##
* *Reflection: High Quality Task
Introduction to Volume: Origami Boxes - Section 1: Launch Origami Boxes

A potential pitfall of this task is that it may seem too simple or even “easy” for some students in this class (So we just fill the boxes with beans? Done!). I wanted to address this feeling head on, acknowledging the task’s deceptively simple nature and promising students that rich and interesting mathematics lay beneath the surface.

I made sure to frame this task in such a way as to validate the positive group norms that would lead to groups’ success on the task. Having taught this lesson before, I have actually witnessed groups of students notice something important in their data—for example, the number of beans does not grow linearly even though the paper does—and completely choose to ignore this observation because it was inconvenient. This is hugely problematic because convenience, in this case, stifles the mathematics that needs to rise to the surface.

For this reason, I reiterated the notion that group norms would be especially important for students to convince themselves, firstly, and ultimately a skeptic, of their ideas. Not only would they need evidence to support their claims, but they would also need to present their ideas in a convincing manner, a process that can yield better results through thoughtful collaboration. I also told students I would circulate the room, taking notes on how group norms enabled groups to ask mathematically important questions and discover insights.

*Framing the Task*

*High Quality Task: Framing the Task*

# Introduction to Volume: Origami Boxes

Lesson 9 of 14

## Objective: Students will be able to collect data, look for patterns, and make predictions about the volume of similar rectangular prisms.

#### Launch Origami Boxes

*5 min*

I launch Origami Boxes by clarifying my expectations for group roles and group norms and highlighting the notion that **multiple intelligences** are necessary for this task. I tell students that their goal is to answer to be able to answer the main question of the day, which is,

**"How does the volume of the box change as the size of the paper increases?" **

After I show students Launch Origami Boxes, I send **Resource Managers** to get the necessary materials and the Origami Boxes Resource Card students will need for the lesson.

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#### Origami Box Work Time

*80 min*

While students work, I like to take **observation notes** on the kinds of strategies students are using--I use these notes to track how groups are approaching the problem, but also to take note of which groups might be resources to others by sharing their ideas (**MP1**, **MP3)**.

Some of the most common approaches I have seen for collecting data on the number of beans that will fill the four given boxes include:

- Finding the average volume of a bean (divide the volume of a box by the number of beans that fit in that box); similarly, determining the number of beans that will fill one cubic centimeter (
**MP2, MP6**) - Making a layer of beans and estimating the number of beans that will fill the box (
**MP4**). - Filling a box halfway or one-third of the way, then using proportional reasoning (
**MP2**).

Some of the most common approaches I have seen for determining the dimensions of the box made from a 20x20 and 30x30 cm square include:

- Looking for patterns in how the dimensions of the box increase (
**MP2**) - Looking for a scale factor between the dimensions of the paper and the dimensions of the square (
**MP2**) - Unfolding a paper to determine the relationship between the length, width, and height of the box and the dimensions of the square (45-45-90 special right triangle!) (
**MP7**)

Depending on how groups are working, I may interrupt them to have **Recorder/Reporters** share out one or two strategies, insights, or questions so that others can offer help or commentary.

During this time, I also remind students of the requirements of the Stand Alone poster (see Origami Boxes Task Card) and encourage them to begin working on this after they have checked in with me about their strategies and predictions (see Origami Box Poster Sample).

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- UNIT 1: Creating Classroom Culture to Develop the Math Practices
- UNIT 2: Introducing Geometry
- UNIT 3: Transformations
- UNIT 4: Discovering and Proving Angle Relationships
- UNIT 5: Constructions
- UNIT 6: Midterm Exam Review
- UNIT 7: Discovering and Proving Triangle Properties
- UNIT 8: Discovering and Proving Polygon Properties
- UNIT 9: Discovering and Proving Circles Properties
- UNIT 10: Geometric Measurement and Dimension
- UNIT 11: The Pythagorean Theorem
- UNIT 12: Triangle Similarity and Trigonometric Ratios
- UNIT 13: Final Exam Review

- LESSON 1: Sectors of Circles
- LESSON 2: Making Sense of Area Formulas for Triangles, Parallelograms, Trapezoids, and Kites
- LESSON 3: Making Sense of Area Formulas for Regular Polygons and Circles
- LESSON 4: Strategies for Decomposing 2-D Figures
- LESSON 5: Sector Area Application: The Grazing Goat
- LESSON 6: Surface Area and Area Differentiation
- LESSON 7: Extreme Couponing: Pizza Edition
- LESSON 8: Area "Quest"
- LESSON 9: Introduction to Volume: Origami Boxes
- LESSON 10: Origami Boxes Gallery Walk
- LESSON 11: Volume Formulas, Cavalieri's Principle, and 2-D Cross-Sections
- LESSON 12: Real World Volume Context Problems
- LESSON 13: Ratios of Similarity and 3D Solids Generated by Revolving 2D Figures
- LESSON 14: Volume "Quest"