Unit 6
Volume and Surface Area of Three Dimensional Figures

 

Grade 8

Math 

Unit Length and Description:

 

15 days

 

In Unit 6, students will know and use formulas for the volume and surface area of cones, cylinders, and spheres to model and solve real-world and mathematical problems.  To solve real life situations, students will model geometric relationships with formulas involving three dimensional figures, as they reason both abstractly and quantitatively.  This unit gives students the opportunity to practice their procedural skill and fluency with irrational numbers and radicals in a geometric context through volume of cones, cylinders, and spheres.  Students will also solve for unknown measures of right triangles in three dimensions including cones, pyramids, and prisms as an application of the Pythagorean Theorem.

 

Standards:

 

8.G.C.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

 

  • Standards Clarification:  It is the expectation of this standard that students have an understanding of why the formula works and how the formula relates to the measure (volume) and the figure.  Students should be able to give approximate answers and answers in terms of pi. 

 

Focus Standards of Mathematical Practice:

 

MP.1 Make sense of problems and persevere in solving them.

MP.2 Reason abstractly and quantitatively.

MP.3 Construct viable arguments and critique the reasoning of others.

MP.4 Model with mathematics.

MP.5 Use appropriate tools strategically.

MP.6 Attend to precision.

MP.7 Look for and make use of structure.

MP.8 Look for and express regularity in repeated reasoning.

 

Instructional Outcomes:

Full Development of the Major Clusters, Supporting Clusters, Additional Clusters and Mathematical Practices for this unit could include the following instructional outcomes:

 

8.G.C.9

·        I can determine and apply the appropriate formula for volume of cones to solve real-world and mathematical problems.

·        I can determine and apply the appropriate formula for volume of cylinders to solve real-world and mathematical problems.

·        I can determine and apply the appropriate formula for volume of spheres to solve real-world and mathematical problems.

·        I can apply the formulas for the volume of different objects, when given the volume of the object and asked to determine other characteristics (i.e. radius, diameter, height, approximate for pi, etc.).

·        I can determine and apply the appropriate cone, cylinder, and sphere volume formula in order to solve real-world and mathematical problems.

·        I can compare the volume of cones, cylinders, and spheres.

 

Enduring Understandings:

 

·        There is a relationship between the volume of cylinders and volume of cones to the corresponding formulas.

·        There is a relationship between the volume of cylinders and volume of spheres to the corresponding formulas.

·        Volume is a measure related to the amount of space occupied.

·        Surface area is a measure of all the areas of all the shapes that cover the surface of an object.

·        Geometric attributes (such as shapes, lines, angles, figures, and planes) provide descriptive information about an object’s properties and position in space and support visualization and problem solving.

 

Essential Questions:

 

·        How does geometry better describe objects?

·        Why are formulas important in math and science?

·        How can volume be relevant in real-life situations?

·        How can surface area be relevant in real-life situations?

·        How are some three-dimensional figures related to a circle?