Characteristics of Polygons
Characteristics of Polygons
Objectives
This unit introduces students to simple polygons and the attributes which make them similar to and different from one another. Students will:
- identify polygons, nonpolygons, parallelograms, quadrilaterals, rectangles, rhombi, squares, trapezoids, convex and concave polygons, describe their attributes, and sort based on attributes.
- Use characteristics to classify quadrilaterals into subcategories of quadrilaterals, including parallelograms, rectangles, rhombi, squares, and trapezoids.
- partition polygons into equal parts and name the equal parts as unit fractions written in words and symbols.
Essential Questions
- How can patterns be used to describe relationships in mathematical situations?
- How can recognizing repetition or regularity assist in solving problems more efficiently?
- How can the application of the attributes of geometric shapes support mathematical reasoning and problem solving?
- How can geometric properties and theorems be used to describe, model, and analyze situations?
- How are spatial relationships, including shape and dimension, used to draw, construct, model, and represent real situations or solve problems?
Related Unit and Lesson Plans
Related Materials & Resources
The possible inclusion of commercial websites below is not an implied endorsement of their products, which are not free, and are not required for this lesson plan.
Polygons
- http://www.math-play.com/Polygon-Game.html
- http://www.mathsisfun.com/geometry/quadrilaterals-interactive.html
- 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/
- http://illuminations.nctm.org/LessonDetail.aspx?ID=L270
- http://www.mathplayground.com/geoboard.html
Unit Fractions
- http://www.topmarks.co.uk/Flash.aspx?f=EggFractions
- http://www.mathopolis.com/games/ordering-frac-unit.php
Formative Assessment
-
View
Multiple-Choice Items:
- Which shows a polygon?
- The park at Beth’s school is in the shape of a quadrilateral. Which of these could be the shape of the park?
- Which of these is a concave polygon?
- Riko saw a building with rhombus-shaped windows. Which of these windows is in the shape of a rhombus?
- Hiro and Yoshi are comparing rectangles and squares. Which is a true statement?
A
All rectangles are squares.
B
All rectangles are rhombi.
C
All rhombi are squares.
D
All rectangles and squares are parallelograms.
- Jericho drew this set of shapes.
Which best describes Jericho’s set of shapes?
A
parallelograms
B
quadrilaterals
C
trapezoids
D
concave polygons
- Together Zach and Jeff ate one-third of a cake. Which shaded region shows the amount of cake the boys ate?
Use the figure below to answer question 8.
- What fraction of the rhombus is shaded?
A
one-half
B
C
D
one-fifth
Use the figure below to answer question 9.
- Al was asked to shade
of the polygon. Which of these is correct?
Multiple-Choice Answer Key:
1. C
2. A
3. B
4. A
5. D
6. B
7. C
8. C
9. D
Short-Answer Items:
- Miguel said, “A triangle is a polygon.” Is Miguel correct? Explain why or why not.
- Anya said, “All rhombuses are squares.” Is Anya correct? Explain why or why not.
Use the figure below to answer question 12.
- Cristofer ate the shaded portion of the cake. He thinks he ate one sixth of the cake.
Is Cristofer correct? Explain why or why not.
Short-Answer Key and Scoring Rubrics:
- Miguel said, “A triangle is a polygon.” Is Miguel correct? Explain why or why not.
A triangle is a polygon, so this statement is true. Students learned about three key attributes of a polygon in the unit. These include that a polygon is (1) a closed shape in the plane, (2) the sides of a polygon are line segments, and (3) the sides of a polygon meet only at endpoints. A correct explanation would include discussing that a triangle is closed and the sides do not intersect and instead meet only at endpoints.
Points
Description
2
- The student explains the triangle is a closed figure AND is composed of line segments that do not intersect but meet only at endpoints.
1
- The student explains the triangle is closed OR explains the line segments do not intersect but meet only at endpoints.
0
- The student provides no valid or correct reasons for why a triangle is a polygon OR the student argues that the triangle is not a polygon.
- Anya said, “All rhombuses are squares.” Is Anya correct? Explain why or why not.
Only some rhombi are squares, so this is a false statement. A correct explanation includes indicating that the statement is false for all rhombi because not all rhombi have four right angles. It is important in a correct explanation for students to acknowledge that some rhombi are squares, but only if they have four right angles.
Points
Description
2
- The student explains that some rhombi are squares because both have four equal sides AND explains that not all rhombi are squares because not all rhombi have four 90-degree angles.
1
- The student explains that some rhombi are squares because both have four equal sides OR explains that not all rhombi are squares because not all rhombi have four 90-degree angles.
0
- The student provides no valid or correct reasons why the statement is not true OR the student argues that the statement is true.
- Cristofer ate the shaded portion of the cake. He thinks he ate one sixth of the cake. Is Cristofer correct? Explain why or why not.
Cristofer did not eat one sixth of the cake. A correct explanation would state that all parts are not equal and that there seven parts instead of only six.
Points
Description
2
- The student correctly explains that the cake was not divided into equal parts AND that the cake was not divided into six parts.
1
- The student correctly explains that the cake was not divided into equal parts OR that the cake was not divided into six parts.
0
- The student provides no correct explanation OR the student argues it does represent one sixth.
Performance Assessment:
Create a picture using polygons. Your picture must include the following:
- At least two concave polygons. (Be sure to label these as concave.)
- At least one of each of these five quadrilaterals: parallelogram, rectangle, rhombus, square, and trapezoid. (Be sure to label these.)
- At least three polygons separated into equal parts. (For each, write the name of one piece using symbols.)
Be creative! For example, use polygons to draw a dog chasing a cat.
Performance Assessment Scoring Rubric:
Points
Description
4
- All required elements are included.
- The concave polygons are labeled correctly.
- All quadrilaterals are labeled correctly.
- The polygons are separated into equal parts, and they are labeled correctly.
- The student demonstrates an advanced understanding of polygons, attributes of polygons, and unit fractions.
3
- Most elements are included.
- Most concave polygons are labeled correctly.
- Most quadrilaterals are labeled correctly.
- Most polygons are separated into equal parts, and labeled correctly.
- The student demonstrates a good understanding of polygons, attributes of polygons, and unit fractions.
2
- Many elements are included.
- Many concave polygons are labeled correctly.
- Many quadrilaterals are labeled correctly.
- Many polygons are separated into equal parts, and labeled correctly.
- The student demonstrates a limited understanding of polygons, attributes of polygons, and unit fractions.
1
- Few elements are included.
- Most concave polygons are not labeled or labeled incorrectly.
- Most quadrilaterals are not labeled or labeled incorrectly.
- Most polygons are not separated into equal parts, and are labeled incorrectly.
- The student demonstrates a very limited understanding of polygons, attributes of polygons, and unit fractions.
0
- Almost no elements are included.
- Most elements are not labeled.
- The student demonstrates little or no understanding of polygons, attributes of polygons, and unit fractions.
Final 05/24/2013
