Unit 5

Area, Surface Area, and Volume Problems

Math

Unit Length and Description:

25 days

In Unit 5, students apply their knowledge of expressions and equations to solve for unknowns in area, surface area, and volume problems. They find the area of triangles and other two-dimensional figures and use the formulas to find the volumes of right rectangular prisms with fractional edge lengths. Students use negative numbers in coordinates as they draw lines and polygons in the coordinate plane. They also find the lengths of sides of figures, joining points with the same first coordinate or the same second coordinate and apply these techniques to solve realworld and mathematical problems.

Standards:

Enduring Understandings:

·        Decomposing and rearranging provide a geometric way of both seeing that a measurement formula is the right one and seeing why it is the right one.

·        Tools provide new sources of imagery as well as specific ways of thinking about geometric objects and processes.

·        Geometry and special sense offer ways to visualize, to interpret, and to reflect on our physical environment.

·        A net is a plane figure that can be folded to make a solid figure.

·        Solid figures can be identified and classified by the number of faces, edges, and vertices.

·        A visual representation of a shape hierarchy is an efficient way to describe the relationship among shapes with similar attributes.

Essential Questions:

·        What is a real world application of surface area?

·        How is a net utilized to represent a 3D figure?

·        How is volume affected by a change in one dimension?

·        What are the similarities and differences between area and surface area?

·        What are the properties of two- and three- dimensional figures?

·        What is the relationship between the areas of rectangles and triangles?

·        How is the formula for the area of a rectangle used to find the volume of a rectangular prism?

·        How is finding the volume of a rectangular prism similar to finding the volume of a pyramid?

·        How does the change in height affect the volume or surface area of a prism?

·       How can you estimate the volume or surface area of a prism or a pyramid?