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Grades 9/10/11 Measurement, Geometry, and Trigonometry
Pythagorean Theorem. Measurement of 2D figures and 3D solids. Optimization. Geometric relationships. Triangle trigonometry. Angles in standard position and trigonometric identities.
This is one of seven strands of the CEMC Grade 9/10/11 courseware. The other strands and more information about this courseware is available on the Grade 9/10/11 homepage.
Unit 1: The Pythagorean Theorem, Measurement, and Optimization
In this lesson, we will explore how rectangles with the same perimeter may have different areas. We will develop strategies and tools to determine the maximum area of rectangles with a fixed perimeter in different settings.
In this lesson, we will explore how rectangles with the same area may have different perimeters. We deepen our understanding of strategies and tools used for mathematical optimization to determine the minimum perimeter for rectangles with a fixed area.
Conservation of materials and heat are some of the applications of minimizing the surface area of 3D objects. In this lesson, we will make connections between the dimensions and surface area of cylinders and square-based prisms using different strategies to find the optimal shape.
This last optimization lesson makes connections between cylinders and square-based prisms with a fixed surface area and its shape when the volume is maximized.