Geometry and Spatial Reasoning Activity: TEKS: Two-Dimensional Figures Important Book (4.8) Geometry and spatial reasoning. The student identifies and describes attributes of geometric figures using formal geometric language. The student is expected to: (A) identify and describe right, acute, and obtuse angles; (B) identify and describe parallel and intersecting (including perpendicular) lines using concrete objects and pictorial models; and (C) use essential attributes to define two- and three-dimensional geometric figures. Note: Portions of this lesson address TEKS at other grade levels as well; however, the intent of the lesson fits most appropriately at the grade level indicated. Overview: Students will investigate attributes of various two-dimensional figures. In addition, students will examine and identify essential attributes for defining two-dimensional figures as they explore relationships among various types of quadrilaterals. Materials: The Greedy Triangle by Marilyn Burns (ISBN: 0-590-48991-7) Construction paper (2 pieces per student) Strips of heavy paper: cardstock or poster board Brads Hole punch Scissors Two-Dimensional Figures Recording Sheet Handout/Transparency 1 The Important Book by Margaret Wise Brown (ISBN: 0-06-443227-0) Glue or paste Markers 3 "O" rings Sample Quadrilaterals Handouts/Transparencies 2a and 2b Quadrilateral Definitions Handout/Transparency 3 What s In A Name? Explaining Quadrilaterals Handout/Transparency 4a What s In A Name? Explaining Quadrilaterals Key Handout/Transparency 4b Sample Word Map Handout/Transparency 5 Words for a Word Map Handout/Transparency 6 Sample Quadrilateral Word Map Handout/Transparency 7 Assessment of Two-Dimensional Figures Handout/Transparency 8 Geoboards Geobands Geoboard Recording Paper Handout/Transparency 9 Two-Dimensional Figures Important Book Page 1
Assessment of Two-Dimensional Figures (Key) Sample Answers 10a, 10b, 10c, and 10d Grouping: Time: Whole group and pairs 3 4 class periods Lesson: Procedures 1. Read The Greedy Triangle by Marilyn Burns to the class. As you read the book, stop and ask the students to predict the number of sides they think will be on the next polygon after the triangle visits the Shape Shifter. Ask the students to provide the geometric term for the figure, and ask if they have ever seen anything made from that shape. Notes In this book, the Greedy Triangle gets tired of having just three sides, so the triangle goes to the local shape shifter to have one more side added. As the new polygon continues to run into troubles and continues to add one more side he finally realizes that his original three sides were just enough, and he returns to his original status. 2. After reading the book, review with students various two-dimensional figures such as triangles, quadrilaterals, pentagons, hexagons, and so on. Have each student take a piece of construction paper and cut it on the diagonal. Ask: What two-dimensional figure have you made? How many sides does it have? How many angles does it have? A right triangle 3 sides 3 angles This cut forms two right triangles. Discuss with students which angle is a right angle. Distribute Two-Dimensional Figures Recording Sheet Handout/Transparency 1. The first row is already completed on the recording sheet for the triangle. 3. Have students make an angle maker using a hole punch, brads, and two strips of heavy paper such as cardstock or poster board. Using the angle maker, have the students Two-Dimensional Figures Important Book Page 2
Procedures show you an acute angle, obtuse angle, and a right angle. As students model each type of angle, ask the class for the definitions of acute, obtuse, and right angles. Notes 4. Ask the students to predict what shape they will have if they cut off one vertex of the triangle. After making their predictions, have each student cut only one vertex. Ask: What two-dimensional figure have you made? How many sides does it have? How many angles does it have? A quadrilateral 4 sides 4 angles Students should again record the name of this polygon, the number of sides and the number of angles on Handout/Transparency 1. Discuss with the class the attributes of each of the different quadrilaterals that occur in the class from cutting one vertex of the triangle. Not all quadrilaterals will look the same. Do they have zero, one, or two pairs of parallel sides? Does the quadrilateral still have a right angle? Students may use their angle makers to determine if the quadrilateral s angles are acute, obtuse, or right angles. 5. Continue this process, cutting just one vertex at a time and naming the new polygon after each cut. Each time, record the polygon s name, number of sides, and number of angles on the recording sheet. Have students discuss distinguishing properties of each figure, including the number of sides and the number of angles. Students should identify any parallel and/or perpendicular sides. 6. Read The Important Book by Margaret Wise Brown to the class. In The Important Book, the author discusses the important attributes Two-Dimensional Figures Important Book Page 3
