This math lesson focuses on area, which will be used to compute surface area of the birdhouses. Important: It is not the goal of this lesson to teach area formulas for triangles (or other figures) but to reinforce the conceptual framework of area: filling in a two-dimensional figure with square units (like tiles). Area is not "length times width;" area is an attribute of plane figures (3.MD.5b: A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units).

The mathematical purpose is for students to develop their understanding of area beyond "length times width," and to deeply explore two-dimensionality with the use of geoboards. Students should make use of the "length times width" area formula for rectangles (developed in third grade; 3.MD.C.7) to figure out the area of other figures. It is not a goal that they discover "one half base times height" area for triangles; if it does emerge from student exploration, it should be emphasized as a geometric idea, and not reduced to a formula. The “one half base times height” formula is not expected until 6th grade. In fourth grade, exploring the additive nature of area, decomposition and conservation of area are critical to bridge from third grade “area of a rectangle” work and sixth grade area of more general polygons via decomposition/composition (6.G.A.1).

Working in pairs, students will use geoboards to explore the area of

- squares
- rectangles in general
- right triangles
- non right triangles
- five sided composite figures (that could be decomposed into a rectangle and a right triangle)

The area of rectangles can be found using a variety of strategies, for example counting square units, counting by rows and skip counting or multiplying, leading to an understanding that multiplication is repeated addition, and informing the area model of multiplication. In third grade, students use these ideas to develop the fact that the area of a rectangle is the product of its side lengths (3.MD.C.7).

The area of triangles and composite shapes can be found using a variety of strategies, including adding strategies and subtracting strategies, separately or in combination. For example: a right triangle can be seen as half a rectangle; a five sided composite figure can be seen as the sum of its parts or as a larger rectangle with sections subtracted.

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### Materials for this Lesson:

Geoboards