

Unit 6 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 realworld 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 realworld and mathematical
problems.
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 realworld and
mathematical problems. ·
I can determine and
apply the appropriate formula for volume of cylinders to solve realworld and
mathematical problems. ·
I can determine and
apply the appropriate formula for volume of spheres to solve realworld 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 realworld 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 reallife situations? ·
How
can surface area be relevant in reallife situations? ·
How
are some threedimensional figures related to a circle? 
