This unit is written for fifth grade students. The unit is written to be taught in a regular elementary classroom and contains six lessons involving geometry. The math lessons are suitable for third through fifth grade. The six lessons teach the state objectives for geometry while incorporating sports, art, architecture, real world concepts, and technology. The unit focuses on learning geometry terminology, determining angles, identifying polygons, distinguishing attributes that quadrilaterals share, and recognizing line and rotational symmetry. The lessons incorporate pop culture by utilizing Google Earth, artwork by Jackson Pollock, Pablo Picasso, Josef Albers, and M.C. Escher. It also incorporates a sport activity and utilizes the features of the courts and fields that sports are played on. After students recognize the symmetry found in historic landmarks, they will create a village out of polygons for their cumulative activity at the end of the unit. This unit was written with access to a classroom interactive whiteboard. If an interactive whiteboard is inaccessible, then most of the visual aids can be transferred to overheads to use with a projector or viewed by a computer.
I have designed this unit for use with elementary students that are in the fifth grade. I teach at JV Washam Elementary in Cornelius, North Carolina. Our teachers are given the freedom to plan a variety of lessons to reach our educational goals, as long as we follow the state curriculum closely. This allows me to incorporate popular culture into my lesson plans and still teach the curriculum objectives. The entire geometry unit will span over twenty-two days. I have written this curriculum unit based on six lessons that will be taught within the entire unit.
Fifth grade students will also be able to classify quadrilaterals by whether they have parallel sides (i.e. trapezoid) and by the lengths of their sides (i.e. kites). Students will observe the angles, length of sides, perpendicularity, and parallelism to determine what attributes different quadrilaterals possess. Students will use their prior knowledge about the sum of interior angles to determine the sum of the interior angles of a quadrilateral. Students will thoroughly investigate these characteristics to infer what shapes share common attributes (i.e. All squares are rectangles).
I will begin the first lesson the same way I begin every math lesson, by introducing the important vocabulary words. I feel that part of the battle of learning is developing the needed vocabulary so that students can comprehend the skill that is being taught. Throughout the unit, my students will keep a geometry notebook. They will record the vocabulary words each day as well as an illustration. Students also will record important facts and notes to be used as a study guide.
After the students have recorded their new vocabulary into their notebooks as well as a drawing of each angle, I will use the website: http://www.hittingthetarget.com to have students work with identifying angles in sports. There are three games they will play. The first game will allow students to come to the interactive whiteboard and identify the right angles on a soccer field. The second game will involve the students identifying angles by the direction a tennis ball is hit in a tennis match. The third game is similar to the second game and the students identify the angles by the direction a cricket ball is hit.
I will then read aloud the book, Shapes in Sports, by Rebecca Rissman. The photographs in the book will show my students how different types of shapes are found in the sports we play. Then I use the website: http://www2.scholastic.com/content/collateral_resources/pdf/g/geometry_sports_examples.pdf for the students to identify polygons that are found in basketball, football, pool, baseball, chess, and cricket. The website displays the area that the different sports are played on. My students will use the interactive whiteboard to circle the particular polygons that they identify.
To end the lesson, I will use the Google search engine to find images of Pablo Picasso’s paintings. I will display different paintings, for example: House in the Garden, Violin and Guitar, or Three Musicians. The following website has a variety of Picasso’s work to view: http://www.abcgallery.com/P/picasso/picasso.html. After having my students identify other polygons located in the paintings, they would begin their own illustration. Using Picasso’s work as an example I would have my students create a picture using coloring utensils that is created out of polygons.
After discussing all of the attributes that the different quadrilaterals possess, I will continue the lesson by introducing the class to Josef Albers. For more background information about Josef Albers visit the website: http://www.metmuseum.org/toah/works-of-art/59.160. Then I will use the Google search engine to display images of Josef Albers painting, Homage to the Square. I will then have my students create their own Homage to a Quadrilateral. The students will choose a shape that has been introduced to them today and will draw their own picture. Students will also describe the different properties of the shape on an index card. This will probably be a homework assignment depending on how much time is left in the class.
The lesson will begin with the students viewing a video found on the website: http://www.linkslearning.org/Kids/1_Math/2_Illustrated_Lessons/4_Line_Symmetry/index.html. The video introduces line symmetry and gives multiple examples of objects in our everyday life that contain line symmetry. My students will sketch or write in their notebooks about the different objects with line symmetry that they viewed in the video.
After the introduction to line symmetry, I will continue the activity by using the website: http://www.mathsisfun.com/geometry/symmetry-reflection.html. I chose this website because of the visuals and the opportunity for students to be able to interact with the interactive whiteboard. The website displays numerous drawings that contain line symmetry. Once the students have seen the artwork and answered the questions from the website’s quiz, I will have each student draw a picture in their notebook that represents line symmetry.
I will continue using visuals that represent line symmetry. Instead of artwork, I will use architecture for the students to determine if line symmetry is present. I will use the Google search engine to find images of the Taj Mahal, the London Bridge, Big Ben, Arche de la Defense, la Geode at La Villette, the Washington Monument, the San Francisco Bridge, and The pyramid at the Louvre. My students will come to the interactive whiteboard and draw the line of symmetry. Other images of line symmetry can be found at http://www.adrianbruce.com/Symmetry/index.html.
I will begin by reviewing with the class the concepts of line and rotational symmetry. Today I will use artwork from M.C. Escher to review line symmetry. Examples of the artwork can be found in the Picture Gallery at http://www.mcescher.com/. There are numerous examples in his artwork of line symmetry and the students can draw where the line of symmetry occurs using an interactive whiteboard. To review rotational symmetry I will have the students use the mandalas that were created yesterday as a visual reminder that the shape has to reappear before it rotates 360 degrees.
The final assessment of the geometry unit will involve a cumulative project about the concepts I have taught. The project is called, The Popular Village of Polygons. Throughout the unit my students have been exposed to geometry that is found in architecture, sports, art, and their everyday world. For their final assessment the students will become architects and design a village from an aerial view, like they viewed on Google Earth.
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3.01 Identify, define, describe, and accurately represent triangles, quadrilaterals, and other polygons.
Students will learn the attributes of each polygon and how to identify the shape.
Sum of the measures of interior angles.
Lengths of sides and diagonals.
Parallelism and perpendicularity of sides and diagonals.