This classroom task gives students the opportunity to prove a surprising fact about quadrilaterals: that if we join the midpoints of an arbitrary quadrilateral to form a new quadrilateral, then the new quadrilateral is a parallelogram, even if the original quadrilateral was not.

This is a reasonably direct task aimed at having students use previously-derived results to learn new facts about parallelograms, as opposed to deriving them from first principles. The solution provided (among other possibilities) uses the SAS trial congruence theorem, and the fact that opposite sides of parallelograms are congruent.

This lesson unit is intended to help teachers assess how well students are able to: choose appropriate mathematics to solve a non-routine problem; generate useful data by systematically controlling variables; and develop experimental and analytical models of a physical situation.

In this unit you will see first how to convert vectors from geometric form, in terms of a magnitude and direction, to component form, and then how conversion in the opposite sense is accomplished. The ability to convert between these different forms of a vector is useful in certain problems involving displacement and velocity, as shown in Section‘_2, in which you will also work with bearings.

Students are challenged to use computer-aided design (CAD) software to create “complete” 3D-printed molecule models that take into consideration bond angles and lone-pair positioning. To begin, they explore two interactive digital simulations: “build a molecule” and “molecule shapes.” This aids them in comparing and contrasting existing molecular modeling approaches—ball-and-stick, space-filling, and valence shell electron pair repulsion (VSEPR)—so as to understand their benefits and limitations. In order to complete a worksheet that requires them to draw Lewis dot structures, they determine the characteristics and geometries (valence electrons, polar bonds, shape type, bond angles and overall polarity) of 12 molecules. They also use molecular model kits. These explorations and exercises prepare them to design and 3D print their own models to most accurately depict molecules. Pre/Post quizzes, a step-by-step Blender 3D software tutorial handout and a worksheet are provided.

This resource was created by Brittany Wolfgram, in collaboration with Dawn DeTurk, Hannah Blomstedt, and Julie Albrecht, as part of ESU2's Integrating the Arts project. This project is a four year initiative focused on integrating arts into the core curriculum through teacher education, practice, and coaching.

This is a lesson plan for a project based learning activity geared towards high school students who are enrolled in a geometry class. The project has the students discover how geometry is connected to real world situations instead of being just a subject taught in a classroom. The Indiana Academic Standards that may apply to this activity are G.LP.2, G.T.1, G.T.5, G.QP.1, G.CI.4, G.TS.3, and G.TS.5.

This is a lesson plan for a project based learning activity geared towards high school students who are enrolled in a geometry class. The project has the students discover how geometry is connected to real world situations instead of being just a subject taught in a classroom. The Indiana Academic Standards that may apply to this activity are G.LP.2, G.T.1, G.T.5, G.QP.1, G.CI.4, G.TS.3, and G.TS.5.

The purpose of this task is to engage students in an open-ended modeling task that uses similarity of right triangles, and also requires the use of technology.

(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.)

Este módulo final del año de 40 días ofrece a los estudiantes una práctica intensiva con problemas de palabras, así como experiencias prácticas de investigación con geometría y perímetro. El módulo comienza con la resolución de problemas de palabras de uno y dos pasos basados ​​en una variedad de temas estudiados durante todo el año, utilizando las cuatro operaciones. A continuación, los estudiantes exploran la geometría. Estudiantes Tessellate para la experiencia de la geometría de puente con el estudio del perímetro. Las parcelas de línea, familiares del Módulo 6, ayudan a los estudiantes a sacar conclusiones sobre las mediciones de perímetro y área. Los estudiantes resuelven problemas de palabras que involucran área y perímetro utilizando las cuatro operaciones. El módulo concluye con un conjunto de lecciones atractivas que revisan brevemente los conceptos fundamentales de grado 3 de fracciones, multiplicación y división.

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

English Description:
This 40-day final module of the year offers students intensive practice with word problems, as well as hands-on investigation experiences with geometry and perimeter.  The module begins with solving one- and two-step word problems based on a variety of topics studied throughout the year, using all four operations.  Next students explore geometry.  Students tessellate to bridge geometry experience with the study of perimeter.  Line plots, familiar from Module 6, help students draw conclusions about perimeter and area measurements.  Students solve word problems involving area and perimeter using all four operations.  The module concludes with a set of engaging lessons that briefly review the fundamental Grade 3 concepts of fractions, multiplication, and division.

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

In this lesson, students will learn that math is important in navigation and engineering. Ancient land and sea navigators started with the most basic of navigation equations (Speed x Time = Distance). Today, navigational satellites use equations that take into account the relative effects of space and time. However, even these high-tech wonders cannot be built without pure and simple math concepts basic geometry and trigonometry that have been used for thousands of years. In this lesson, these basic concepts are discussed and illustrated in the associated activities.

This task applies geometric concepts, namely properties of tangents to circles and of right triangles, in a modeling situation. The key geometric point in this task is to recognize that the line of sight from the mountain top towards the horizon is tangent to the earth. We can then use a right triangle where one leg is tangent to a circle and the other leg is the radius of the circle to investigate this situation.

Do you like to paint? Watch this step by step video as artist Kristin Farr demonstrates how to paint your very own "Magic Hecksagon," which is a colorful, geometric design inspired by folk art. She uses a plethora of different colors to bring a sense of motion to her work. Watch and learn more in the interview with Kristin Farr: http://youtu.be/OX1r-3-VK-0

Do art and math have anything in common? How do artists and architects use math to create their works? In these lessons, students will explore the intersection of math and art in the works of two artists and one architect for whom mathematical concepts (lines, angles, two-dimensional shapes and three-dimensional polyhedra, fractions, ratios, and permutations) and geometric forms were fundamental.

This shows how Newton's method (also known as Newton-Raphson) is used to find a root of a function. You can show/hide various parts of the construction, and edit the particular function being considered.

 This problem-based learning module is designed to engage students in solving a real problem within the community.  The question being “How can I help my community get digitally connected?”  Students will choose to investigate one of three solutions of making wifi available in our school district to the most populated areas. They will either choose to put Wifi on bus, placing hotspots in the community or using kajeet.   The students will be using Google Earth Pro to place circles on a map and calculating the area of these circles.  Students will make a model of these circles onto a hard copy using scale factor. At the conclusion, the students will present findings to administration, the board of education, state and local leaders as well as their peers.  These findings can be presented through the choice of a display board, flyer, video production or prezi.This blended module includes teacher-led discussion, group-led investigation and discussions along with technology integration.