Student Actions

Teacher Actions

• Develop the Ability to Make Conjectures, Models, and Generalizations by examining the characteristics of various special quadrilaterals and making conjectures about the specific properties for any type of special quadrilateral.

• Develop Mathematical Reasoning by modeling the characteristics of quadrilaterals to prove or disprove statements about a given diagram.

• Develop the Ability to Communicate Mathematically by comparing the similarities and differences between various special quadrilaterals to interpret and translate properties for solving mathematical problems.

• Develop Strategies for Problem-Solving by using properties of quadrilaterals and algebraic reasoning to solve for missing angle measures and side lengths. 

• Present engaging problems by implementing a variety of tasks that will allow students to analyze mathematical situations to develop properties for classifying special quadrilaterals..

• Develop procedural fluency by using a variety of diagrams and representations to model quadrilateral problems.

• Pose purposeful questions by encouraging students to share their reasoning about the characteristics of quadrilaterals.

• Encourage productive struggle by having students solve problems algebraically and using proofs.

• Encourage the use of technology when available 

Key Understandings

Misconceptions 

• Classify quadrilaterals by their key characteristics and properties

• All types of special quadrilaterals can be decomposed into triangles.

• Algebraic equations can be made when applying properties of special quadrilaterals to solve for unknown measurements.

• Correctly set up and solve problems using proofs

• A square can be classified as a rectangle but a rectangle can not be classified as a square.

• A rhombus is a special case of a parallelogram. 

• Students may confuse the multiple characteristics and be unable to correctly classify quadrilaterals 

• Students do not understand all squares are classified as rectangles.

• Students do not apply properties of more generic quadrilaterals to very specific quadrilaterals (i.e. Squares have properties of rhombi, rectangles, and parallelograms).

• Students may incorrectly use quadrilateral properties to create an equation while using algebraic methods to solve for angle measures and side lengths.

• Students may not correctly recognize and/or use reasons for statements when using proofs of quadrilateral properties. 

  Knowledge Connections

Prior Knowledge

Leads to 

• Students learned key characteristics and properties of squares, rectangles, trapezoids, isosceles trapezoids, rhombuses, kites, and parallelograms in the middle school grades.

• Represent real-world situations using equations involving one variable. (PA.A.4.3)

• 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 theorems involving the interior and exterior angle sums of polygons to solve problems using mathematical models, algebraic reasoning, and proofs. (G.2D.1.4) 

• Use coordinate geometry and algebraic reasoning to represent and analyze line segments and polygons, including determining lengths, midpoints, and slopes of line segments. (G.2D.1.6) 

• Apply the properties of polygons, and use them to represent and apply mathematical models involving perimeter and area (e.g., triangles, special quadrilaterals, regular polygons up to 12 sides, composite figures). (G.2D.1.7)

• 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)