QUADRILATERALS

This week, I thought it would be helpful to merge some of the activities we did in class into one lesson plan to help introduce fourth grade level students to quadrilaterals.

I also drew some information from the Utah Education Network:

“To aid understanding, teach quadrilaterals as a whole. Define quadrilaterals as a four-sided figure and give students the opportunity to create a variety of quadrilaterals. They look for similarities and differences and sort them into several different categories according to their attributes. The sorting activity offers insight into the mathematical hierarchy used in classifying quadrilaterals. It will become clear that every quadrilateral falls into three categories:

  1. those with two pairs of parallel sides,
  2. those with only one pair of parallel sides, and
  3. those with no parallel sides.

This activity will set the stage for students to understand that many types of quadrilaterals exist and that these shapes have some elements in common.”

Another introduction activity I find essential would be to make poster boards with different comparisons like “rhombus vs. square,” “rectangle vs. square,” etc. over large Venn diagrams. and split the classroom into groups so they can write down what they think are different and similar between them. After the groups are finished they can present their findings to the class. Allow the rest of the class to respond to what other groups found.

Here is more from UEN that I would borrow for my classroom. Some of the activities are similar to what we did in class with geoboards, sorting, and Venn diagrams.

Invitation to Learn
Provide each student with a geoboard and geoband. Ask them to create several four-sided polygons, then choose their most unique quadrilateral to share with their group.

Instructional Procedures

  1. Ask the students to compare their quadrilateral with those made by other members in their group. Are all quadrilaterals different? If not, agree on how to make them look different. Record quadrilateral on Geodot Paper and cut shape out for display.
  2. Invite each group to post their quadrilaterals in one of three columns:
    1. those with one pair of parallel sides,
    2. those with two pairs of parallel sides, and
    3. those with no parallel sides.

    Give students time to determine if all the quadrilaterals are in their appropriate columns. Discuss congruent and similar shapes and remove any duplicates.

  3. Identify the columns with the appropriate headings: trapezoids (one pair of parallel sides),parallelograms (two pair of parallel sides), and trapeziums (no parallel sides).
  4. Use the Quadrilateral Family Tree handout to discuss the properties, attributes, and characteristics, as well as the interconnective and hierarchical commonalities and differences, between and among quadrilateral shapes.
    1. Have the students look at the relationship between squares and rectangles. What are the characteristics of each? Is a square a rectangle? (Yes, it has four equal angles.) Are all rectangles squares? (No, many rectangles do not have four equal angles and four equal sides.)
    2. Have the students look at the relationship between squares and rhombuses. What are the characteristics of each? Is a square a rhombus? (Yes, it has four equal sides.) Are all rhombuses squares? (No, many rhombuses do not have four equal sides and four equal angles.)
    3. A Venn Diagram is a good visual aid to illustrate that a square is both a rectangle and a rhombus.
  5. Further explore the relationships between quadrilaterals by having the students work with roping quadrilaterals. Provide each pair of students a set Quadrilateral Pieces and two or three pieces of string to make a Quadrilateral Venn Diagram. Ask them to place the appropriate quadrilateral pieces in each ring according to the following labels:

    Ring 1 (Left side): At least one pair of parallel sides
    Ring 2 (Right side) No sides parallel

    Ask students to justify their placement of different pieces. What do all the shapes in one ring have in common? How might the shapes in one ring be different? (Some shapes in Ring 1 are trapezoids, and some are parallelograms.) What different label would eliminate one or more of the shapes from a ring? (Only one pair of parallel sides.) If we drew a giant circle around everything, including any shapes that are outside the rings, what might the label for this new ring be? (Quadrilaterals) Try further explorations using the following labels:

Ring 1 (Inner ring): All sides of equal length
Ring 2 (Outer ring): At least one pair of parallel sides

Ring 1 (Left side): At least one right angle
Ring 2 (Right side): No right angles

Ring 1 (Left side): All sides the same length
Ring 2 (Right side): At least one acute angle

Ring 1 (Left side): At least one set of parallel sides
Ring 2 (Right side): At least one obtuse angle

To test for understanding I could have my students write reflections explaining where they would place quadrilaterals or have them place them on a Venn diagram. A good relationship to have students explain is between the rectangle, rhombus, and square.

As I reflect on this activity, I wonder how I would choose to break up these activities in a unit and what things would be important to include that I may have forgotten. I also wonder if there is anything that I could cut out or if I need to take a different direction with some activities to aid learning of students with different abilities. Overall, I enjoyed looking through our work over this unit, and learned a lot when reflecting on what was helpful for me as a learner.

I think this lesson adds a sense of ownership to the material for the students. They can work in a small group setting and share some ideas that they might not have in front of the whole class. They also have the opportunity to share what they have done- to feel some pride over their work.

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