ECED 7259 Enhancing Coherent Understanding of Mathematics Curriculum Standards (ECUMCS) Exploring Plane Figures

1. ECED 7259 Enhancing Coherent Understanding of Mathematics Curriculum Standards(ECUMCS)Exploring Plane Figures Bachelor’s Degree in ECED from West Georgia Specialize in teaching reading and writing Just completed my fifth year of teaching Teri Elliott Temple Elementary School claire1999@aol.com Summer 2008 News Crew director, grant and newsletter writer Obtaining my Master’s degree in ECED EIP teacher at Temple Elementary School

2. Exploring Plane FiguresMatrix of Content Strands and Grade Levels

3. Rationale • The reason I chose to do this project on Geometry was because the Geometry section of the CRCT was one math area that my school’s third, fourth, and fifth grade students were consistently weak in. • I chose the children’s literature approach because I primarily teach reading, not math. I wanted to use some type of language approach, so that I would get more use out of this project in my classroom. I also took an EIP standpoint, concentrating on appealing to more types of learners through multiple books and activities.

4. Strands Tree • Plane Figures Strands Tree

5. Developing a Standards-Based Mathematics Activity ProjectGrade 2Name That Shape and Shape Hide and Seek • GPS content standard: M2G1. Students will describe and classify plane figures (triangles, square, rectangle, trapezoid, quadrilateral, pentagon, hexagon, and irregular polygonal shapes) according to the number of edges and vertices and the sizes of angles (right angle, obtuse, acute). • Lesson/Activity Plan:M2G1Elliott1M2G1Elliott2

6. Developing a Standards-Based Mathematics Activity ProjectGrade 3Making a “Hex Hero” and Shapes and Straws • GPS content standard:M3G1. Students will further develop their understanding of geometric figures by drawing them. They will also state and explain their properties. • b. Identify and explain the properties of fundamental geometric figures. • Lesson/Activity Plan: M3G1Elliott1 M3G1Elliott2

7. Developing a Standards-Based Mathematics Activity ProjectGrade 4Tangram Trouble • GPS content standard:M4G1. Students will define and identify the characteristics of geometric figures through examination and construction. • c. Examine and classify quadrilaterals (including parallelograms, squares, rectangles, trapezoids, and rhombi). • d. Compare and contrast the relationships among quadrilaterals • Lesson/Activity Plan: M4G1Elliott

8. Developing a Standards-Based Mathematics Activity ProjectGrade 5 Congruent Buttons and “Glorified” Congruency • GPS content standard:M5G1. Students will understand congruence of geometric figures and the correspondence of their vertices, sides, and angles. • Lesson/Activity Plan: M5G1Elliott1 M5G1Elliott2

9. Developing a Standards-Based Mathematics Activity ProjectGrade 6“Natural” Symmetry and Symmetrical Logos • GPS content standard:M6G1. Students will further develop their understanding of plane figures. • a. Determine and use lines of symmetry. • b. Investigate rotational symmetry, including degree of rotation. • Lesson/Activity PlanM6GIElliott1 M6G1Elliott2

10. Using PB Wiki in my classroom Parents • Post homework assignments • Post daily schedule and calendar • Have comment area for questions and concerns Colleagues • Share ideas and lessons • Share links and games from internet sources Students • Create web pages for sharing assignments • Post questions for teachers and group members/classmates

11. THE END Thanks for your attention.

12. M2G1- lesson 1: Name That Shape Objectives: Students will identify certain geometric shapes, such as triangles, squares, rectangles, trapezoids, quadrilaterals, pentagons, and hexagons, based on the number of edges and angles, with 90% accuracy.  Content Standard(s): M2G1. Students will describe and classify plane figures (triangles, square, rectangle, trapezoid, quadrilateral, pentagon, hexagon, and irregular polygonal shapes) according to the number of edges and vertices and the sizes of angles (right angle, obtuse, acute). Process Standard(s):M2P3. Students will communicate mathematically. a. Organize and consolidate their mathematical thinking through communication. b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others. c. Analyze and evaluate the mathematical thinking and strategies of others.  Description/Illustration: 1.   1. Teacher will introduce the book Shapes, Shapes, Shapes by Tana Hoban. 2.    2.  While reading and discussing the book with students, the teacher will reference multiple shapes within the pages, such as triangles, squares, rectangles, trapezoids, quadrilaterals, pentagons, and hexagons. For example, one of the pages has a checkered picnic blanket and dishes on it. Within that scene, the teacher will point out squares, rectangles, and pentagons. The teacher will ask the students to identify a shape with 4 sides and 4 right angles. The teacher will say: “Where is that shape? Do you know what it is called? What makes it a square?” 3.     3. Students will be asked to orally identify these shapes individually. 4.     4. Once the book has been read, students will be given a baggie filled with shapes that match the ones introduced at the beginning of the lesson. 5.     5. The teacher will read the book again, asking students to choose one shape from his or her bag that represents a shape seen on the current page. Students will be asked to hold the shape up instead of orally responding. 6. Teacher observation will be used to assess student comprehension and participation.

13. M2G1- lesson 2: Shape Hide and Seek Objectives: Students will classify certain geometric shapes, such as triangles, squares, rectangles, trapezoids, quadrilaterals, pentagons, and hexagons, • based on the number of edges and angles, with 90% accuracy.  • Content Standard(s): M2G1. Students will describe and classify plane figures (triangles, square, rectangle, trapezoid, quadrilateral, pentagon, hexagon, and irregular polygonal shapes) according to the number of edges and vertices and the sizes of angles (right angle, obtuse, acute). • Process Standard(s): M2P3. Students will communicate mathematically. • a. Organize and consolidate their mathematical thinking through communication. • b. Communicate their mathematical thinking coherently and clearly to peers, • teachers, and others. • c. Analyze and evaluate the mathematical thinking and strategies of others.Description/Illustration: • 1.      Teacher will draw the shapes introduced in the previous lesson on the board: triangles, squares, rectangles, trapezoids, quadrilaterals, pentagons, and hexagons. • 2.      Students will be asked to orally identify these shapes individually. • 3.      With the teacher leading the discussion, students will count the edges and vertices of the drawn shapes, classifying them into categories using a Venn diagram. (See below) • 4.      The teacher will re-read the book Shapes, Shapes, Shapes by Tana Hoban, as used in the previous lesson. As it is being read aloud, students will choose a favorite scene within the book. • 5.      Students will work with a group to recreate their chosen scene. The students will be assigned three shapes to “hide” within their drawn page. Students will be given blank white copy paper, crayons, and a ruler. They will draw and color a page similar to one seen in the shared book. Somewhere on that page, they must draw the three assigned shapes. The purpose of this is for the other students to carefully study the drawn page, searching for the missing shapes. • 6.      Students will share their pages when finished. Once everyone has presented and all the hidden shapes have been found, the pages will be laminated and bound together to create a classroom book.Teacher observation will be used to assess student comprehension.

14. M3G1- lesson 1: Making a “Hexagon Hero” • Objectives: Students will identify geometric shapes based on their properties with 90% accuracy.  • Content Standard(s): M3G1. Students will further develop their understanding of geometric figures by drawing them. They will also state and explain their properties. b. Identify and explain the properties of fundamental geometric figures. • Process Standard(s): M3P5. Students will represent mathematics in multiple ways. • a. Create and use representations to organize, record, and communicate mathematical ideas. • Description/Illustration: • 1.  Teacher will draw the basic geometric shapes on the board: triangles, squares, rectangles, trapezoids, quadrilaterals, pentagons, circles, and hexagons.Students will be asked to orally identify these shapes individually. • 2.   With the teacher leading the discussion, students will count the edges and vertices of the drawn shapes, classifying them by their properties. (Triangles have three sides and three angles, squares have four equal sides and four right angles, etc...).. • 3   The teacher will read the book The Greedy Triangle by Marilyn Burns. The book discusses the joys of being a triangle, and all the fun activities triangles can do. However, the triangle becomes bored and wishes to change into a square, then a pentagon, and so on. Ultimately, the triangle misses the simplicity of being a triangle and converts back, realizing that he should be happy as himself. As the teacher is reading the book, he or she should point out what the shape-shifter does to the triangle to change it into a square, pentagon, etc… Ask students, “How many edges and angles does this new shape have? What is it called? How do you know? How is it different from the triangle?” • 4   After the book has been read and discussed, students will choose a partner to create their own geometry story. Each set of partners will receive white paper, a ruler, and crayons, with instructions to choose one main shape, make a character out of that shape, and illustrate a comic strip type story featuring the main character. (I created Hex Hero as an example of a character who is created from one basic shape, a hexagon) • 5  Students will share their stories when finished. Once everyone has presented and all questions answered, stories will be posted for all to review.Teacher observation will be used to assess student comprehension and participation. Also, completed comics will be graded for accuracy, originality, and neatness.

