# Eighteen Sides

Practices
Explaining and justifying
Representing and connecting
Topics
• Geometry
1
2
Use an App
Geoboard
452P-NYBM
Number Line
465D-G472

How can you make a group of shapes that has a total of 18 sides?

Kayla drew 4 two-dimensional shapes. She counted a total of 18 sides. What 4 shapes might she have? How many answers can you find?

How could you get started?
• What 2-dimensional shapes do you know? How many sides does each shape have?
• What 4 shapes might you start with? What changes can you make to your shapes so that the total number of sides is exactly 18?
• Is it possible to solve this problem using 4 matching shapes? Why or why not?
• Can you figure out a way to solve the problem with 3 of the 4 shapes matching each other?
• A decagon is a shape with 10 sides. Is it possible to draw 4 shapes with a total of 18 sides if one of the shapes is a decagon? How do you know?

In this open-ended activity, students use what they know about the attributes of two-dimensional shapes to make sets of shapes with a given total number of sides. Solving this problem requires students to represent or describe two-dimensional shapes with a focus on the number of sides and to show multiple ways to make a sum of 18 with 4 unknown addends. This activity also provides opportunities for students to make generalizations. For example, students may note that any polygon must have at least 3 sides or that they can take a side from one shape and give it to another shape while conserving the overall quantity of sides. This latter generalization is an exciting opportunity to connect geometric and algebraic reasoning.