Page 189 - Mathematics GRADE 9, DE-STREAMED (MTH1W)

E1.4 Geometric and Measurement Relationships
show how changing one or more dimensions of a two-dimensional shape and a three-dimensional object affects perimeter/circumference, area, surface area, and volume, using technology when appropriate
Teacher supports
Examples
• dimensions that may change:
o side length(s) of a polygon
o radius or diameter of a circle
o side length(s) and/or height of a prism or pyramid o height and/or radius of a cylinder or cone
• technology: o coding
o interactive simulations
o spreadsheets
o dynamic, interactive geometry tools
Instructional Tips
Teachers can:
• support students in visualizing, verbalizing, and verifying problems by having them:
o visualize the results of a change in one or two dimensions of a two-dimensional shape or
one, two, or three dimensions of a three-dimensional object;
o verbalize to other students what they were visualizing in their thinking; o verify their thinking with or without the use of technology;
• provide tasks that involve making connections to proportional reasoning, such as doubling or tripling side lengths.
Teacher Prompts
• If you double the height and the base of a rectangle, what happens to its perimeter? What happens to its area?
• If one of the dimensions of a right prism increases, what needs to happen to the other dimensions for the volume to stay the same?
• If the height of a cylinder is halved, and all other dimensions stay the same, what happens to the area of its curved surface?
• Is it possible to have pyramids with different dimensions and the same volume? Explain why or why not.
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