# Project M³ Curriculum Units — Level 5-6

## Fun at the Carnival: Using Proportional Reasoning

(get the book choose grades 5-6)

In Fun at the Carnival, students explore proportional reasoning with a focus on similarity and congruence. They study ratio as a comparison of two quantities. They discover that if the ratio between the corresponding side lengths and angle measures of two figures is 1:1 (i.e., the measures are identical), then the figures are congruent. They learn that for two figures to be similar, their corresponding side lengths must be in proportion and their corresponding angles must be congruent. Students also explore the relationship between congruence and similarity, learning that all congruent figures are similar, but not all similar figures are congruent.

After learning these basic concepts, students explore applications of similarity and congruence (mainly enlargements and reductions). All the lessons in the entire unit revolve around Stretch the Clown. Students have fun exploring body ratios using Stretch and his cousin, Juggles the Clown. Students also take a look at Stretch’s miniature car collection and learn how important the concept of similarity is in creating reductions.

In Chapter 2, students become set designers and use their creativity and newfound knowledge to design drawings for new rooms and mirrors for the Fun House. They investigate how 2- and 3-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!