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 what they know about finding the areas of basic figures to find areas of composite figures.Key ConceptsA composite figure is a figure that can be divided into two or more basic figures.The area of a composite figure can be found by dividing it into basic figures whose areas can be calculated easily.For some figures, the area can also be found by surrounding the figure with a basic figure, creating other basic figures “between” the original figure and the surrounding figure. The area of the original figure can then be found by subtracting the basic figure.Goals and Learning ObjectivesFind the area of composite figures by decomposing and composing them into more basic figures. 

This lesson is from Tools for NC Teachers. In this lesson, students design four flower beds and explore various strategies for finding the areas and perimeters of rectilinear figures. This is remixable.

This lesson is from Tools 4 NC Teachers. In this lesson students will apply their previous knowledge of finding the volume of rectangular prisms to more complex figures which can be decomposed into rectangular prisms. Students will explore the additive nature of volume in these types of figures.

This lesson is from Tools 4 NC Teachers. In this lesson, students explore finding volume of two non-overlapping rectangular prisms using the context of a toy factory called Cubix. It is remixable.

This lesson is from Tools 4 NC Teachers. In this lesson students will explore volume as additive using concrete objects and pictorial representations. This is remixable.

This lesson is from Tools 4 NC Teachers. In this lesson students will explore volume as additive by looking at non overlapping rectangular prisms. This is remixable.

This task is from Tools 4 NC Teachers. Students determine the volume of joined, non-overlapping rectangular prisms. This is remixable.