Location and Movement
(taken from “Big Ideas by Dr. Small”):
- Locations can be described using maps, using length and angle measurements, and using coordinate grids.
- Congruent shapes have identical side lengths, angles, perimeters, and areas.
- Similar shapes have identical angles and are the same shape but are a different size.
- There are three motions, or transformations, that change the position of a shape or possibly its orientation, but do not change its size and shape (translations, reflections, and rotations). Other transformations (like dilatations) can affect size.
- Transformations are frequently observable in our everyday world. One example context is a tessellation.
STUDENT LEARNING GOALS:
GOAL #1: I can plot and identify points in all quadrants on the Cartesian plane.
- QUIZ: Coordinates (Source: Nelson Education)
- QUIZ: Coordinate Points (Source: ThatQuiz)
- GAME: Catch the Fly (Source: HotMath)
GOAL #2: I can identify congruent shapes and justify why certain triangles are considered congruent.
- VIDEO: Corresponding Sides and Angles (Source: Virtual Nerd)
- VIDEO: Triangle Congruence Theorems (Source: MashUp Math)
- VIDEO: Proving Triangle Congruence (Source: MathHelp.com)
- QUIZ: Proving Triangles Congruence (Source: ThatQuiz.com)
GOAL #3: I can identify similar shapes and perform dilatations.
- VIDEO: Difference between Congruent and Similar Shapes (Source: MashUp Math)
- VIDEO: Similar Figures (Source: Shmoop)
- VIDEO: Understanding Dilations (Source: Planet Nutshell)
- VIDEO: Dilations (Source: Khan Academy)
- VIDEO: How to Dilate a Shape (Source: MashUp Math)
- VIDEO: Dilations around the Origin (Source: Khan Academy)
- PRACTICE: Dilating Points (Source: Khan Academy)
- PRACTICE: Determining Scale Factors (Source: Khan Academy)
- PRACTICE: Dilating Triangles (Source: Khan Academy)
GOAL #4: I can identify and perform transformations and tessellations.
- Develop an understanding of similarity, and distinguish similarity and congruence;
- Plot points using all four quadrants of the Cartesian coordinate plane;
- Describe location in the four quadrants of a coordinate system, dilatate two-dimensional shapes, and apply transformations to create and analyse designs;
- Identify, through investigation, the minimum side and angle information (i.e., side-side-side; side-angle-side; angle-side-angle) needed to describe a unique triangle (e.g., “I can draw many triangles if I’m only told the length of one side, but there’s only one triangle I can draw if you tell me the lengths of all three sides.”);
- Determine, through investigation using a variety of tools (e.g., dynamic geometry software, concrete materials, geoboard), relationships among area, perimeter, corresponding side lengths, and corresponding angles of congruent shapes;
- Demonstrate an understanding that enlarging or reducing two-dimensional shapes creates similar shapes;
- Distinguish between and compare similar shapes and congruent shapes, using a variety of tools (e.g., pattern blocks, grid paper, dynamic geometry software) and strategies (e.g., by showing that dilatations create similar shapes and that translations, rotations, and reflections generate congruent shapes).
- Identify, perform, and describe dilatations (i.e., enlargements and reductions), through investigation using a variety of tools (e.g., dynamic geometry software, geoboard, pattern blocks, grid paper);
- Create and analyse designs involving translations, reflections, dilatations, and/or simple rotations of two-dimensional shapes, using a variety of tools (e.g., concrete materials, Mira, drawings, dynamic geometry software) and strategies (e.g., paper folding);
- Determine, through investigation using a variety of tools (e.g., pattern blocks, Polydrons, grid paper, tiling software, dynamic geometry software, concrete materials), polygons or combinations of polygons that tile a plane, and describe the transformation(s) involved.