Procedures Discuss the pattern used in the book. 7. Using Sample Quadrilaterals (see Handouts/Transparencies 2a and 2b) and Quadrilateral Definitions (see Handout/Transparency 3), have students discuss the attributes of quadrilaterals. Then, ask students to complete What s In A Name? Explaining Quadrilaterals (see Handout/Transparency 4a). Students should compare and contrast the differences between these quadrilaterals. Notes of familiar objects. She highlights what each object looks like, what it is used for, and what she believes is its most important attribute. Many quadrilaterals share the same attributes. This discussion should lead students to identify the most important attribute of a quadrilateral. A key for What s in a Name? Explaining Quadrilaterals is provided on Handout/Transparency 4b. 8. Divide the class into groups or pairs of students. Assign a different two-dimensional figure to each group or pair and have them write a page for a class book, The Important Book of Two-Dimensional Figures. They may glue their assigned two-dimensional figure at the top of their paper or decorate their paper with the assigned figure. The class book should follow the pattern found in The Important Book. Before writing their page, the group must decide what the distinguishing attribute of their figure is. Then they may list other attributes, classifications, examples of where their figure might be found in real life, lines of symmetry, and other descriptive characteristics. When all of the groups have completed their writing, collect the pages, add a front and back cover, and assemble the pages into a class book that can be placed in the library or the mathematics center. Allow students time to present their page of the class book. A class discussion of student s reflections should take place. For example, the group with the square might write something like the following: The important thing about a square is that it has 4 congruent sides and 4 right angles. It is true that it is a polygon and a quadrilateral. It is a special kind of rectangle. It is also a special kind of rhombus. It has 4 lines of symmetry. You see squares on checkerboards and chessboards and lots of other places. But the important thing about a square is that it has 4 congruent sides and 4 right angles. Two-Dimensional Figures Important Book Page 4
Procedures 9. Model a word map for the students using the Sample Word Map (Handout/Transparency 5). Explain that a word map is a visual way to represent the relationships among various two-dimensional figures. Distribute Words for a Word Map (see Handout/Transparency 6.) Each group of students should have a set of words. Tell the students that they are now going to create a Quadrilateral Word Map to represent the relationships among the various two-dimensional figures and terms that the students have investigated during the lesson. Have the groups cut out the words and make a Quadrilateral Word Map with them. When complete, have each group present its word map to the class. Notes Each column on Words for a Word Map (Handout/Transparency 6) contains a complete set of terms, so each page will be enough for two groups. A Sample Quadrilateral Word Map is provided at the end of this lesson (Handout/Transparency 7). Homework: Assessment: Extensions: Resources: Have students cut out pictures from a magazine of examples of twodimensional figures. Assign students Assessment of Two-Dimensional Figures (see Handout/Transparency 8) to complete. Students should read the description of the polygon, create the polygon on the geoboard and record it on the Geoboard Recording Paper (Handout/Transparency 9). Repeat the process using three-dimensional figures to create a new class book, The Important Book of Three-Dimensional Figures. Burns, M. and Silveria, G. (1994). The greedy triangle. New York: Scholastic. Brown, M. W. and Weisgard, L. (1999). The Important Book. New York: Haper Collins. Two-Dimensional Figures Important Book Page 5
Two-Dimensional Figures Recording Sheet As you construct polygons, record the name of each polygon, its number of sides, and its number of angles in the table below. Name of Polygon Number of Sides Number of Angles Triangle 3 3 Handout/Transparency 1 Two-Dimensional Figures Important Book Page 6
