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.

In this activity, learners use a hand-made protractor to measure angles they find in playground equipment. Learners will observe that angle measurements do not change with distance, because they are distance invariant, or constant. Note: The "Pocket Protractor" activity should be done ahead as a separate activity (see related resource), but a standard protractor can be used as a substitute.

This lesson unit is intended to help you assess how well students are able to use geometric properties to solve problems. In particular, it will support you in identifying and helping students who have the following difficulties: Solving problems relating to using the measures of the interior angles of polygons; and solving problems relating to using the measures of the exterior angles of polygons.

In this math activity, learners explore the history of the Stomachion (an ancient tangram-type puzzle), use the pieces to create other figures, learn about symmetry and transformations, and investigate the areas of the pieces. The Stomachion, believed to have been created by Archimedes, consists of 14 pieces cut from a square, which can be rearranged to form other interesting shapes.

This 3 lesson instructional unit helps students investigate many different aspects of triangles including basic properties of triangles, building other shapes from triangles, the dependence of the third side length on the other two (Triangle Inequality Theorem), and the Sierpinski Triangle fractal. The lesson includes student activity sheets and links to interactive applets.

This 3 lesson instructional unit helps students investigate many different aspects of triangles including basic properties of triangles, building other shapes from triangles, the dependence of the third side length on the other two (Triangle Inequality Theorem), and the Sierpinski Triangle fractal. The lesson includes student activity sheets and links to interactive applets.

This familiar game can be played by one or two players taking turns. Players choose to match equivalent representations of numbers, shapes, fractions, or multiplication facts. The game can be played in clear pane mode, or for added challenge, with the windows closed.

In this primary grades Illuminations lesson, students identify figures on a football field. They look for both congruent and similar figures, and they consider figures that are the same but that occur in a different orientation because of translation, rotation, or reflection. The lesson includes a student worksheet and discussion questions.

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.

Using this tool, students build these classic fractals: the Koch snowflake, a fractal tree, a reduced square, and the Sierpinksi triangle. As these shapes grow and change using an iterative process, students can observe patterns in the images created and in the table of values as the fractals progress through several stages.

In Module 3, students learn about dilation and similarity and apply that knowledge to a proof of the Pythagorean Theorem based on the Angle-Angle criterion for similar triangles.  The module begins with the definition of dilation, properties of dilations, and compositions of dilations.  One overarching goal of this module is to replace the common idea of “same shape, different sizes” with a definition of similarity that can be applied to geometric shapes that are not polygons, such as ellipses and circles.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

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.

The applets in this Interactive Geometry Dictionary (IGD) will allow students an opportunity to explore finding the area of some common shapes. The applets demonstrate how to find the area of a triangle using the area of a parallelogram, which in turn can be found using the area of a rectangle. This tool also supports the lesson "What's My Area" cataloged separately.

This Java interactive tool can be used to create dynamic drawings on an isometric dot grid, and to explore volume, surface area, and congruence concepts. Users can draw figures using edges, faces, or cubes and can shift, rotate, color, decompose, and view figures in 2‑D or 3‑D with this applet. Instructions on using and exploring with the tool are included on the page. A related multi-lesson unit from Illuminations for middle school students is linked to the side.

In this activity, learners slide shapes to create unusual tiled patterns. Learners transform a rectangle into a more interesting shape and then make a tessellation by repeating that shape over and over again. Learners will also calculate the area of a rectangle. This activity works best as a "centers" activity.

In this three-lesson unit, students participate in activities in which they focus on connections between mathematics and children’s literature. Three pieces of literature are used to teach geometry and measurement topics in the mathematics curriculum, i.e. using and describing geometric figures, estimating the volume of an irregular solid, and exploring the need for a standard unit of length. Activity worksheets and ideas for extension are included.

In this series of three hands-on activities, students develop an understanding of the relationship between fractions, decimals, and percents based upon models of hundredths. Each activity requires students to display their one hundred pieces of candy in a different way: linear model, grid model (rectangular area), and region model (circle graph/pie chart). This lesson includes student worksheets, assessment questions, extension suggestions, and a link to a circle graph tool.

(Nota: Esta es una traducción de un recurso educativo abierto creado por el Departamento de Educación del Estado de Nueva York (NYSED) como parte del proyecto "EngageNY" en 2013. Aunque el recurso real fue traducido por personas, la siguiente descripción se tradujo del inglés original usando Google Translate para ayudar a los usuarios potenciales a decidir si se adapta a sus necesidades y puede contener errores gramaticales o lingüísticos. La descripción original en inglés también se proporciona a continuación.)

En el módulo 3, los estudiantes aprenden sobre la dilatación y la similitud y aplican ese conocimiento a una prueba del teorema de Pitagorean basado en el criterio de ángulo de ángulo para triángulos similares. El módulo comienza con la definición de dilatación, propiedades de las dilataciones y composiciones de dilaciones. Un objetivo general de este módulo es reemplazar la idea común de la misma forma, diferentes tamaños con una definición de similitud que se puede aplicar a formas geométricas que no son polígonos, como elipses y círculos.

Encuentre el resto de los recursos matemáticos de Engageny en https://archive.org/details/engageny-mathematics.

English Description:
In Module 3, students learn about dilation and similarity and apply that knowledge to a proof of the Pythagorean Theorem based on the Angle-Angle criterion for similar triangles.  The module begins with the definition of dilation, properties of dilations, and compositions of dilations.  One overarching goal of this module is to replace the common idea of “same shape, different sizes” with a definition of similarity that can be applied to geometric shapes that are not polygons, such as ellipses and circles.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

This math meets ecology lesson provides hands-on experiences with mixing oil and water, provides surface area information about the 2010 oil spill in the Gulf of Mexico, and gives learners opportunities to estimate small oil spills of their own making. This lesson guide includes questions for learners, assessment options, extensions, and reflection questions.

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