The purpose of this lesson is to further student knowledge and experience with formulas. The students will use the knowledge from the previous lessons in this unit to work problems involving composite figures. This lesson will involve problems requiring various formulas to solve for volume and surface area of composite figures.
Students will use many previously learned skills in this lesson in order to calculate surface area and the missing dimensions when given the surface area or volume. Students will need to have an understanding of substitution and solving equations for a variable. Students will also need to be familiar with converting units of measure.
At the end of this lesson, students will be able to:
use formulas to solve for problems involving volume of composite figures. use formulas to solve for problems involving surface area of composite figures. use formulas to solve for missing dimensions involving volume of composite figures. use formulas to solve for missing dimensions involving surface area of composite figures. apply concepts of density in the context of area and volume.
Student Target
“I can use formulas to calculate
the volume of composite figures.” the surface area of composite figures.” the missing dimensions when given the volume of a composite figure.” the missing dimension when given the surface area of a composite figure.” “I can apply concepts of density for a given area or volume.”
CCR Focus Standards
Geometry - Level D
Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
Geometry - Level E
Supporting Standards
Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.
Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole- number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s^3 and A = 6 s^2 to find the volume and surface area of a cube with sides of length s = 1/2.
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.*
Standards for Mathematical Practice
Make sense of problems and persevere in solving them. (MP.1)
Reason abstractly and quantitatively. (MP.2)
Attend to precision. (MP.6)
KYAE Employability Standards
E.1 Effectively contribute to a team through cooperation, leadership, and giving and accepting critical feedback to work toward a common goal.
E.6 Identify and effectively use skills and materials needed for a particular task.
E.7 Accurately analyze information and respond appropriately.