Sample Quadrilaterals Handout/Transparency 2a Two-Dimensional Figures Important Book Page 7
Sample Quadrilaterals (continued) Handout/Transparency 2b Two-Dimensional Figures Important Book Page 8
Quadrilateral Definitions Quadrilateral any closed, four-sided shape. Parallelogram a quadrilateral with two pairs of parallel sides. Rectangle a parallelogram with four right angles. Rhombus a parallelogram with four equal or congruent sides. Square a parallelogram with four right angles and four equal or congruent sides. Trapezoid a quadrilateral with only one pair of parallel sides. Handout/Transparency 3 Two-Dimensional Figures Important Book Page 9
What s In A Name? Explaining Quadrilaterals Instructions: Place a check mark in the box of each geometry term that applies to each quadrilateral. Quadrilateral Parallelogram Rectangle Rhombus Square Trapezoid Handout/Transparency 4a Two-Dimensional Figures Important Book Page 10
What s In A Name? Explaining Quadrilaterals (Key) Instructions: Place a check mark in the box of each geometry term that applies to each quadrilateral. Quadrilateral Parallelogram Rectangle Rhombus Square Trapezoid Handout/Transparency 4b Two-Dimensional Figures Important Book Page 11
Sample Word Map Handout/Transparency 5 Two-Dimensional Figures Important Book Page 12
Words for a Word Map Cut out the following words and use them to create a word map: Cut out the following words and use them to create a word map: Parallelogram Parallelogram Polygon Polygon Quadrilateral Quadrilateral Rectangle Rectangle Rhombus Rhombus Square Square Trapezoid Trapezoid Handout/Transparency 6 Two-Dimensional Figures Important Book Page 13
Sample Quadrilateral Word Map Handout/Transparency 7 Two-Dimensional Figures Important Book Page 14
Assessment of Two-Dimensional Figures Make the following polygons on your geoboard and record on dot paper. 1. Make a 3-sided polygon. What is this polygon called? 2. Make a triangle with 1 right angle and no 2 sides the same length. What is this triangle called? 3. Make a 4-sided polygon with no parallel sides. What is this polygon called? 4. Make a 4-sided polygon with all sides different lengths. What is this polygon called? 5. Make a 4-sided polygon with no right angles but with 2 pairs of sides parallel. What is this polygon called? 6. Make a 4-sided polygon with right angles and two pairs of sides parallel. What is this polygon called? 7. Make a 4-sided polygon with 4 right angles and all sides congruent. What is this polygon called? 8. Make a 4-sided polygon with no right angles and all sides congruent. What is this polygon called? 9. Make a 5-sided polygon that has exactly one pair of parallel sides. What is this polygon called? 10. Make a 6-sided polygon with one pair of perpendicular sides. What is this polygon called? 11. Make a 7-sided polygon. What is this polygon called? Handout/Transparency 8 Two-Dimensional Figures Important Book Page 15
Geoboard Recording Paper Handout/Transparency 9 Two-Dimensional Figures Important Book Page 16
Assessment of Two-Dimensional Figures (Key) Make the following polygons on your geoboard and record on dot paper. Note: Geoboard figures may vary on each question. 1. Make a 3-sided polygon. What is this polygon called? Triangle 2. Make a triangle with 1 right angle and no 2 sides the same length. What is this triangle called? Right triangle 3. Make a 4-sided polygon with no parallel sides. What is this polygon called? Quadrilateral Sample Answers 10a Two-Dimensional Figures Important Book Page 17
4. Make a 4-sided polygon with all sides different lengths. What is this polygon called? Quadrilateral 5. Make a 4-sided polygon with no right angles but with 2 pairs of sides parallel. What is this polygon called? Parallelogram 6. Make a 4-sided polygon with right angles and two pairs of sides parallel. What is this polygon called? Rectangle Sample Answers 10b Two-Dimensional Figures Important Book Page 18
7. Make a 4-sided polygon with 4 right angles and all sides congruent. What is this polygon called? Square 8. Make a 4-sided polygon with no right angles and all sides congruent. What is this polygon called? Rhombus 9. Make a 5-sided polygon that has exactly one pair of parallel sides. What is this polygon called? Pentagon Sample Answers 10c Two-Dimensional Figures Important Book Page 19
10. Make a 6-sided polygon with one pair of perpendicular sides. What is this polygon called? Hexagon 11. Make a 7-sided polygon. What is this polygon called? Heptagon Sample Answers 10d Two-Dimensional Figures Important Book Page 20