Understanding Hexagons In Mathematics
A hexagon is a closed, six-sided polygon with six angles, and six vertices. It can be classified as regular, where all sides and angles are equal, or irregular, where side and angle measures vary.
Why Understanding Hexagons Is Important
Hexagons and Spatial Reasoning
Exploring hexagons helps students build spatial reasoning by encouraging them to visualize, analyze, and manipulate geometric structures in meaningful ways. When students break a hexagon into smaller shapes (e.g., triangles, trapezoids, or parallelograms), they strengthen their understanding of composition and decomposition. This ability to reconfigure shapes supports later work in area, symmetry, and geometric problem-solving.
Hexagons also offer a rich opportunity to explore tessellation. Because regular hexagons can tile a surface without gaps, students can investigate how certain shapes fit together efficiently.
Comparing hexagons to other polygons, such as pentagons or octagons, further supports classification and helps students see how attributes like number of sides and angles define and differentiate shapes.
Hexagons In The Real World
Hexagons are more than just geometric figures on paper! They appear frequently in everyday objects and natural structures, making them highly relatable for students. Pointing out real-world examples helps students recognize the usefulness and practicality of geometry in their surroundings.
For example, many tools, such as nuts, bolts, Allen keys, and socket wrenches, are designed with hexagonal heads. This shape provides multiple flat surfaces for gripping and turning, making it both strong and efficient.
In nature, honeycombs are famously made of hexagons, which maximize space while using the least amount of wax.
In construction and interior design, hexagonal tiles are popular for flooring and wall patterns because they fit together perfectly without leaving gaps.
These everyday examples not only help students connect geometry to the world around them but also reinforce the idea that shape choices are often intentional and purposeful.
Teaching Strategies For Hexagons
Hands-On Exploration of Hexagons
Before students are expected to classify or measure hexagons, they benefit from building and manipulating them to develop an intuitive sense of their properties.
Using materials like toothpicks, straws, or craft sticks, students can construct polygons with varying numbers of sides, from triangles to octagons. This hands-on experience invites comparison and deepens spatial reasoning.
As they build, prompt them to examine how a hexagon compares to other shapes. For example, “What do you notice about a hexagon compared to a pentagon or an octagon?” or “How do the angles and the shape change as you add more sides?”
These explorations help students internalize what makes a hexagon distinct and a recognizable structure that differs from other polygons. When students are given the opportunity to construct shapes themselves, they become active investigators of geometry, building a foundation for later classification, measurement, and reasoning tasks.
Visual Models for Understanding Hexagons
After physically constructing hexagons, students benefit from engaging with drawn representations to sort, classify, and decompose polygons. This stage helps solidify their understanding by prompting them to analyze shape attributes visually.
Begin by providing students with a variety of pre-drawn polygons (e.g, hexagons, pentagons, quadrilaterals, and triangles), and asking them to sort the shapes into categories of their own choosing. This open-ended sorting allows students to notice patterns and develop informal definitions before formal terminology is introduced. As they sort, guide their thinking with questions like, “What do all these hexagons have in common?” or “How are hexagons different from quadrilaterals or pentagons?”
Once students are comfortable identifying hexagons, invite them to draw their own and compare them with classmates’ drawings. Comparing drawings allows students to see variation in hexagon shapes while reinforcing the idea that six straight sides and six angles are defining features.
To deepen analysis, offer a second task focused on decomposition. Provide printed hexagons and challenge students to divide them into smaller shapes in different ways. Ask, “How many triangles can you fit inside?” or “Can you decompose the hexagon using other shapes?” These questions encourage multiple solution paths and help students understand that breaking complex shapes into familiar parts reveals more about structure and composition.
The lesson can conclude with a class-created definition of a hexagon, drawing on the shared insights from both sorting and decomposition work.
Abstract Reasoning With Hexagons
Once students can recognize and analyze hexagons, they should apply their understanding to logical reasoning and geometric relationships. One effective activity at this stage is a tessellation challenge.
Provide students with cut outs of regular polygons and challenge them to cover a surface without leaving gaps or overlaps. This task pushes students to apply their understanding of shape properties in a purposeful way, while also introducing them to the concept of tiling and spatial efficiency.
As students work, encourage them to test different combinations and adjust their arrangements. Afterwards, facilitate a discussion around what they noticed. Ask, “Which shapes fit together easily? Which ones left gaps?” and “Were hexagons able to tessellate on their own, or did they need help from other shapes?” These types of questions promote reasoning about angle measures and side lengths without requiring formal calculations.
