This is a lesson for learning about area and perimeter of rectangles.

This corresponds to "College and Career Ready" standard (3.MD.7a) -- Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
(I was not able to find that standard here.)

This is a hands-on guided lesson for relating area to factors. Students will model area of rectangles using Cheez-Its and define factors as the dimensions of the rectangles.

An interactive applet and associated web page showing how to find the area and perimeter of a square from the coordinates of its vertices. The square can be either parallel to the axes or rotated. The grid and coordinates can be turned on and off. The area and perimeter calculation can be turned off to permit class exercises and then turned back on the verify the answers. The applet can be printed as it appears on the screen to make handouts. The web page has a full description of the method for determining area and perimeter, a worked example and has links to other pages relating to coordinate geometry. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

An interactive applet and associated web page that demonstrate the area of a square. The applet shows a square with all vertices draggable. As you drag any one, the area id continuously calculated and shown on the applet. The square is filled with a unit grid to allow class estimation of area. The displayed calculation can be turned off. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

Through this lesson and its two associated activities, students are introduced to the use of geometry in engineering design, and conclude by making scale models of objects of their choice. The practice of developing scale models is often used in engineering design to analyze the effectiveness of proposed design solutions. In this lesson, students complete fencing (square) and fire pit (circle) word problems on two worksheets—which involves side and radius dimensions, perimeters, circumferences and areas—guiding them to discover the relationships between the side length of a square and its area, and the radius of a circle and its area. They also think of real-world engineering applications of the geometry concepts.

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.

Overall Goal: During this lesson we will cover basic shapes and learn how they can be used in everyday objects. Our goal is for students to know the basic shapes, find them in objects such as playgrounds, be able to create their own playground using shapes, and finally be able to tell the class about the playground they made and the shapes used.  Standard: K.G.3: Model shapes in the world by composing shapes from objects (e.g., sticks and clay balls) and drawing shapes. Learning Objectives: The students will be able to show they know what each of the basics shape are by correctly drawing a square, triangle, rectangle, circle, and oval.Students will be able to create playground with the basic shapes by using everyday objects such as play-doh, craft sticks, etc.Students will be able to complete the project by creating their dream playground; using all of the shapes covered in the lesson.Students can explain their playgrounds and shapes they used, and why their specific playground represents their “dream playground” by presenting their project to the class. Key Terms:SquareRectangleTriangleOvalCircle Lesson Introduction:We will visit the school playground to have the students find the different shapes in the playground equipment. We want students to use the playground visit to help them decide how they would build their dream playground using the basic shapes. We will give the students a packet (found in the Resources section) that includes a few activities for them to do before the main lesson. They will take this to the playground and fill out the second page by writing down the different playground structures that fit each shape. They will be able to explore the playground on their own, so that they can have different answers than each other. Main Lesson:In class, we will have the students create, by drawing, their ‘dream playground’ using the specific basic shapes they are given to work with (squares, triangles, circles, rectangles, and ovals). They will be given 20 minutes to complete their drawing. They will be able to draw this on paper or use a computer application to create this.After this, the students will be given play-doh and popsicle sticks to recreate the shapes and structures that they had on their paper. The crafting process should take around 50 minutes. The drawings and crafts will be assessed by if the students correctly demonstrate their knowledge of the different shapes and how to create them.At the end, the kids will present their own playgrounds to the class and show what shapes they used and be able to explain and defend why it is their dream playground. This is so that the teacher can tell if the student knows the shapes and is able to defend their argument of what makes it a dream playground. The students will be able to use pencil and paper to draw or use tablets/iPads and use a drawing application. Lesson Ending:When the students are done creating their projects, they will each present their playgrounds to the class and explain the individual shapes that they used. The students will also explain why they believe their playground model is the best. The students should answer the following questions when they defend why their playground is the best. How many of each shape are in your playground? Is one of the five shapes better for making playgrounds than the others and why? The way that we can assess is if the student created the shapes correctly and correctly referenced them in their presentation. Rubric:The students will be graded as Good, Average, or Poor. The following is what they are going to be graded on:Students know basic shapesStudents use shapes correctly to build a playgroundStudents complete all parts of the projectStudents present their playgrounds to the class and can explain how they built their playground with the basic shapes Differentiation:This project should not affect students of different gender, race, culture, or sexual identity. Students with behavioral challenges will be worked more one-on-one than the other students to make sure that any confusion or frustration will be handled. The higher ability learners can go beyond the four shapes specified, if they feel comfortable. The project does not require out of school time where they would absolutely need a computer or Wifi access.Examples:If high ability students feel like they can add shapes that are not on the required list, they may do so with permission from the teacher. They will not be given any extra credit for adding other shapes, but this is a good way for the teachers to see where some students are at academically.If there is a child with dyslexia they will receive extra help from the teacher to be sure that they can accurately read the instructions on the papers.If a student needs to use a computer drawing application for sketching the playground because of a disability but doesn’t understand how to use it, they may come into class early to spend some extra time navigating the site.Since the students will be doing a worksheet after the activity, there might be students who struggle with reading. If the students struggle with reading the worksheet, they may ask, and we will help them through the parts that they find confusing. If the student has translation issues with some of the words, we will also help them translate it. This will be done just through being familiar with the material and specific language. Anticipated Difficulties:There could be difficulty with children being distracted at the playground and while crafting. We will need to be sure that everyone is staying on task by keeping them engaged during all of the activities. Children can sometimes become distracted if they are just listening to someone speak and by keeping them engaged and involving them during all of the lesson they will be more likely to stay focused. When on the playground we can use students to help point out the shapes that we find and also ask questions during this time to keep students attentive. Students might be at different learning levels and could struggle with learning the shapes. If so, we could always split the children into a few groups based on learning levels to help the lesson run smoother.

Students will look at examples and non-examples of squares and rectangles to determine properties of the two shapes. Students practice drawing the shapes with specific dimensions and building up to is a square also a rectangle and is a rectangle also a square?

Students will look at examples and non-examples of squares and rectangles to determine properties of the two shapes. Students practice drawing the shapes with specific dimensions and building up to is a square also a rectangle and is a rectangle also a square?

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. 

(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.

During the warm-up students will review how to sign shapes and the cardinal numbers from the slideshow. For the main activity, students will pair up and each grab a picture card without showing it to their partner. One student will describe the picture card being specific to location, color, etc, while the other draws what their partner just described to them. The partners will then switch roles.

Students investigate parallelogram properties to figure out which properties apply to special parallelograms.

From paving your patio to measuring the ingredients for your latest recipe, squares, roots and powers really are part of everyday life. This unit reviews the basics of all three and also describes scientific notation, which is a convenient way of writing or displaying large numbers.