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.
The alternative formats for some lessons are currently under construction. These will be completed in the coming months.
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.
Unit 2: Geometric Relationships
In this lesson, we will explore the properties and relationships of the interior and exterior angles of quadrilaterals and other polygons. We will apply these properties in solving angle problems and to verify conjectures.
In this lesson, we will investigate and describe properties of polygons. These properties will involve either the midpoints of the sides of the polygon, or the diagonals of the polygon.
Unit 3: Trigonometry
In this lesson, we learn how to compute the sine, cosine, and tangent ratios corresponding to oblique angles and vice versa. We see that determining the oblique angle associated with a given sine ratio can give rise to ambiguities. This leads into a discussion of the ambiguous case of the sine law.
In this lesson, we use trigonometric tools developed for two-dimensional right-angled and oblique triangles to solve problems in three-dimensional settings.
Unit 4: Angles in Standard Position and Trigonometric Identities
This lesson introduces angles drawn in standard position in order to extend our understanding of trigonometric ratios beyond acute angles.
In this lesson, we connect angles in standard position to their related acute angles to evaluate trigonometric ratios and find angles. We will also relate negative angles and angles greater than \(360^\circ\) to their coterminal angles between \(0^\circ\) and \(360^\circ\).