Unit 1 - Shapes and Designs

By the end of this unit, students are expected to:

Properties of Polygons: 

• Explore the ways that polygons are sorted into families according to the number and length of their sides and the size of their angles

• Explore the patterns among interior and exterior angles of a polygon

• Explore the patterns among side lengths in a polygon

• Investigate the symmetries of a shape-rotation or reflection

• Determine which polygons fit together to cover a flat surface and why

• Reason about and solve problems involving various polygons

Relationships Among Angles: 

• Investigate techniques for estimating and measuring angles

• Use tools to sketch angles

• Reason about the properties of angles formed by parallel lines and transversals

• Use information about supplementary, complementary, vertical, and adjacent angles in a shape to solve for an unknown angle in a multi-step problem

Constructing Polygons: 

• Draw or sketch polygons with given conditions by using various tools and techniques such as freehand, use of a ruler and protractor, and use of technology

• Determine what conditions will produce a unique polygon, more than one polygon, or no polygon, particularly triangles and quadrilaterals

• Recognize the special properties of polygons such as angle sum, side-length relationships and symmetry, that make them useful in building, design, and nature

• Solve problems that involve properties of shapes

Helping At Home

When your child encounters a new problem, it is a good idea to ask questions such as:

• What determines whether two shapes are similar?

• What is the same and what is different about two similar figures?

• When figures are similar, how are the side lengths, areas, and scale factors related?

• How can I use similar figures to find missing measurements?

Shapes and Designs - Explanation of Concepts for Those Helping at Home - Connected Mathematics 3 Resource