15. M3G1- lesson 2: Shapes and Straws • Objectives: Students will identify fundamental geometric shapes based on their properties with 90% accuracy.  • Content Standard(s): M3G1. Students will further develop their understanding of geometric figures by drawing them. They will also state and explain their properties. • b. Identify and explain the properties of fundamental geometric figures. • Process Standard(s): M3P5. Students will represent mathematics in multiple ways. • a. Create and use representations to organize, record, and communicate mathematical ideas. • Description/Illustration: • 1.  Teacher will draw the basic geometric shapes on the board, as a review from the previous lesson: triangles, squares, rectangles, trapezoids, quadrilaterals, pentagons, circles, and hexagons. • 2.   Students will be asked to orally identify these shapes individually. • 3.  With the teacher leading the discussion, students will count the edges and vertices of the drawn shapes, classifying them by their properties. (Triangles have three sides and three angles, squares have four equal sides and four right angles, etc...).. • 4.  The teacher will read the book The Silly Story of Goldilocks and the Three Squares by Grace MacCarone. The book follows Goldilocks on her journey to visit the Three Squares. Inside the Square’s home, there are many different shapes. The author introduces the properties of these shapes and gives basic math information. As the teacher is reading, he or she should ask questions like, “What shape do you see here? How do you know it is a ______?” • 5.  After the book has been read and discussed, students will choose a partner to work with. Students will be using straws to create shapes. Bend a straw at the “elbow”, pinch the long end, and insert it into the short end of another straw. Connect three straws to create a triangle and four straws to create a square. • 6.  While they are working, the teacher should ask the students, “How many straws would it take to make a hexagon? What other shapes can you make with the straws?” • 7.  Students will then compare the shapes they are making with the shapes found in the Goldilocks story. The teacher should ask, “Which ones are alike? What makes them the same?”

16. M4G1: Tangram Trouble • Objectives: Students will identify certain quadrilaterals, including parallelograms, squares, rectangles, trapezoids, and rhombi, with 90% accuracy.  • Content Standard(s): M4G1. Students will define and identify the characteristics of geometric figures through examination and construction. • c. Examine and classify quadrilaterals (including parallelograms, squares, rectangles, trapezoids, and rhombi). • d. Compare and contrast the relationships among quadrilaterals • Process Standard(s): M4P1. Students will solve problems (using appropriate technology). • a. Build new mathematical knowledge through problem solving. • b. Solve problems that arise in mathematics and in other contexts. • c. Apply and adapt a variety of appropriate strategies to solve problems. • d. Monitor and reflect on the process of mathematical problem solving. • Description/Illustration: • 1.      Teacher will draw multiple quadrilaterals on the board, reviewing the definition and asking students to classify each one. • 2.      Teacher will introduce the book The Warlord’s Puzzle. • 3.      While reading and discussing the book with students, the teacher will point out the different quadrilaterals, asking questions like “What shape is this part of the tangram made of? How do these two pieces fit together? What can you make if you use all the pieces of the tangram?” • 4.      Students will be asked to orally identify these shapes individually. • 5.      Once the book has been read, students will be given an activity sheet containing a chart with tangrams in it, all made up of shapes that match the ones introduced at the beginning of the lesson. • 6.      Students will be asked to identify the quadrilaterals and other shapes used to create the animal tangrams in the chart by writing the names of the quadrilaterals used under each animal. • 7.      Students will then be given tangram tiles and encouraged to create their own shapes, working with a partner to classify each quadrilateral.

