Page 46 - Math 9-10 (2009)

FOUNDATIONS OF MATHEMATICS, GRADE 9, APPLIED (MFM1P) 45
show that the volume of a pyramid [or cone] is the volume of a prism
[or cylinder] with the same base and height, and therefore that
Vpyramid = or
– solve problems involving the volumes of prisms, pyramids, cylinders, cones, and spheres (Sample problem: Break-bit Cereal is sold in a single-serving size, in a box in the shape of a rectangular prism of dimen- sions 5 cm by 4 cm by 10 cm.The manu- facturer also sells the cereal in a larger size, in a box with dimensions double those of the smaller box. Make a hypothesis about the effect on the volume of doubling the dimensions. Test your hypothesis using
the volumes of the two boxes, and discuss the result.).
Investigating and Applying Geometric Relationships
By the end of this course, students will:
– determine, through investigation using a variety of tools (e.g., dynamic geometry software, concrete materials), and describe the properties and relationships of the interior and exterior angles of triangles, quadrilaterals, and other polygons, and apply the results to problems involving the angles of polygons (Sample problem: With the assistance of dynamic geometry soft- ware, determine the relationship between the sum of the interior angles of a poly- gon and the number of sides. Use your conclusion to determine the sum of the interior angles of a 20-sided polygon.);
Vprism
3
Vpyramid =
1 3
(area of base)(height)
3
);
– determine, through investigation using a variety of tools (e.g., dynamic geometry software, concrete materials), and describe the properties and relationships of the angles formed by parallel lines cut by a transversal, and apply the results to prob- lems involving parallel lines (e.g., given
a diagram of a rectangular gate with a supporting diagonal beam, and given the measure of one angle in the diagram, use the angle properties of triangles and paral- lel lines to determine the measures of the other angles in the diagram);
– create an original dynamic sketch, paper- folding design, or other illustration that incorporates some of the geometric properties from this section, or find and report on some real-life application(s) (e.g., in carpentry, sports, architecture)
of the geometric properties.