LESSON PLAN

Regular and Irregular Polygons

Apothem Team

Grade 4 · Geometry

LESSON AT A GLANCE

Warm-up

5 min

Explore

15 min

Consolidate

10 min

Practice

12 min

Exit ticket

3 min

Warm-up

Hold up a square. Is this a regular polygon? (Yes: 4 equal sides, 4 equal angles.) Hold up a rectangle. Is this regular? (No: angles are equal but sides are not all equal.) Hold up a rhombus. Regular? (No: sides equal but angles not all equal.) The distinction requires checking BOTH conditions.

Explore

Polygon classification challenge: 12 polygon cards including regular and irregular examples of each named polygon. Students sort into: regular (both conditions) / irregular (one or both conditions fail). For each, record: number of sides, are sides all equal? are angles all equal? Therefore: regular or irregular?

Consolidate

Practice

Students sort 10 polygon cards, build regular versions of triangles, quadrilaterals, and hexagons on geoboards, and replicate one Yup'ik border pattern segment. Exit ticket: name 2 irregular quadrilaterals and explain why each is irregular.

Exit ticket

TIP Students often think only squares are regular quadrilaterals. A rhombus has equal sides but unequal angles. A rectangle has equal angles but unequal sides (unless it is a square). The square is the only regular quadrilateral.

WORKED EXAMPLES

Is an equilateral triangle regular?

Check: all sides equal? Yes (equilateral means equal sides). All angles equal? Yes (each is 60 degrees). Both conditions: regular polygon.

Name a quadrilateral that has equal sides but is not regular.

A rhombus: 4 equal sides but 2 pairs of equal angles (not all 4 angles equal). It is a diamond shape.

MATERIALS

•Attribute blocks and pattern blocks

•Geoboards

•Ruler and protractor

•Yup'ik border pattern images

•Polygon sorting mats

WATCH FOR

!Students may think any quadrilateral with equal sides is a square. Rhombuses have equal sides but unequal angles: they are not regular.

!Students may not know that all triangles can be classified as scalene (no equal sides), isosceles (2 equal), or equilateral (3 equal, the only regular triangle).