17. M5G1- lesson 1: Congruent Buttons • Objectives: Students will identify congruency within geometric shapes and symbols with 90% accuracy. • Content Standard(s): M5G1. Students will understand congruence of geometric figures and the correspondence of their vertices, sides, and angles. • Process Standard(s): M6P4. Students will make connections among mathematical ideas and to other disciplines. • a. Recognize and use connections among mathematical ideas. • b. Understand how mathematical ideas interconnect and build on one another to • produce a coherent whole. • c. Recognize and apply mathematics in contexts outside of mathematics. • Description/Illustration: • 1.  Teacher will draw the following shapes on the board: circle, square, heart, and smiley face. • 2.  With the teacher leading the discussion, students will study the shapes, deciding whether the shapes have any symmetrical lines. Upon deciding that they all do, the teacher will then draw lines of symmetry through each shape, pointing out the line and rotational symmetry patterns. • 3.  The teacher will read the book Grandma’s Button Box by Linda Williams Aber. This book tells the tale of a young girl and her friends who accidentally spill Grandma’s box of buttons. Panicking, the girls try to sort the buttons into groups to put them back in the box the correct way. As the teacher is reading, he or she should ask questions like, “Do you see how these buttons are the same shape? Are they the same size? Does this make them congruent? What would make them congruent?” • 4.  After the book has been read and discussed, students will be broken down into cooperative groups. Each group will be given a Congruent Figures worksheet and a box of buttons. • 5.   First, the teacher will review the Congruent Figures worksheet, soliciting student responses about what makes shapes congruent. Then, the teacher will give these instructions: “Working within your groups, sort the buttons into congruent pairs or groups. The group with the most correctly sorted button pairs/groups will win.” • 6.  While they are working, the teacher should walk around, monitoring the groups and asking the students, “How do you know these buttons are congruent? Can you find any more buttons congruent to these? How do you know?”

18. M5G1- lesson 2: “Glorified” Congruency • Objectives: Students will identify congruency within geometric shapes and symbols with 90% accuracy. • Content Standard(s): M5G1. Students will understand congruence of geometric figures and the correspondence of their vertices, sides, and angles. • Process Standard(s): M6P4. Students will make connections among mathematical ideas and to other disciplines. • a. Recognize and use connections among mathematical ideas. • b. Understand how mathematical ideas interconnect and build on one another to • produce a coherent whole. • c. Recognize and apply mathematics in contexts outside of mathematics. • Description/Illustration: • 1.      The teacher will read the book Stars and Stripes: The Story of the American Flag by Sarah L. Thomson. This book is about the history of the American flag and all the forms and styles it has held for past 200 years. As the teacher is reading, he or she should ask questions like, “What do you notice about the stars on the flag? What about the stripes? How are they congruent?” • 2.      After the book has been read and discussed, students will be given the Congruency Practice sheet as a quiz. Completed sheets will be collected. • 3.      Next, the teacher will distribute white paper, a ruler, and a pencil to each student, then review the basic shape and components of the American flag, soliciting student responses about what makes the stars and stripes congruent. Finally, the teacher will give these instructions: “Using the paper, pencils, and ruler provided to you, draw the American flag, taking care to make all the stars and stripes congruent.” • 4.      While they are working, the teacher should walk around, monitoring the groups and asking the students, “How do you know these stars and stripes are congruent? How are you making sure yours are also congruent? What does it mean when shapes are congruent?” • 5. Once all students have completely finished their flags, they will share and post the flags around the room. Teacher observation will be used to assess student comprehension and participation. Completed flags will be graded for accuracy, neatness, and correct congruency.

