Overview
This unit is created to teach third graders about the mathematical concept of symmetry. The unit can be adapted for other grade levels. Students get the opportunity to learn about symmetry over the course of 5 weeks. Instruction is given in whole and small group settings. Students work in cooperative groups, pairs, and on their own. Each lesson takes about 45 minutes to complete. Students receive a hands-on math experience. I integrate math with language arts and art. For the language arts component, we read math related picture books. Students discuss the books and apply learned information to the math lessons. The books provide additional background information for the students. Many of my students come with limited background information. I expose students with this information; to ensure they have a basic understanding of the concepts before starting the unit. During math lessons, language arts are incorporated by discussing word problems in class, asking such questions as, what is this problem asking, how you know, and comparing problems. Art is immersed throughout the unit; students create different symmetrical designs/projects.
Students learn how symmetry is all around us. Students look at symmetry through nature (insects, flowers, and trees), architecture, and art. Students get the opportunity to take a look around the city of Chicago; and identify symmetrical objects. As they walk around areas in Chicago, I ask questions about symmetry and the type of patterns they see on the buildings. During this walk, students sketch objects and patterns. In this unit, third graders are challenged to think beyond understanding lines of symmetry. We study the seven different types of frieze patterns. As we look at the frieze patterns, we learn about translations, reflections, rotations (only by 180 degrees), and glide reflections. Students reflect, write, and explain their thinking.
This unit incorporates real life experiences with math. Students use resources from outside, home, and school for some of the activities. They talk about how math connects to the world. These experiences help students see the value of the math they are studying. By linking a math concept to something relevant in a student's life, you can help increase a student's interest in the topic, and help make math more meaningful. When students are interested, the levels of motivation increase.
Rationale
Geometry is important for students to know because it provides methods of reasoning and solving problems. The world is made up of geometrical objects and figures. (1) Symmetry is a part of geometry that is found all around us. Symmetry is found in a variety of things, such as clothes, flags, and buildings. Many of our jobs contain components of understanding math as well as using geometry. This statement answers the question: Why do we need to do this? You cannot get away from math. It is everywhere! Math is unavoidable. It's a deeply important thing. Without math, there would be no science, no music, and no art. Math is part of all of those things. This unit will convince my students of this universal truth.
In the state of Illinois, third graders are required to learn about the strand of geometry. Students must know how to compare geometric figures and determine their properties including i) when two lines are parallel, ii) when two lines are perpendicular, iii) when two figures or configurations are congruent, and iv) when a figure has a line of symmetry. Students will begin to see the power and utility that math brings to expressing, understanding and solving problems in diverse settings beyond the classroom. (1)
The study of geometry including symmetry is taught in my school's Everyday Math Curriculum, a research based curriculum that connects math to real world applications. It also integrates mathematics into other subject areas so math becomes part of ongoing classroom and external events. Since the curriculum is spiraled, students learn many concepts at once. They are constantly revisiting some of the concepts. Third graders using Everyday Math are supposed to learn about two-dimensional symmetric shapes or designs; locate multiple lines of symmetry in a two-dimensional shape, and create symmetric shapes. Students apply Transformations and Symmetry in Geometric Situations. (2) However, we only have a few symmetry lessons in the curriculum for third graders. The data at my school shows that our students' geometry scores need to improve. So as a teacher, I must bring in additional resources to expand the geometry section of the text. The resources must provide meaningful opportunities for the students to learn and retain the information.
The majority of my students enter third grade with little knowledge of geometry. They can tell you the basic names of polygons, such as rectangles, triangles, and squares. Some students have a difficult time explaining the number of sides and vertices on certain polygons. Identifying patterns also is a difficult task for some students. They need concrete examples/models to grasp the concept. At the beginning of third grade, the term symmetry is new to most of the students. They never heard of symmetry or have forgotten what symmetry means. I know that this topic is covered briefly towards the end of second grade.
According to the National Council for Teachers of Mathematics, "Students enter grade 3 with an interest in learning mathematics. Nearly three-quarters of U.S. fourth graders report liking mathematics, seeing it as practical and important. If mathematics continues to be seen as interesting and understandable, students will remain engaged. If learning becomes simply a process of mimicking and memorizing, students' interest is likely to diminish." (3)
As teachers we must provide learning opportunities in which students can inquire, think, and apply math to real world situations. Students at all grade levels need to be challenged, but not to the point of frustration. Adding a touch of fun in math, will keep most students actively engaged and motivated to learn math.
To help them compete with the world, I want to equip my students with the necessary math skills. As an intermediate teacher, I want to provide students with a solid math foundation. This foundation helps students make sense of the world around; students will be ready for the advancements in technology. "Through math, students learn to reason, to connect ideas, and to think logically. Math is more than the rules and operations we learned in school." Math is about making connections and seeing relationships in everything we do. (4)
I want my students to have conversations and not be afraid to tackle a math problem/concept. Some adults do not like math based on experiences they have had in elementary/high school; math is feared by them. I do not want my students to be categorized as these adults. Students need to have fun and learn at the same time.
Putting the Pieces Together is a curriculum unit that students will enjoy; the curriculum provides an unforgettable learning experience. Students will learn the state required math goals in addition to other ways to think about math.
Comments: