Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
INTERPRETATION OF OBJECTIVE - G.GMD.A.3
I hope you don't need me to interpret this one :)
(1) The student will be able to calculate the perimeter and circumference of 2-D figures.
(2) The student will be able to calculate the area of 2-D figures.
(3) The student will be able to calculate the volume of prisms, cylinders, pyramids, cones and spheres.
THE BIG IDEA
Now that we have established the origin of the formulas we will use them to solve problems. Area and Volume problems arise in many fields - shipping, efficiency, optimization....
TRAPS & PITFALLS
Often problems are made more complex by not simply giving the student the height of the solid. These problems definitely make the situation more difficult - using the slant height or even a lateral edge to get the height forces the student to visualize those relationships and that is often difficult.
The student needs to come with the area and volume formulas and a strong skill base when working with irrational values.
Area and volume are topics that continue at the next levels. Optimization questions, area under the curve, volume through rotation all come in later math and this objective sets the stage for them.
MY REFLECTIONS (over line l)
This unit has some of my favorite demonstrations and problems. I love doing the relationship between the prism and the pyramid pouring demonstration. I love the classic area problem of the goat tied to the barn. Area and volume are just great problems - not too difficult but often the limiter is not the formula but the visualization skills of the students. I love the visual nature of the unit and how depending on the way you see it - it will alter your approach compared to another. We have been teaching this stuff in geometry forever....