This lesson focuses on using attributes to define categories of shapes. Polygons are the first category of shapes that are defined using attributes.
Polygons and Nonpolygons
Distribute a copy of the What Is a Polygon? practice worksheet (M-3-4-1_What is a Polygon and KEY.docx) to each student.
Explain that both a set of polygons and a set of nonpolygons are shown. Ask students to review the polygons and nonpolygons and look carefully for the differences between these two sets. Using these two sets, ask students to work in groups of 2 or 3 to decide if all of the six figures are polygons or not.
When the groups are finished, discuss each figure as a class. Ask different groups to indicate if each shape is a polygon or not. Ask students to explain their thinking. Students will likely use informal language to describe characteristics of the shape and make comparisons to the sets of polygons and nonpolygons. The informal language may include closed, straight, round, crossing, sides, and so on. Use a document camera, if possible, to project the worksheet so students can point out characteristics of a shape as they are discussing whether or not it is a polygon.
After all six examples have been discussed, ask students to describe polygons and shapes that are not polygons. Record the characteristics of polygons and nonpolygons in a table on the board as shown.
Polygons
|
Not Polygons
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sides are straight
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some sides are curvy
|
sides don’t cross
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some sides cross
|
closed
|
not closed
|
many straight sides
|
|
After this discussion, ask students to draw an example of a polygon and a nonpolygon in the space provided. Use this opportunity to informally assess students’ understanding of polygons. Observe students as they are drawing these examples, and help any struggling students by reviewing the characteristics of a polygon as listed in the table.
Finally, ask all students to work together as a class to describe a polygon. Help students agree on a way to describe a polygon using words. This will result in an informal student-created definition of a polygon. An informal definition is acceptable for third grade students, but be sure the definition is accurate. It is important that students realize a polygon is closed, all sides are line segments and not curves, and the sides only meet at the endpoints and do not intersect elsewhere. Following is a formal definition of a polygon.
- A polygon is a closed plane figure bounded by three or more line segments that only meet at their endpoints.
Once the class has generated an informal definition, ask students to record the definition on their What Is a Polygon? practice worksheets.
Quadrilaterals and Nonquadrilaterals
Distribute a copy of the What Is a Quadrilateral? practice worksheet (M-3-4-1_What is a Quadrilateral and KEY.docx) to each student.
Explain that both a set of quadrilaterals and a set of nonquadrilaterals are shown. Ask students to review the quadrilaterals and nonquadrilaterals and look carefully for the differences between these two sets. Using these two sets, ask students to work in groups of 2 or 3 to decide if each of the six figures are quadrilaterals or not.
[Note: This activity is likely to be easier for students than the previous What Is a Polygon? activity. Quadrilaterals can be identified merely by counting the number of sides of polygons to determine if there are exactly four.]
When the groups are finished, discuss each figure as a class. Ask different groups to discuss whether or not each shape is a quadrilateral. Ask students to explain their thinking.
After this discussion, ask students to draw an example of a quadrilateral and a nonquadrilateral in the space provided, and ask students to write sentences to describe a quadrilateral. Use this opportunity to informally assess students’ understanding of quadrilaterals through observation.
Finally, ask all students to work together as a class to describe a quadrilateral. This is a formal definition of a quadrilateral that is very accessible to third grade students:
- A quadrilateral is a polygon with exactly four sides.
Students will likely not have been so succinct in their description, so encourage them to use this definition.
Concave and Convex Polygons
Distribute a copy of the Concave or Convex? practice worksheet (M-3-4-1_Concave or Convex and KEY.docx) to each student.
Explain that both a set of concave polygons and a set of convex polygons are shown. Ask students to review the concave and convex polygons and look carefully for the differences between these two sets. Using these two sets, ask students to work in groups of 2 or 3 to decide if each of the six polygons are concave or convex.
When the groups are finished, discuss each figure as a class. Ask different groups to discuss whether each polygon is convex or concave. Ask students to use words to prove their answers. Students will likely use informal language to describe characteristics of the convex and concave polygons. Students are often successful in remembering concave polygons as those that have a cave, whereas convex polygons do not. Use a document camera, if possible, to project the worksheet so students can point out characteristics of a shape as they are discussing whether a polygon is concave or convex.
After all six examples have been discussed, ask students to draw an example of a convex and a concave polygon in the space provided, and ask students to write sentences to describe convex and concave polygons. Use this opportunity to informally assess students’ understanding of convex and concave polygons through observation.
[Note: Although concave and convex seem to be challenging terms, it is important to introduce these terms to students. From earlier grades, students tend to only be familiar with convex polygons such as squares, rectangles, trapezoids, pentagons, and so on. Without considering concave polygons, students could mistakenly believe the only quadrilaterals are squares, rectangles, parallelograms, rhombi, and trapezoids. Students need to understand that other concave quadrilaterals exist in order to be able to identify quadrilaterals that do not belong to any of the previously listed subcategories. This task is specifically required of third grade students as stated in the standards, and this task is the focus of Lesson 2 in this unit.]
Extension:
Use the suggestions in this section to tailor the lesson to meet the needs of the students. Students who are ready for a challenge beyond the requirements of the standard should be introduced to new terms and additional properties of polygons. Specific resources to support these students are provided in the Expansion section.
- Routine: During the school year, ask students to describe objects in the classroom using the appropriate vocabulary, including polygons, quadrilaterals, and concave and convex polygons. For example, ask them to identify three quadrilaterals in the classroom. Continue to emphasize that a circle is not a polygon, as this is a common misconception.
- Small Groups: Students who need additional practice may by pulled into small groups to work on the following activity.
Create a set of index cards that includes examples and nonexamples of each term, including polygons, quadrilaterals, concave and convex polygons. (You may choose to cut out the examples and nonexamples from the practice worksheets used in this lesson and paste them individually on index cards.) Create an index card with each term, such as polygons and nonpolygons, and place these on the table apart from one another.
Flip the pile of index cards over so the shapes are not showing. Be sure they are shuffled. Ask individual students to pick one index card, look at the shape, and place it in the appropriate group. The other students must decide why they agree or disagree about the placement of the card. Be sure to ask them to explain their reasoning, using specific terms about the attributes of the shape. Continue this until all shapes have been sorted into the groups.
Repeat the game using quadrilaterals and nonquadrilaterals and concave and convex polygons.
Students who may benefit from additional practice can use the games found using the links below to identify and name triangles, rectangles, squares, pentagons, hexagons, and so on.
http://www.mathplayground.com/matching_shapes.html
http://illuminations.nctm.org/ActivityDetail.aspx?ID=73
http://www.bbc.co.uk/bitesize/ks1/maths/shapes/play/
- Expansion: The Polygon Capture game is recommended for students who are ready for a challenge beyond the requirements of the standard:
http://illuminations.nctm.org/LessonDetail.aspx?ID=L270
[Note: Although there are side cards and angle cards, it would be appropriate to have students play with only the side cards. Once they have mastered playing with only the side cards, you can encourage them to play with both side and angle cards.]