Curriculum Units – Level 5

Geometry is one of the areas of mathematics that is readily apparent in the world around us and practical applications abound. In our unit, Funkytown Fun House: Focusing on Proportional Reasoning and Similarity, students are introduced to similarity and congruence. The foundational mathematics behind these concepts is proportional reasoning. Students explore ratio as a comparison of two quantities. They discover that if the ratio between side lengths and angle measures of two figures is 1:1 (i.e., the measures are identical), then the geometric figures are congruent. They learn that for two figures to be similar their corresponding side lengths must be in proportion, meaning that there is a common ratio that relates corresponding lengths of the sides, and their corresponding angles must be congruent. Students also explore the relationship between congruence and similarity.

After learning about these basic concepts, they explore applications of similarity and congruence, mainly enlargements and reductions in Chapter 1. All the lessons in the entire unit revolve around the Funkytown Fun House in which Stretch the Clown resides. Stretch’s body enlarges and shrinks depending on which day you visit the Funhouse. He also changes shape depending on which room he is in. Students have fun exploring body ratios using Stretch. They also take a look at his miniature car collection and learn how important the concept of similarity is in creating reductions.

In Chapter 2, students become set designers for the Funkytown Fun House. They use their creativity and newfound geometry knowledge to design scale drawings for new rooms in the fun house. They investigate how two- and three-dimensional shapes change when they are scaled up or down. In particular, they examine changes in perimeter, area and volume when dimensions are changed. Some startling mathematical discoveries are made!

These investigations into the properties of, and relationships among, similar shapes afford students many opportunities to develop and evaluate conjectures inductively and deductively. Our focus on verbal and written communication throughout the unit clearly prepares students for creating and understanding more formal proofs as they continue their study of geometry in the upper grades.