Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.
In this 90 minute lesson/exploration of Cavalieri's Principle using technology (GeoGebra 5.0), students calculate volume of oblique solids and determine if Cavalieri's applies to given scenarios.
Students will perform transformations of a base figure in a 3 dimensional coordinate system to observe the creation of right and oblique solid figures. After these observations, students will create a conjecture about calculating the volume of the oblique solids. Students will use the conjecture to determine situations in which Cavalieri's applies and calculate volumes of oblique solids.
The teacher may choose to split lesson into two 45 minute sessions.
Variable representation of volume formulas V = BH and V = 1/3BH:
B = Base Area
H = Height of Solid
b = length of base figure
h = height of base figure
The differentiation is used so that the height of the solid is not confused with the height of the base.