Student Actions

Teacher Actions

• Develop a Deep and Flexible Conceptual Understanding by identifying the difference between area and perimeter and explaining the units for the area are squared.

• Develop Accurate and Appropriate Procedural Fluency by modeling diagrams and descriptions of polygons to find the area and perimeter.

• Develop a deep and flexible conceptual understanding by analyzing mathematical situations and determining how and when to apply specific properties of polygons to solve problems involving perimeter and area.

• Develop accurate and appropriate procedural fluency when developing efficient procedures and flexibility in utilizing properties of polygons to solve area and perimeter problems.

• Develop strategies for problem-solving when examining a variety of mathematical models of polygons and determining appropriate strategies for application of polygon properties in contexts of perimeter and area 

• Pose purposeful questions by guiding classroom discussions and encouraging students to explain their reasoning when applying properties of polygons to solving problems involving area and perimeter  

• Promote reasoning and problem-solving skills by implementing tasks that encourage students to analyze and decipher information from diagrams to solve for perimeter and area

• Use and connect mathematical representations that allow students to apply properties of polygons to model contextual situations involving area and perimeter.

• Encourage the use of technology when available. 

Key Understandings

Misconceptions 

• Calculate the perimeter of various polygons in mathematical situations

• Calculate the area of various regular and non-regular polygons in mathematical situations by applying the appropriate properties of the polygon (such as side length).

• Calculate the side length of a polygon when given area or perimeter and other side lengths.

• A regular polygon has congruent side lengths.

• Composite figures are shapes created by combining two or more polygons. 

• Students confuse area with perimeter.

• Students do not use the correct units of measurement when labeling the perimeter or area of a polygon.

• Students may not recognize appropriate polygon properties for determiningthe area or perimeter of a composite figure.

• Students don’t know how to calculate a side length when given area or perimeter and other side lengths.

• Students struggle with identifying the formula for area of a specific polygon. 

  Knowledge Connections

Prior Knowledge

Leads to 

• Calculate the surface area of a rectangular prism using decomposition or nets. Use appropriate units (e.g., cm2).(PA.GM.2.1) 

• Use knowledge of solving equations with rational values to represent, use and apply mathematical models (e.g., angle measures, geometric formulas, dimensional analysis, Pythagorean theorem, science, statistics) and interpret the solutions in the original context. (A1.A.1.1)  

• Apply the properties of special quadrilaterals (square, rectangle, trapezoid, isosceles trapezoid, rhombus, kite, parallelogram) to solve problems involving angle measures and segment lengths using mathematical models, algebraic reasoning, and proofs. (G.2D.1.5) 

• Apply the properties of congruent or similar polygons to solve problems using mathematical models and algebraic and logical reasoning. (G.2D.1.8)

• Represent, use, and apply mathematical models and other tools (e.g., nets, measuring devices, formulas) to solve problems involving surface area and volume of three-dimensional figures (prisms, cylinders, pyramids, cones, spheres, composites of these figures). (G.3D.1.1) 

• Use ratios derived from similar three-dimensional figures to make conjectures, generalize, and to solve for unknown values such as angles, side lengths, perimeter, and circumference of a face, area of a face, and volume. (G.3D.1.2)