick check in. (4.IE.6b, 4.IE.6c, 4.IE.6e, 4.MD.6; Journal/Whiteboard/Signals)
    2. 5m: Note, Turn + Teach—Hypothesize; what are you guys thinking/anticipating? (4.IE.6c, 4.IE.6a; Journal)
    3. 5m: Large Group Discussion—Discuss polygons. Discuss angles as degrees of a circle (dimension). Guesstimate angles through process. (4.MD.5, 4.IE.6b, 4.IE.6c; WB, A/V)
    4. 5m: Small groups discuss angles/curve, following multistep instructions (AoC 77-79), observing and discussing tension, progression of angles; measuring and noting along the way. Graph results on WB. Discuss any measurement variances—why are they there? How precise do we need to be for this project? (4.SLS.1, 4.SLS.1b, 4.MD.5, 4.MS; WB, Journal)
    5. 5m: Sketch, Measure and Label polygon and caternary angle/arch. (4.IE.6b, 4.MD.6; Journal)
    6. 5m: Catenary curve to arch; does anyone else see anything familiar? Maybe something we studied earlier in the unit, strong in compression instead of tension? Can we turn this curve into a polygon? Do our angles add up to 360? (Journal/Groups/Whiteboard)
    7. Ext: Journal—extrapolate/extend—a) How many corners on a circle? b) What means dimension? Explain dimension, how and what it is/means and anything else you know about dimension. (essential and unanswered questions, thoughts welcomed in both Collection Basket and C3 Chest).

In addition to visual check ins and auditory amblings (eavesdropping and note taking) aligned with individual student goals, the following relics serve to archive and gain deeper insight into student understanding. 

  • Whiteboard—our CTO of the day will ensure that an image of the whiteboard is snapped and emailed to our blog for later review. 
    • Total Recall: Rope
    • S+J (2, 3.3, 3.4, 3.6)
    • Notes
  • A/V—Audio and Visual cues serve as data points also. I listen and note in my own Field Notes
    • QCHK
    • T+T
    • Discussion
  • Journals—our Math Journals serve as ongoing documentation of our mathematical explorations. These are returned to the Collection Basket. 
    • Venn Diagram: cables/twizzler/thread
    • Sketch each version; label with estimated angle.
    • Various Notes; polygons etc.
    • Vocab/label: tension, angles, measure angles, caternary angle, polygon, cable

Field Notes

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Field Notes

These are our personal journals—our Field Notes. In here we note what we see in the wild, patterns we suspect and detect, challenges and maps to solutions...Questions, ideas, thoughts we want to explore, small celebrations and gratitudes throughout the day—this is what we scientists do; observe and note curiosities and patterns and things that grab our attention. I say "we" because I, too, participate and benefit from this exercise.

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How many corners on a circle?

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How many corners on a circle?

We need more patient problem solvers. And that starts with the cornerstone of mathematical reasoning. 

We need humans with initiative, perseverance, retention and a willingness and curiosity to dig in and uncover the treasures all around and throughout us. 

Sitcoms are robbing us of the superpower, literally rewiring the neurons in our brains, and current educational practices are doing the same. The good news is that we're at the wheel, and we can steer in a better direction. 

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