Lesson 5

The purpose of this What Do You Know About Trapezoids is for students to share what they know about and how they can represent trapezoids.

• “What do you know about trapezoids?”
• 1 minute: quiet think time

• Record responses.

• “Draw some examples of trapezoids.”
• Invite a few students to share their trapezoids with the rest of the class.
• “How do you know these are trapezoids?” (They have one pair of parallel sides or they have at least one pair of parallel sides.)

The purpose of this activity is for students to define a trapezoid and to explore two definitions for a trapezoid. The exclusive definition of a trapezoid states that a trapezoid has exactly one pair of opposite sides that are parallel. The inclusive definition states that a trapezoid has at least one pair of opposite sides that are parallel. Students choose whichever one makes sense to them and look at a parallelogram through the lens of that definition. In the synthesis, students see how the different definitions impact how a trapezoid fits into the hierarchy of quadrilaterals (MP7). This activity also gives students a chance to plot and label coordinates on the coordinate grid.

• Display:
  • “Some parallelograms are rectangles.”
  • “All parallelograms are squares.”
• “Is each statement true or false?” (I think that a parallelogram can be a rectangle but it does not have to be a square.)
• 1 minute: partner discussion

• Groups of 2
• 5 minutes: independent work time
• 5 minutes: partner work time
• Monitor for students who:
  • draw an isosceles trapezoid
  • draw a non-isosceles trapezoid

If a student does not recognize whether their trapezoid is a square, rectangle, or rhombus, co-create an anchor chart with examples and characteristics of these shapes.

• Display: isosceles trapezoid and non-isosceles trapezoid from student solution or use student work
• “How are these two shapes the same? How are they different?” (They both have a pair of parallel sides. One has a pair of equal sides. The other one does not.)
• Display parallelogram from the last problem in student workbook and this text:

  “A trapezoid . . .”

  “. . . has exactly one pair of opposite sides parallel.”

  “. . . has at least one pair of opposite sides parallel.”

• “According to which definition is this shape a trapezoid? Why?” (the second definition because it has 2 pairs of parallel sides)
• “We’ll continue to explore these two definitions further in the next activity.”

The purpose of this activity is to further explore the two definitions of trapezoids and the hierarchy of quadrilaterals. Students evaluate different statements relating trapezoids and parallelograms deciding whether they are true or false with each definition. The activity synthesis establishes the convention for these materials that a trapezoid is a quadrilateral with at least one pair of parallel sides. As students discuss and justify their decisions, they reason clearly using the 2 definitions of trapezoid (MP6).

• Groups of 2.
• Display 2 Venn diagrams for parallelograms and trapezoids.
• “What do you notice? What do you wonder?” (One diagram shows parallelograms are part of trapezoids and the other one shows there is no overlap.)
• 1 minute: partner discussion

• 5 minutes: independent work time
• 5 minutes: partner work time
• Monitor for students who:
  • can articulate the differences between the two definitions
  • draw examples of shapes to help evaluate each statement
  • accurately explain the difference between the two definitions

If students do not sort the statements correctly, suggest they sort the shape cards from an earlier lesson according to the two definitions. Then show them one statement at a time and ask, “Is this statement true of all the shapes in one of these groups?”

• Invite previously selected students to share.
• “Some people use the first definition of the trapezoid. We will be using the second definition.”
• Display Venn diagrams from student workbook.
• “What does each diagram mean?” (Definition 2 shows that a parallelogram is a trapezoid but a trapezoid doesn’t have to be a parallelogram. Definition 1 shows that trapezoids and parallelograms are distinct: a parallelogram can't be a trapezoid and a trapezoid can't be a parallelogram.)
• “Which diagram matches the definition of trapezoid we will use?” (The one on the right, Definition 2, because if a shape is a parallelogram it is also a trapezoid, but if a shape is a trapezoid, it doesn’t have to be a parallelogram.)
• Consider asking students to draw:
  • A trapezoid that is also a parallelogram.
  • A trapezoid that is not a parallelogram.