In the first lesson of the course, students compare the amounts of a plane covered by different shapes and recall what they know about area. The investigations allow students to experience two important ideas that will be made explicit in the next lesson:

• If two figures can be placed one on top of the other so that they match up exactly, then they have the same area.
• The area of a region does not change when the region is decomposed and rearranged.

At the end of this lesson, students are asked to write their best definition of “area.” It is important to let them formulate their definition in their own words. It is especially important to encourage Multilingual learners to use their own words and the words of their peers. In a future lesson, students will revisit the definition of “area” as “the number of square units that cover a region without gaps or overlaps.”

While the mathematics that students explore in this lesson is not complicated and offers a low threshold for entry, it does prompt students to make sense of problems and persevere in solving them (MP1). The activities also enable the teacher to begin setting the expectations for mathematical discourse; that is for students to construct logical arguments and listen to the reasoning of others (MP3).

The lesson allows some time for the teacher to begin establishing classroom norms and routines.

A note about terminology: 

In these materials, when we talk about a two-dimensional figure, such as a rectangle, triangle, or circle, we usually mean the boundary of the figure (such as the sides of a rectangle), not including the region inside. However, we also use shorthand language such as “the area of a rectangle” to mean the “the area of the region inside the rectangle.” The term “shape” could refer to a figure with or without its interior. Although the terms “figure,” “region,” and “shape” are used without being defined precisely for students, help students understand that sometimes our focus is on the boundary (which in this unit will always be composed of black line segments), and sometimes it is on the region inside (which in this unit will be shown in color and referred to as “the shaded region”).

This is the first exercise that focuses on the work of building a mathematical community. Students have the opportunity to think about what a mathematical community is and to share their initial thoughts about what it looks like and sounds like to do math together in a community.