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Geometry and More with Geoboards

The geoboard just might be my all-time favorite math manipulative. There are so many interesting questions that can be explored with this easy to use math tool. When I first introduce students to their geoboards, I encourage open-ended exploration. At this phase, students usually create various shapes without consideration of each shape's properties. Once they're comfortable with this, I then engage my students with specific questions:

- Can you make a rectangle whose perimeter is 10?
- How many shapes can you make whose area is 12?
- Can you make a shape whose perimeter is larger than its area?
- How about a shape whose area is larger than its perimeter?

After my students understand the difference between perimeter and area, I then focus on patterns and relationships and provide even greater challenges:

- Build a rectangle and a square with equal areas. What do you notice about the perimeters? Is this always true? Can you find a counterexample?
- How can you find the area of a right triangle? What about other types of triangles?

Geoboards can be used throughout our students' study of math. Preschoolers can simply design various shapes while middle school students can explore advanced topics like Pick's Theorem . In addition to geometry, the geoboard can also serve as a tool for exploring fractions and algebraic thinking.

Are geoboards part of your math program? How do use this manipulative to promote mathematical reasoning in your students?

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