Florida B.E.S.T. MA.912.GR.5.4
The Standard
Construct a regular polygon inscribed in a circle. Regular polygons are limited to triangles, quadrilaterals and hexagons.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use a compass, straightedge, protractor, or geometry software to place equally spaced points on a circle. They connect the points to make equilateral triangles, squares, and regular hexagons.
What Mastery Looks Like
- Students accurately create an equilateral triangle, square, and regular hexagon inside given circles. They use compass arcs, diameters, perpendicular lines, or equal central angles, and their construction marks show why the sides are equal.
Common Misconceptions
- Students may place vertices by eye instead of using equal central angles or equal chords. They may confuse any inscribed triangle or quadrilateral with an equilateral triangle or square, or erase the construction marks that show their method.
How to Assess It
- Give students three circles with centers marked, a compass, and a straightedge. In six minutes, have them inscribe an equilateral triangle, square, and regular hexagon, leaving all construction marks.
Lesson moves
Ways to Teach It
Use a compass to step the radius around a paper circle, then connect consecutive marks to build and verify a hexagon.
Explain why perpendicular diameters create a square, using central angles and equal chords in your reasoning.
Run a construction relay where teams draw a shape card, complete it accurately, and leave marks for another team to check.
Design a circular window containing a triangle, square, or hexagon, then list the tools and steps a builder would need.
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Related Standards
- MA.912.GR.6.3
Solve mathematical problems involving triangles and quadrilaterals inscribed in a circle.
- MA.8.GR.1.6
Develop and use formulas for the sums of the interior angles of regular polygons by decomposing them into triangles.
- MA.912.GR.5.3
Construct the inscribed and circumscribed circles of a triangle.
- MA.2.GR.2.2
Find the perimeter of a polygon with whole-number side lengths. Polygons are limited to triangles, rectangles, squares and pentagons.
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