Learn about the properties of rectangles, rhombuses, and squares, and practice identifying them. Includes hints for questions. CCSS.Math.Content.3.G.A.1 Understand that shapes in different categories

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This QuickTime movie provides an opportunity to learn about the characteristics of a rectangle. As you watch and listen to the teacher and student interact it helps clarify the thinking behind applying this concept.

Surface Area and Volume

Type of Unit: Conceptual

Prior Knowledge

Students should be able to:

Identify rectangles, parallelograms, trapezoids, and triangles and their bases and heights.
Identify cubes, rectangular prisms, and pyramids and their faces, edges, and vertices.
Understand that area of a 2-D figure is a measure of the figure's surface and that it is measured in square units.
Understand volume of a 3-D figure is a measure of the space the figure occupies and is measured in cubic units.

Lesson Flow

The unit begins with an exploratory lesson about the volumes of containers. Then in Lessons 2–5, students investigate areas of 2-D figures. To find the area of a parallelogram, students consider how it can be rearranged to form a rectangle. To find the area of a trapezoid, students think about how two copies of the trapezoid can be put together to form a parallelogram. To find the area of a triangle, students consider how two copies of the triangle can be put together to form a parallelogram. By sketching and analyzing several parallelograms, trapezoids, and triangles, students develop area formulas for these figures. Students then find areas of composite figures by decomposing them into familiar figures. In the last lesson on area, students estimate the area of an irregular figure by overlaying it with a grid. In Lesson 6, the focus shifts to 3-D figures. Students build rectangular prisms from unit cubes and develop a formula for finding the volume of any rectangular prism. In Lesson 7, students analyze and create nets for prisms. In Lesson 8, students compare a cube to a square pyramid with the same base and height as the cube. They consider the number of faces, edges, and vertices, as well as the surface area and volume. In Lesson 9, students use their knowledge of volume, area, and linear measurements to solve a packing problem.

Lesson OverviewStudents use scissors to transform a net for a unit cube into a net for a square pyramid. They then investigate how changing a figure from a cube to a square pyramid affects the number of faces, edges, and vertices and how it changes the surface area and volume.Key ConceptsA square pyramid is a 3-D figure with a square base and four triangular faces.In this lesson, the net for a cube is transformed into a net for a square pyramid. This requires cutting off one square completely and changing four others into isosceles triangles.It is easy to see that the surface area of the pyramid is less than the surface area of the cube, because part of the cube's surface is cut off to create the pyramid. Specifically, the surface area of the pyramid is 3 square units, and the surface area of the cube is 6 square units. Students will be able to see visually that the volume of the pyramid is less than that of the cube.Students consider the number of faces, vertices, and edges of the two figures. A face is a flat side of a figure. An edge is a segment where 2 faces meet. A vertex is the point where three or more faces meet. A cube has 6 faces, 8 vertices, and 12 edges. A square pyramid has 5 faces, 5 vertices, and 8 edges.Goals and Learning ObjectivesChange the net of a cube into the net of a pyramid.Find the surface area of the pyramid. 

This tutorial provides a brief introduction about what area is, then gives the formulas for area of a square, rectangle, parallelogram, trapezoid, triangle, and circle. Examples of each formula are provided.

Learn how to find the root of a number. Topics covered include two roots, roots of negative numbers, and imaginary numbers. This site offers descriptions along with multiple examples.

Solve this square lamina problem using your visualization skills and other mathematical prolem solving strategies.

Resize and rotate different types of quadrilaterals--square, rectangle, rhombus, trapezoid, and kite--while learning the definitions of these different shapes and labeling the angles and diagonals. CCSS.Math.Content.3.G.A.1 Understand that shapes in different categories

(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 este módulo de 20 días, los estudiantes exploran el área como un atributo de figuras bidimensionales y lo relacionan con su comprensión previa de multiplicación. Los estudiantes conceptualizan el área como la cantidad de superficie bidimensional que está contenida dentro de una figura plana. Llegan a comprender que el espacio puede estar mortal con cuadrados unitarios sin huecos o superposiciones. Hacen predicciones y exploran qué rectángulos cubren la mayor cantidad de área cuando las longitudes laterales difieren. Los estudiantes progresan del uso de manipulaciones de baldosas cuadradas hasta dibujar sus propios modelos de área y manipular matrices rectangulares para demostrar concretamente las propiedades aritméticas. El módulo culmina con estudiantes que diseñan un plano de planta simple que se ajusta a las especificaciones de área dadas.

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

English Description:
In this 20-day module students explore area as an attribute of two-dimensional figures and relate it to their prior understandings of multiplication. Students conceptualize area as the amount of two-dimensional surface that is contained within a plane figure.  They come to understand that the space can be tiled with unit squares without gaps or overlaps.  They make predictions and explore which rectangles cover the most area when the side lengths differ.  Students progress from using square tile manipulatives to drawing their own area models and manipulate rectangular arrays to concretely demonstrate the arithmetic properties. The module culminates with students designing a simple floor plan that conforms to given area specifications.

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

In this lesson on 2D shapes, students will learn to discriminate quadrilaterals from other polygons. Additionally, they will be able to identify attributes of a square, rectangle, and rhombus.

This lesson plan helps students explore the mathematical concept of perimeter. Resources are available to support teacher and students.

Use this applet to find the perimeter of a variety of shapes with the same or different areas.

Students connect algebra to geometric concepts with polygons as they explore the distance formula, slope criteria for parallel and perpendicular lines, and learn to calculate and justify the area and perimeter of polygons.

Purplemath gives several examples which clearly show the process of completing the square to find the maximum and minimum solutions to a quadratic equation.

We are learning about how shape attributes helps us to see how shapes are alike and different. This site provides four resources for shapes including 3-D.

The CyberSquad builds a raft out of squares in order to cross a river in this Cyberchase video [2:05] segment.

In this video segment [2:01] from Cyberchase, the CyberSquad finds that by arranging triangle tiles they are able to create a path that will allow them to cross a river of hot lava.

Find a quick, concise explanation of square roots. An example is given and clearly explained.

Find a quick, concise explanation of area and the formulas for different shapes. An example is given to help you understand how find the area of a shape. The area formulas are listed for different types of shapes.