Reflection: Real World Applications Origami Boxes Gallery Walk - Section 2: Reflect on Feedback


This is a question I typically brush off, but given the amount of time we have invested in the Origami Box problem, it seems like the right thing to do is to answer the question once and for all.  This year, I decided to have students build a box made from a 20x20 cm paper and a 30x30 cm paper.  We then filled up each box to compare groups’ predictions were to the actual number.


Finding the actual answers and displaying the data in a table was beneficial for a couple of reasons.  First of all, the data is real; the numbers aren’t the nice, round ones students want (~470 for the 20x20, ~1608 for the 30x30), yet the students have to trust the data because they actually counted out enough beans to fill the boxes.  Second, showing the results in a table allowed for students to share out immediate impressions, like “I’m surprised at how many beans there are in the box made from the 30x30 paper” or “it’s so obvious now that the number of beans isn’t growing the same each time.”


Additionally, having real data allowed us to discuss how groups’ predictions may have been wrong, but how their thinking might have been mathematically sound.  For example, one group concluded that their thinking was correct, but that they could have gotten more accurate results had they taken more samples to find a better approximation for the volume of a bean.


Lastly, I checked students’ understanding about area and volume ratios of similarity by asking them how they could predict the number of beans that a box made from a 57x57 paper could hold.  Students were able to say that the ratio of the sides from the 10x10 cm to the 57x57 cm paper was 5.7, so the area would be 5.7^2 times bigger and the volume would be 5.7^3 times bigger.

  Real World Applications: So What's the Answer?
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Origami Boxes Gallery Walk

Unit 10: Geometric Measurement and Dimension
Lesson 10 of 14

Objective: Students will be able to make sense of and critique others' reasoning about how volume grows.

Big Idea: By participating in a Gallery Walk and reflecting on cool and warm feedback, students will revise their work on Origami Boxes.

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Math, Geometry, Measurement, modeling, space, shapes
  45 minutes
poster revision
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