Student Actions

Teacher Actions

• Develop a deep and flexible conceptual understanding by actually decomposing polygons into rectangles (physically cutting paper polygons, breaking apart manipulative and computer models, drawing decomposition lines on pictorial models).

• Develop strategies for problem solving by identifying multiple ways a figure may be decomposed into rectangles, while concluding that the total area does not change.

• Develop mathematical reasoning by applying understanding of the properties of rectangles, recognizing that opposite sides of a rectangle are congruent, and using this understanding to find unlabeled measures in a pictorial model of a polygon.

• Implement tasks that promote reasoning and problem solving by giving students multiple opportunities to apply their growing understanding of this objective in varied contexts (physically cutting paper polygons, breaking apart manipulative and computer models, drawing decomposition lines on pictorial models).

• Elicit evidence of student thinking by asking students to share their solution strategies and justify their conclusions, and use this evidence to assess progress toward student understanding.

Key Understandings

Misconceptions

• When a polygon can be decomposed into rectangles, it is possible to find the area of the polygon by finding the area of each rectangle, then adding the areas together. 

• The area of a figure is related to, or is the same as, its perimeter.
• Only squares can be labeled with "square units".
• Adding the length of the sides of a figure is the way to find area.