Unit Overview: Have a Ball with Polygons!
Can you make a soccer ball out of recycled materials?
Have you ever thought about designing a soccer ball? What would it look like? What would it be made from? What kinds of polygon shapes make suitable surfaces for soccer balls? What are the criteria and constraints of a soccer ball?
This inquiry unit takes students through a sequence of lessons that focus on polygonal properties addressed in CCSS.Math.Content.6.G.A.1 . Students inspect a need to create a different type of soccer ball out of recycled materials. Students investigate polygons that compose into rectangles and those that decompose into triangles and other shapes, and they find the areas of right triangles, other triangles and other shapes. Students analyze polygons that fit together on a flat plane and those that fit together to approximate curved surfaces. In the final Design Challenge, students prototype, test, retest, and design “soccer balls” that meet all criteria and constraints.
- Lesson 1: Empathy: Students watch a video about a boy from another country who doesn’t have the means to acquire a real soccer ball but is determined to make his own soccer ball with readily available recycled materials. Further inquiry leads students to empathize with a real-world reason for recycling and for repurposing materials to help solve problems; such as making a soccer ball out of plastic bags and string!
- Lesson 2: Define: The surfaces of actual soccer balls are comprised of adjoining polygons. In this lesson students explore and define polygonal attributes; including the area of right triangles, other triangles, special quadrilaterals, and polygons by composing them into rectangles and/or decomposing them into triangles and other shapes; students demonstrate understanding of polygonal attributes in the process of constructing all 7 parts of a Tangram puzzle.
- Lesson 3: Define: Real soccer ball surfaces are made out of (slightly curved) pentagons and hexagons that adjoin without spaces and without overlaps. In this lesson, students investigate characteristics of polygons that fit together on a flat surface without spaces or overlaps (e.g., those that “tessellate”) and create surfaces made from tessellating polygons.
- Lesson 4: Define: From flat tessellated surfaces made of polygons, students investigate how to make curved bowls with polygonal surfaces. Given a budget and prices for each type of polygon, student teams explain choices for combinations of polygons that best meet cost restrictions in their bowl surfaces.
- Lesson 5: Design Challenge — Ideate, Prototype, & Test: The final Design Challenge has students iterate ideating a model, prototyping, testing, redesigning, and retesting the model until all requirements are met; resulting in a soccer ball having polygonal surfaces and made entirely with recycled materials.
In this Inquiry Unit, students investigate various properties and attributes of different polygons by analyzing the surfaces of soccer balls and then recreating soccer balls made from recycled materials. Through the lessons in this unit, student teams find the areas right triangles, other triangles, special quadrilaterals, and polygons by composing them into rectangles or decomposing them into triangles and other shapes (CCSS.Math.Content.6.G.A.1 ). Then they apply these techniques in the context of solving a real-world problem — in this case, finding a way to make a soccer ball out of recycled materials so playing a game of soccer is accessible for anyone anywhere.
In the Empathy phase of Lesson 1, students identify the story of a boys’ dilemma; wanting to play soccer but not having access to a soccer ball. The boy solves the problem by creating a “soccer ball” out of readily available recycled plastic bags and string. In this lesson, students investigate attributes of soccer balls and creative solutions for repurposing recycled materials to solve a variety of problems. In the Define phase of Lesson 2, students examine the types of polygons that appear on actual soccer balls. This leads to exploring and defining polygonal attributes through the process of making a Tangram puzzle; including finding the area of right triangles, other triangles, special quadrilaterals, and polygons by composing them into rectangles and/or decomposing them into triangles and other shapes; CCSS.Math.Content.6.G.A.1. Pentagons and hexagons on soccer balls align together on a curved surface without gaps or overlaps. Prior to investigating polygons on curved surfaces, in the Define phase of Lesson 3 students consider attributes of “regular” polygons that align together without gaps or spaces on flat surfaces. In the Define phase of Lesson 4, student teams contemplate how to “tessellate” a curved surface by creating bowls with combinations of polygons. Student teams must choose combinations of polygons that best meet cost restrictions given a set budget and prices for each type of polygon. In the Design Challenge (Ideate, Prototype, & Test) of Lesson 5, student teams iterate ideating a model, prototyping, testing, redesigning, and retesting the model until all requirements are met; resulting in a soccer ball made entirely out of recycled materials.