Lesson 4

Sort Quadrilaterals

Warm-up: What Do You Know About Quadrilaterals? (10 minutes)

Narrative

The purpose of this What Do You Know About _____ is for students to share what they know about and how they can represent quadrilaterals. In previous courses students have drawn and described squares, rectangles, and rhombuses and they will revisit and classify all of these shapes over the next several lessons.

Launch

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

Activity

  • Record responses.

Student Facing

What do you know about quadrilaterals?

Student Response

For access, consult one of our IM Certified Partners.

Activity Synthesis

  • “Draw some examples of quadrilaterals that you know.”
  • Invite a few students to share their quadrilaterals with the rest of the class.
  • “What is this shape called?” (a rectangle)
  • “How else can we draw a rectangle?” (The sides can be longer or shorter.)

Activity 1: Guess Which One? (15 minutes)

Narrative

The purpose of this activity is for students to use language to describe and distinguish quadrilaterals (MP6). The activity has the same structure as the activity where students tried to identify which rectangle on the coordinate grid their partner was thinking of. Students rely on what they remember about categories of quadrilaterals, such as rectangles and rhombuses. They can also use informal language such as tilted, arrow, or red pattern block. The goal of the synthesis is to share and gather language which was helpful for distinguishing the quadrilaterals. 

This activity uses MLR2 Collect and Display. Advances: Conversing, Reading, Writing. 

Representation: Internalize Comprehension. Activate or supply background knowledge. Provide a graphic organizer that lists characteristics of different quadrilaterals for students to use as a reference as they ask questions about the shape.
Supports accessibility for: Memory, Attention, Conceptual Processing

Required Materials

Materials to Gather

Materials to Copy

  • Guess Which One

Required Preparation

  • Consider giving each student a sheet protector and a dry-erase marker so that students can easily reuse the blackline master for multiple rounds of the game.

Launch

  • Groups of 2
  • Distribute the blackline master with the sheet protectors and dry-erase marker to each group or instruct students to use the image of quadrilaterals in their workbook.

Activity

  • 8 minutes: partner work time

MLR2 Collect and Display

  • Circulate, listen for and collect the language students use to describe the quadrilaterals as they sort. Listen for:
    • language and gestures used to describe angles, such as: wide, open, skinny, square, big, small, obtuse, acute, right
    • language and gestures used to describe sides, such as: straight, cross, intersect, parallel, perpendicular
    • language used to describe shapes, such as: square, tilted, flat, trapezoid, rhombus, diamond, arrow, parallelogram
  • Record students’ words and phrases on a visual display and update it throughout the lesson.

Student Facing

  1. Play a round of Guess Which One.

    Partner A: Select one of the quadrilaterals. Do not reveal your choice to your partner.

    Partner B: Ask “yes” or “no” questions to guess which shape your partner picked. After each question, cross out or remove quadrilaterals based on your partner’s answers.

    4 quadrilaterals, left to right, 1 set of parallel sides, 2 sets of parallel sides, 2 sets of parallel sides, looks like arrow head. 
    8 quadrilaterals. 
    5 quadrilaterals. 

    Use the space to record your questions for this round.

  2. Han and Mai were playing Guess Which One. These are the last two shapes. What question can Mai ask to determine which shape is the one that Han picked?

    2 shapes. Both, 2 sets of parallel sides. Both, all equal sides. On right, one right angle labeled. 

If there is time: Switch roles and play Guess Which One again.

Student Response

For access, consult one of our IM Certified Partners.

Advancing Student Thinking

If students do not ask specific questions during this task, collect a set of questions during a practice round and ask, “Which questions could you ask to find out which shaped your partner chose?”

Activity Synthesis

  • “Are there any other words or phrases that are important to include on our display?”
  • As students share responses, update the display, by adding (or replacing) language, diagrams, or annotations.
  • Remind students to borrow language from the display as needed.
  • Invite previously selected students to share.
  • Display rhombus card that is not a square.
  • “What are some names we can use to describe this shape?” (quadrilateral, diamond, parallelogram, rhombus)

Activity 2: Card Sort: Quadrilaterals (20 minutes)

Narrative

The purpose of this activity is for students to sort quadrilaterals that they have worked with in previous grades. Students sort twice using categories of their own choosing and then again using parallel lines. Some categories students may choose include squares, rectangles, and rhombuses but they may also sort according to whether or not the shapes are labeled, how they are oriented, angle size, or side lengths (MP7).

As students work, encourage them to refine their descriptions of quadrilaterals using more precise language and mathematical terms (MP6).

Required Materials

Materials to Copy

  • Card Sort Quadrilaterals (Grade 5)

Required Preparation

  • Create a set of cards from the blackline master for each group of 2. 

Launch

  • Groups of 2
  • Distribute a set of cards to each pair of students.

Activity

  • “In this activity, you will sort some cards into categories of your choosing. When you sort the quadrilaterals, you should work with your partner to come up with categories.”
  • 8 minutes: partner work time
  • Select groups to share their categories and how they sorted their cards.
  • Choose as many different types of categories as time allows.
  • “Now work with your partner to sort your cards using parallel lines.”
  • 5 minutes: partner work time

Student Facing

Your teacher will give you a set of cards.

  1. Sort all of the quadrilateral cards in a way that makes sense to you. Name the categories in your sort.
  2. Sort the quadrilateral cards in a different way and name each of the categories in your new sort.

Student Response

For access, consult one of our IM Certified Partners.

Advancing Student Thinking

If a student does not know whether or not a shape has parallel lines, choose a shape that does have parallel lines and draw dashes to show what the lines would like if they were extended. Choose a shape that does not have parallel lines and prompt the students to draw dashes to extend the lines. Ask, “What is the same and different about the lines in these two shapes?”

Activity Synthesis

  • Invite previously selected students to share.
  • As students share their sorts, ask, “What attributes do all of these shapes have in common?”
  • “How did you use parallel lines to sort the quadrilaterals?” (Some of the quadrilaterals did not have any parallel sides. Some had one pair of parallel sides. And some had two pairs of parallel sides.)
  • Invite students to share examples of the quadrilaterals with no parallel sides, one pair of parallel sides, and two pairs of parallel sides.

Lesson Synthesis

Lesson Synthesis

“Today, we sorted quadrilaterals based on their attributes.”

As students respond to questions, create a large display to be revisited and edited throughout the next few lessons as students learn more about the relationships between different quadrilaterals.

“What are some categories of shapes that are quadrilaterals?” (rhombuses, squares, rectangles, trapezoids, parallelograms)

Draw the shapes as students name them or ask the students to draw the shapes.

“Pick two of the different shapes and share a way they are the same.” (Squares and rectangles have angles that are all 90 degrees. Rhombuses and squares have 4 sides of the same length.)

“Pick two of the different shapes and share a way they are different.” (A trapezoid can have angles of any size while a square always has 90 degree angles. A trapezoid can have all different side lengths while a rhombus has 4 sides that are the same length.)

Keep this as an anchor chart to revisit for the next few lessons as students revise their thinking.

Cool-down: Choose Two (5 minutes)

Cool-Down

For access, consult one of our IM Certified Partners.