Stretching Young Minds with Geoboards

Ana Butler

Recently I watched a toddler in a doctor’s office working to sort shapes in one of those wooden shape sorter benches. He concentrated intently on his work. Rather than trying a block in each opening, he would study the block in his hand carefully before attempting to fit it into the correct spot. Often he had the right shape but needed to reposition it to fit.

We become aware of shapes around us at a very early age. And the exploration of shapes continues throughout our lives. Physical manipulatives and visual models help children make sense of mathematical concepts, and the toddler playing with his toy is laying the groundwork for future geometry understanding. Another appealing tool for exploring shapes is a geoboard—usually a 7- by 7-inch plastic square, consisting of a 25-peg array with colored rubber bands. 

As with so many good manipulatives, geoboards feel like toys in a child’s hands but perform as powerful math tools. The stretchy bands invite exploration across a range of age and mathematical understanding. In the very early grades, teachers often introduce the geoboard by modeling how to use it safely and encouraging students to experiment by stretching the bands to form parallel lines. Then young learners can transform the lines into stars and other shapes of their own design. These simple constructions set the foundation for learning about edges, corners, sizes of shapes, and area. 

At every stage, teachers can support students’ growth through questioning and asking students to explain their reasoning. When teachers model geometric concepts, it’s important they use proper terminology. By grade 1, students begin to model position and size while using shape vocabulary (next to, above, at the top, in the middle, big, small, square, triangle, rectangle, line, and so on). 

Stretching young minds with geoboards

In grade 2 and beyond, students are exposed to the concept of area, a measure of the interior region of a two-dimensional shape. Geoboards give them the opportunity to make different sizes of the same shape and can be used to introduce fractions of square units. The language of geometry begins to take shape as students learn terms like scalene, isosceles, and right triangle while building examples of different triangles. 

The simplicity of this grid of pegs is the source of its strength and versatility as a mathematical model. It invites students to experiment with shapes, to modify the lengths of the sides and the measures of the angles. It shows them that if they push or pull a side too far, a square becomes a different quadrilateral. With geoboards, there is no record of error that may inhibit inquiry. Students can restore the square again or create a new shape by moving the rubber band to a different peg. As students learn and explore, the teacher introduces concepts, guides investigations, asks questions, and provides opportunities to demonstrate new skills.

Be sure to check out Geoboard, a free math app from The Math Learning Center.

Ana Butler is a professional services coordinator for MLC.