• ## Module 5: Constructing and Measuring

In this module, students build on their experiences with angles and triangles and introduce the construction of familiar geometric objects. They will construct basic geometric objects with a compass and straightedge and later use these techniques to construct triangles. Students will use patty paper to investigate special types of angle relationships and then use those relationships to write and solve equations to determine unknown values in a figure. They will use their knowledge of polygons and polyhedra to create and describe cross-sections of right rectangular prisms and pyramids. Finally, students will extend their knowledge of volume and surface area to solve problems involving a variety of three-dimensional solids.

• This topic begins by establishing the building blocks of geometry, using appropriate drawings, vocabulary, and notation. Students use construction tools to duplicate segments and angels, explore different pairs of angles, and write and solve equations involving the angle pairs. Then they use patty paper and formal construction tools to determine if given information defines a unique triangle, multiple triangles, or no triangles.
• MATHia Workspaces (2)
• Calculating Angles
• Classifying Angles and Determining Unknown Measures

Topic 2: Three-Dimensional Figures

• This topic builds students' spatial sense and visualization abilities to help them see connections between two- and three-dimential objects. Students practice using volume formulas to investigate the effect on the volume of doubling and tripling dimensions and to solve composite volume problems and calculate surface areas of pyramids and prisms.
• MATHia Workspaces (5)
• Visualizing Cross Sections of Three-Dimensional Shapes
• Understanding Volume Formulas for Right Prisms
• Using Volume of Right Prisms
• Calculating Volume of Pyramids
• Using Volume of Pyramids