19. M6G1- lesson 1: “Natural” Symmetry • Objectives: Students will identify lines of symmetry and their applications to shapes and symbols with 90% accuracy.  • Content Standard(s): M6G1. Students will further develop their understanding of plane figures. A. Determine and use lines of symmetry. B. Investigate rotational symmetry, including degree of rotation. • Process Standard(s): M6P4. Students will make connections among mathematical ideas and to other disciplines. • a. Recognize and use connections among mathematical ideas. b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole. c. Recognize and apply mathematics in contexts outside of mathematics.Description/Illustration: • 1.  The teacher will draw the following shapes on the board: circle, square, heart, and smiley face. • 2.  With the teacher leading the discussion, students will study the shapes, deciding whether the shapes have any symmetrical lines. Upon deciding that they all do, the teacher will then draw lines of symmetry through each shape, pointing out the line and rotational symmetry patterns. • 3.  The teacher will read the book Symmetry in Nature by Allyson Valentine Schrier. The book depicts different scenes in nature, refocusing the reader’s attention to the symmetrical side of natural concepts, such as leaves, trees, etc... As the teacher is reading, he or she should ask questions like, “What symmetry do you see in this shape? What type of symmetry is it? How do you know? What properties tell you that it is an example of rotational or line symmetry?” • 4.   After the book has been read and discussed, students will be broken down into cooperative groups. All students will be given a clipboard, crayons, pencils, and paper. • 5.  The teacher will lead the groups outside, giving these instructions: “Working within your groups, go forth and find five items that exist on this playground/sidewalk/common area that contain lines of symmetry. Using your paper and crayons, make a rubbing of each of them. Then, using your pencil, label the symmetrical lines for each rubbing.” • 6.  While they are working, the teacher should walk around, monitoring the groups and asking the students, “What type of symmetry is this an example of? What types of items have you found so far? Have you thought about using a leaf, tile, fence post, etc…?” • 7.  Students will compare their final rubbings once everyone is finished. The rubbings will be sorted into two separate piles: those containing line symmetry and those containing rotational symmetry. Rubbings will be posted inside the classroom.

20. M6G1- lesson 2: Symmetrical Logos • Objectives: Students will identify lines of symmetry and their applications to shapes and symbols with 90% accuracy.  • Content Standard(s): M6G1. Students will further develop their understanding of plane figures. • A. determine and use lines of symmetry. B. Investigate rotational symmetry, including degree of rotation. • Process Standard(s): M6P4. Students will make connections among mathematical ideas and to other disciplines. • a. Recognize and use connections among mathematical ideas. b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole. c. Recognize and apply mathematics in contexts outside of mathematics.Description/Illustration: • 1.      Teacher will draw the following shapes on the board: circle, square, heart, and smiley face. • 2.      With the teacher leading the discussion, students will study the shapes, deciding whether the shapes have any symmetrical lines. Upon deciding that they all do, the teacher will then draw lines of symmetry through each shape, pointing out the line and rotational symmetry patterns. • 3.      The teacher will read the book Symmetry: a Unifying Concept by István & Magdolna Hargittai. This is primarily a picture book, so there is not much “reading”. The book depicts different items found in nature, art, logos, and everyday life. The book refocuses the reader’s attention to the symmetrical side of concepts. For the purposes of this lesson, the teacher will focus on the pictures of logos primarily. As the teacher is reading, he or she should ask questions like, “What symmetry do you see in this logo? What type of symmetry is it? How do you know? What properties tell you that it is an example of rotational or line symmetry?” • 4.      After the book has been read and discussed, the logo worksheet will be distributed for students to practice on. • 5.      Once students have completed their worksheets, the teacher will review the sheet, providing the correct answers (All the logos on the sheet contain lines of symmetry) and drawing the lines out on the overhead projector, superimposed over the logos. • 6.      The students will now work individually to create their own logos, using the pictures found in the shared book and the logos on their worksheets as a reference. The logo they draw must be completely original. Their logo should include line symmetry, be neatly drawn, labeled with the lines of symmetry drawn on, and in color.