Curated OER
Area and Perimeter of Regular Polygons - An Extension
Pupils explore the relationship between area and perimeter of polygons.They measure the area and perimeter of regular polygons inscribed in a circle. Learners then discuss how as the number of sides of a regular polygon increase, the...
Willow Tree
Area of Common Geometric Figures
Scholars can use area formulas, but can they apply what they know about area? The lesson challenges learners to think logically while practicing finding area of shapes such as rectangles, circles, parallelograms, triangles, and other...
EngageNY
Proving the Area of a Disk
Using a similar process from the first lesson in the series of finding area approximations, a measurement resource develops the proof of the area of a circle. The problem set contains a derivation of the proof of the circumference formula.
Curated OER
What's your favorite pi?
Sixth graders toss popcorn kernels at a 12? circle inscribed in a 12? square. By counting the number of popcorn kernels that land inside the circle and inside the square the students calculate estimates for the value of pi.
Curated OER
Inscribed Quadrilaterals and Parallelograms
Learners differentiate between inscribed quadrilaterals and parallelograms. In this geometry lesson, students identify the shaped of the polygons when it is inscribed inside of a circle. They calculate the missing angles of the inscribed...
EngageNY
Cyclic Quadrilaterals
What does it mean for a quadrilateral to be cyclic? Mathematicians first learn what it means for a quadrilateral to be cyclic. They then investigate angle measures and area in such a quadrilateral.
Virginia Department of Education
Angles, Arcs, and Segments in Circles
Investigate relationships between angles, arcs, and segments in circles. Pupils use geometry software to discover the relationships between angles, arcs, and segments associated with circles. Class members use similar triangles to...
Willow Tree
Angle Sum Property of Triangles
All triangles have some things in common. Using these properties of triangles, learners find missing angle measures. Scholars use the Angle Sum Property and properties of special triangles throughout the lesson.
Curated OER
The Overlooked Regular Pentagon
Tenth graders discuss the history of geometry as it relates to pentagons. In this geometry lesson, 10th graders solve problems of a pentagon inscribed inside of a circle using ratio. They review other properties for shapes of polygons...
Curated OER
Around The Stop Sign
Learners analyze a drawing of a regular octagon inscribed in a circle to determine angle measures, using knowledge of properties of regular polygons and the sums of angles in various polygons to help solve the problem. They use...
Curated OER
Properties of Arcs, Lengths and Chords
Students differentiate between the different properties of arcs, arc lengths, chords, and chord lengths. For this circles lesson, students calculate the arc length of a given circle, and find the measure of the inscribed angles of a...
Curated OER
Traditional American Indian Lodges
Students explore the mathematical properties of traditional American Indian lodges. They examine the effect of increasing sides of a polygon, calculate the surface area of prisms and cylinders, and construct a classroom size pyramid...
Curated OER
Moving On: Octagoning the Circle
Students explore circles through the use of octagons. They inscribe a circle in a regular octagon and find the area and perimeter of the hexagon with respect to the radius of the circle. Students present their findings to the class.
Curated OER
Infinite Secrets
Students duplicate the method that Archimedes used to estimate the value of pi. They complete a data table and find the approximate values of pi for three sets of polygons.
Curated OER
Pape's Theorems
In this math worksheet, students find the length of the side of a regular hexagon whose area is numerically equal to its perimeter.
EngageNY
How Do Dilations Map Angles?
The key to understanding is making connections. Scholars explore angle dilations using properties of parallel lines. At completion, pupils prove that angles of a dilation preserve their original measure.
Curated OER
History and the Approximations of pi
Middle schoolers investigate Pi. For this mathematics lesson, learners discuss the history of Pi and determine how the approximation of Pi was discovered.
Curated OER
Area Of A Circle
Fifth graders experience a lesson to investigate the methods for finding the area of a circle. They use the drawing of segments in order to visualize how a circle can be proposed of many parts. Then students brainstorm in order to derive...
Curated OER
Mineralogy, Astronomy, & Ancient Wisdom
Students complete a variety of activities surrounding minerals, crystals, and mineralogy. They locate common minerals on a world map, complete a lab in which they identify the chemical and physical properties of various minerals, etc.
Curated OER
Exploring Centers of a Triangle: Part 1
Students use problem solving skills, formal geometry, and The Geometer?s Sketchpad. They model and solve two real-world problems by constructing the in center and circumcenter of triangles.