Students will identify the attributes of shapes and use those attributes to draw and describe shapes. This lesson contains a detailed plan, pictures of student work, and videos of the lesson in action.

Quadrilaterals are explored in this video lesson. The tutorial describes the characteristics of various quadrilaterals. Students can check their understanding with an assessment. [6:17]

This lesson will demonstrate how to use slope, midpoint, and distance formulas to determine from the coordinates of the vertices if a quadrilateral is a parallelogram in a coordinate plane. Students can check their understanding with an assessment. [12:13]

Coordinate geometry of rectangles is investigated in this video lesson. The tutorial demonstrates how to use the midpoint, distance, and slope formulas to determine if a quadrilateral is a rectangle on a coordinate plane. [17:26]

Shows how to locate a missing vertex of a rectangle when you know the coordinates of the other three vertices. [2:40]

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How do shape and weight impact the performance of a fidget spinner? This challenge will explore how shapes, weight and force impact the performance of a fidget spinner. Engineering a mechanical device involves designing with a result in mind. This challenge will ask students to explore math, science and engineering design through the device of a fidget spinner.

This is a 3-hour lesson that includes a self-paced interactive module and classroom activities. The teacher guide includes a challenge sequence (timeline), relevance to standards, materials list, assessment, evaluation rubric, and learning extensions.

Lesson objectives: (1) Investigate the basic shapes that make up a fidget spinner. (2) Explore how a fidget spinner works. (3) Design, build and test your own fidget spinner.

This video tutorial investigates how to draw three-dimensional figures in a three-dimensional space. [5:44]

Demonstrates how to follow written directions for drawing a trapezoid on a coordinate plane. [2:41]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

Browse resources related to second-grade math standards. Click on a topic for interactive lessons, videos, and extra practice.

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Students watch a video overview on lines, curves and vertices of two dimensional shapes.

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Graph geometric figures given the ordered pairs of vertices.

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The instructional tool explores various geometric solids and their properties. Student can manipulate and color the different shapes. Learners examine the edges, faces, and vertices of the different solid figures.

An interactive game to find number of edges, surfaces and vertices of different geometric shapes.

In this lesson, students will form cubes and discuss their attributes including edges, faces, vertices, and angles. Media resources and teacher materials are included.

In this lesson, students will create cubes and identify the attributes of a cube, including discussion of edges, faces, vertices, and angles. Teacher resources are provided.

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 resource provides in depth information on the conic sections. Click on the underlined words for definitions and diagrams.

Challenge problems involving the coordinates of the vertices of the quadrilaterals Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.