This task examines the ways in which the plane can be covered by regular polygons in a very strict arrangement called a regular tessellation. These tessellations are studied here using algebra, which enters the picture via the formula for the measure of the interior angles of a regular polygon (which should therefore be introduced or reviewed before beginning the task). The goal of the task is to use algebra in order to understand which tessellations of the plane with regular polygons are possible.

This activity reinforces the concepts of area and perimeter and their independent relationship. Students analyze and compose shapes made from unit squares that satisfy area and perimeter specifications. Ideas for implementation, extension and support are included along with printable sheets and shape cards.

In this video segment from Cyberchase, the CyberSquad measures Judge Trudy's land claim by using tarps, fence posts and a grid made with rope.

This activity gives students a chance to relate some common three-dimensional solids to their polygonal faces. The object is to put solids in a sequence in which adjacent solids have a polygonal face in common. Ideas for implementation, extension, hints and support are included along with printable cards of the polyhedra.

The CyberSquad proves that the area of Hacker's land is equal to the area of Judge Trudy's land in this video segment from Cyberchase.

This series of problems requires students to apply their knowledge of area and perimeter to find the optimal area given a specified amount of fencing. The problems progress in difficulty as new elements are added to the situation, therefore changing the outcome. This page includes tips for getting started, solution, teachers resource page, and a printable problem page.

The purpose of this task is to have students work on a sequence of area problems that shows the advantage of increasingly abstract strategies in preparation for developing general area formulas for parallelograms and triangles.

The goal of this task is to use geometry study the structure of beehives. Beehives have a tremendous simplicity as they are constructed entirely of small, equally sized walls. In order to as useful as possible for the hive, the goal should be to create the largest possible volume using the least amount of materials. In other words, the ratio of the volume of each cell to its surface area needs to be maximized. This then reduces to maximizing the ratio of the surface area of the cell shape to its perimeter.

This activity allows students to investigate line symmetry and reflections. Using a mirror, students locate the lines of symmetry. in a square and then proceed to find other shapes by reflecting parts of the square. Ideas for implementation, extension and support are included along with a printable worksheet of squares (.doc)

This challenging problem and brainteaser gives students an opportunity to compose and decompose polygons to make rectangles.

Students will take photos of polygons in the real world, find their perimeter, and present their photos and findings in an Adobe Spark creation.

This interactive Flash animation allows students to explore size estimation in one, two and three dimensions. Multiple levels of difficulty allow for progressive skill improvement. In the simplest level, users estimate the number of small line segments that can fit into a larger line segment. Intermediate and advanced levels offer feature games that explore area of rectangles and circles, and volume of spheres and cubes. Related lesson plans and student guides are available for middle school and high school classroom instruction. Editor's Note: When the linear dimensions of an object change by some factor, its area and volume change disproportionately: area in proportion to the square of the factor and volume in proportion to its cube. This concept is the subject of entrenched misconception among many adults. This game-like simulation allows kids to use spatial reasoning, rather than formulas, to construct geometric sense of area and volume. This is part of a larger collection developed by the Physics Education Technology project (PhET).

Learn about the dynamic relationships between a jet engine's heat loss, surface area, and volume in this video adapted from Annenberg Learner's Learning Math: Patterns, Functions, and Algebra.

This lesson focuses on quadrilaterals and attributes in order to classify each shape (parallelogram, rhombus, square, rectangle, and trapezoid). Students will review traits, identify shared traits and names of quadrilaterals, by identifying quadrilaterals in a video story. Then they will show their understanding by creating a quadrilateral story that explains traits and shared traits/names between quadrilaterals.This lesson will take approx 2 math sessions (or approx 120 min.)Thumbnail Image Citation: Bouwhuis, Laura. "Quadrilateral Stories." Canva.com, 11 July 2022, https://www.canva.com/design/DAFGK89WzOM/A_89J6XLB-lNJrcMHjihgg/edit?utm_content=DAFGK89WzOM&utm_campaign=designshare&utm_medium=link2&utm_source=sharebutton

In this problem students use spatial awareness and visualization to solve problems related to reflection (bilateral) symmetry. Learners are given three shapes and must assemble as many different but symmetrical composites as possible. Ideas for implementation, extension and support are included along with printable sheets of the shapes and a poster.

This interactive activity adapted from the Wisconsin Online Resource Center challenges you to plan, measure, and calculate the correct amount of roofing material needed to reroof a house.

This is a lesson plan that introduces rotational and reflectional symmetry with geometric shapes, focusing on regular polygons. Notes (two copies: a student version and also an answer key, both as a Word doc and a PDF), assignment, and cut-out shapes are provided.

This is a lesson plan that introduces rotational and reflectional symmetry with geometric shapes, focusing on regular polygons. Notes (two copies: a student version and also an answer key, both as a Word doc and a PDF), assignment, and cut-out shapes are provided.***The BULK of this lesson (All the really well done parts) were not me, but were done by Kimberly. My addition was the Geogebra aspect

This is a lesson plan that introduces rotational and reflectional symmetry with geometric shapes, focusing on regular polygons. Notes (two copies: a student version and also an answer key, both as a Word doc and a PDF), assignment, and cut-out shapes are provided. There is a final project, with both instructions and an example included. Cover image: Christensen, K., 2022. Reflectional Symmetry of an Atom [screenshot] (Keynote presentation, Rotational and Reflectional Symmetry Assignment).

In this open investigation, students look for connections between shape and number by generating star patterns (regular n-grams) inside a circle. Ideas for implementation, extension and support are included along with a printable sheet (pdf) of circles with marked circumferences.