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.
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.
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).
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 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. 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.
In this activity students try to visualize 3-D shapes from given 2-D silhouettes (projections). Students can describe, draw, model or relate their ideas to objects in their environment. With several possible answers for each silhouette, students become more familiar with using the terms and describing the properties of solid figures. The Teachers' Notes page includes suggestions for implementation, discussion questions, ideas for extension and support. A warmup activity called "Skeleton Shapes" is offered (cataloged separately). [Note: "torch" in the UK = "flashlight" in the US.]
This activity gives students practice drawing straight lines with a ruler and looking for and categorizing shapes, for example, by the number of sides in polygons. The Teachers' Notes page includes suggestions for implementation, discussion questions and ideas for extension.
This activity gives students an opportunity to explore some of the common 3-D shapes and their names and properties. After discussion and an example, it asks students to count the required number of edges and vertices (corners) to build each of 5 given shapes. The Teachers' Notes page includes suggestions for implementation, discussion questions, ideas for extension and support, and a printable recording sheet (pdf).
This problem provides students with an opportunity to discover algebraic structure in a geometric context. More specifically, the student will need to divide up the given polygons into triangles and then use the fact that the sum of the angles in each triangle is 180_.
This activity asks students to visualize shapes, paying close attention to the definitions of special polygons. Learners are given a sheet of isometric grid paper and asked to find and sketch 12 specific shapes. Ideas for implementation, extension and support are included along with printable grids and shape definitions.