Sketching Quadrilaterals

Getting Started

The student does not understand how to use attributes to classify quadrilaterals.

The student makes mistakes with each of the descriptions. He or she does not have an effective strategy to use the ruler and protractor to ensure that the sketches match the given descriptions. The student:

• Does not understand the defining attributes of parallelograms, rhombi, trapezoids, and rectangles. He or she cannot explain the differences in the shapes, even in general terms.
• Does not understand the meaning of perpendicular sides. 

What do you know about parallelograms? What do you know about the sides of a parallelogram?

What is the definition of a rhombus? Can a square also be a rhombus? Why or why not?

What do you know about right angles? Can you use this protractor to draw a right angle? What type of sides do the rays of the right angle form? If we are trying to sketch a parallelogram, how would you draw the opposite sides? If the opposite side must also have perpendicular lines and perpendicular lines form a right angle, is it possible for a parallelogram to have exactly one right angle?

What are trapezoids? How would you explain the definition of a trapezoid to someone?

What is the definition of a rectangle? Can a rectangle also be a parallelogram? Why or why not?

How are parallel and perpendicular sides different?

Provide opportunities for the student to sort quadrilaterals based on attributes of the shapes. Have the student work with a partner and discuss similarities and differences between the shapes.

Have the student keep a math journal of shapes, write the attributes of the shapes, and then draw pictures to represent each of the shapes based on their attributes.

Provide instruction on rhombi. Model describing the shapes based on their attributes using formal language (e.g., a rhombus is a quadrilateral that has four equal sides and its opposite sides are parallel).

Provide instruction on the meaning of perpendicular sides. Consider using the MFAS task Parallel and Perpendicular Sides.

Making Progress

The student makes errors in his or her explanations and sketches.

The student has some understanding of the defining attributes of quadrilaterals, but he or she makes some errors. He or she understands some defining attributes, but only explains shapes in general terms (e.g., a parallelogram is always slanted). The student:

• Says a parallelogram with exactly one right angle is impossible because:
  
  • Parallelograms have slanted corners.
  • Parallelograms do not have right angles.
• Says a trapezoid with at least one right angle is impossible because:
  
  • A trapezoid does not have a right angle.
  • Trapezoids only have acute and obtuse angles.
• Struggles to correctly draw a rhombus with at least one set of perpendicular sides. 

What do you know about parallelograms? What do you know about the sides of a parallelogram?

What is the definition of a rhombus? Can a square also be a rhombus? Why or why not?

What do you know about right angles? Can you use this protractor to draw a right angle? What type of lines do the rays of the right angle form? If we are trying to sketch a parallelogram, how do you draw the opposite sides? If the opposite side must also have perpendicular lines and perpendicular lines form a right angle, is it possible for a parallelogram to have exactly one right angle?

What are trapezoids? How would you explain the definition of a trapezoid to someone?

What is the definition of a rectangle? Can a rectangle also be a parallelogram? Why or why not?

Provide additional opportunities for the student to sketch quadrilaterals based on given attributes. Have the student work with a partner to discuss and determine if a shape can be sketched or if it is impossible.

Provide opportunities for the student to explain quadrilaterals and their attributes using precise language.

Got It

The student provides complete and correct responses to all components of the task.

The student correctly sketches the quadrilaterals and clearly articulates, using precise language, why some of the shapes are impossible. The student:

• Says that a parallelogram with exactly one right angle is impossible. He or she explains that if a parallelogram has one right angle, it must have more than one. The student says that a parallelogram is a quadrilateral that has two pairs of parallel sides. So if a parallelogram has one right angle, a parallelogram actually has four right angles if the sides are parallel.
• Says that a rhombus with at least one set of perpendicular sides is possible. The student then sketches a square. The student explains that a rhombus has four sides that are equal in length.
• Says a trapezoid with at least one right angle is possible. He or she correctly draws a trapezoid with a right angle.
• Says a rectangle that is not a parallelogram is impossible. He or she explains that a rectangle has two pairs of parallel sides and that a parallelogram has two pairs of parallel sides. Therefore, a rectangle is also a parallelogram. 

What are all the ways a square can be classified?

Another student said that a parallelogram only has slanted sides. How would you convince the student this is incorrect?

Can a square be a rectangle? Can a square be a rhombus?

Can a rhombus also be a rectangle? How do you know? Can also rectangles also be classified as rhombi? Why or why not?

Consider using the MFAS task Sketching Triangles.

Encourage the student to sort various quadrilaterals into a Venn Diagram.