ND Curriculum Initiative

Subject & Standards

Needs Assessment/Rational

Symmetry is a very important topic in mathematics, but it can sometimes be very difficult to understand, and at times, boring. I have come to this conclusion based on previous years’ classroom tests on this topic. With “No Child Left Behind”, improvement needs to be shown every year and the goal is to eventually have all students “proficient”. I feel there is a large gap between how much my students are learning and what needs to be learned in this area. After reviewing the Terra Nova test results of the last two years, I noticed that 35.2% of the students were not proficient in mathematics in general. When looking at Standard 2: Geometry and Spatial Sense, 41.1% were not proficient. Breaking it down even further, I looked specifically at four benchmarks that I would use in my unit. The first was benchmark 12.2.1, “Understand and apply the properties of two- and three-dimensional figures.” The average number correct for this benchmark was 58%. The second and third benchmarks I looked at were 12.2.3 and 12.2.4, “Understand the concepts of congruence, similarity, and symmetry”, and “Apply transformations to basic shapes”. The combined average score for these benchmarks was 80%. The fourth benchmark I looked at actually fell under Standard 4: Measurement. The benchmark was 12.4.2, “Apply a variety of techniques, tools, and formulas to determine measurements”. The average score for this benchmark was 62%. The average score in general for mathematics was 74%. Everyone scored above average or average in the general mathematics category, but there is definitely room for improvement. I then examined the NWEA test results from the fall of 2003 and the spring and fall of 2004. 23% of the students were considered to be low scorers in the Geometry and Spatial Sense area. For the Measurement standard, 33% of the students scored “low”. (This is based on a low, average, high grading scale.) Our school district is currently working on our School Wide Title plan and our School Improvement plan. One of our improvement areas in each of these plans is mathematics. I feel that this unit will be one way of reaching our improvement goal.

Understandings & Goals

Enduring Understanding: Students will understand reflectional and rotational symmetry, and their relationship to beauty, art, nature, science, and other areas other than just mathematics.
Goal(s): 1. Students will understand reflectional and rotational symmetry.  2. Students will identify symmetries in nature, art, and other real-world objects. 3. Students will understand the connection between symmetry and beauty and the effects it has on mankind.

Questions Answered

Essential questions: 1. What are some examples of symmetry in nature and real-world objects? 2.  How is symmetry related to beauty?  3. What biological events does symmetry cause?  4. What did you learn about your own facial symmetry?
Objectives: 1. Students will define polygon, regular polygon, center of a regular polygon, central angle of a regular polygon, reflectional symmetry, rotational symmetry, and axis of symmetry with 90% accuracy.  2. Students will demonstrate knowledge of polygons, reflectional, and rotational symmetry by creating tessellations at a “B” level or better.  3. Students will define and identify trapezoids, parallel lines, and alternate interior angles with at least 90% accuracy.  4. Students will analyze facial features to determine if they are truly symmetrical by using the concepts of symmetry, trapezoids, parallel lines, and reflections at a “B” level or better. 5.  Students will produce truly symmetrical photographs of people using reflectional symmetry at a “B” level or better.

Assessment

What quiz and test items (e.g. simple content-focused questions that require a single, best answer) will provide evidence of understanding? 1. How many lines of symmetry does an equilateral triangle have?  2. What is a six-sided polygon called?  3. Does this figure have rotational and/or reflectional symmetry? 4.  Many more questions such as this will be asked during lecture (using the Qwizdom system) and by a lesson quiz and chapter test.
What academic prompts (e.g. open-ended questions or problems that require students to think critically and then to prepare a response / product / performance) will provide evidence of understanding? 1. What are some examples of symmetry in nature?  2. What are some examples of symmetry in art?  3. How is symmetry related to beauty?  4. How is a tessellation created? 5.  How can you determine if you have true facial symmetry?  6. Produce two new images of yourself that have true and perfect symmetry.
What performance tasks and projects (e.g. complex challenges that are authentic, mirror the real world and require a performance or product) will you include that will provide evidence of student understanding? 1. Students will create reflectional and rotational tessellations by using geometry software.  2. They will iron on these tessellations to a t-shirt and will wear these shirts in and out of the classroom.  3. They will explain to others how they were made.  4. Students will take digital pictures of themselves and they will determine (with the help of geometry software) if they have perfect facial symmetry.  5. They will reflect the left side of their face to make a “new face” with perfect symmetry. 6. They will do the same thing with the right side of their face.  7. By examining these faces, and by measuring the angles made by parallel lines, they will determine how symmetric their faces really are.  8. All of these projects will be shared with classmates and will be posted in the school.  9. All projects will be assessed using a student/teacher created rubric.
What other evidence (e.g. observations, work samples, dialogues, student self-assessment) of understanding will you collect?  1. Students will help in creating a rubric for each of the projects. 2. I will also use a remote controlled software system before we even start the projects to determine if they have the basic understanding of symmetry and polygons are. 3.  By observing and collecting the projects I will have a good idea if they understand.  4. Finally, students will discuss and write about their feelings on whether symmetry really determines beauty.

Instructional Strategies

I will be using combination of the inquiry-based and project-based teaching and learning strategies. One example of inquiry based will be used when students are asked to research “Is there symmetry in things (people) that are considered beautiful?” They will gather at least 3 examples of symmetry (this could be from the human body, other sources of nature, or art), record their results, and discuss their results in a presentation to the class. Once the students have made their presentations, I hope the students will see the relevance of symmetry to their lives. Once their results have been given, the expectation is that they will see a connection between symmetry and how it influences the health, reproduction, and longevity of not only humans, but many organisms. Another expectation is that they will see how symmetry has been involved in many works of art. Most of my student activities will be project based activities. One such activity will be having the students take digital pictures of each other and downloading them to their computers. Working in pairs, the students will reflect both sides of their faces using imaging software. Once this has been done, they will use geometry software to determine what they symmetry index is. They must come up with a way to find this index on their own. One way is to create trapezoids (connecting left eye to right eye, leftmost part of nose to rightmost part of nose, and left corner of mouth to right corner of mouth). Once their pictures are completed, all of their projects will be gathered and put on the same Power Point presentation to be viewed by the class and the community at parent-teacher conferences. During the projects I will be helping out the students, but I want them to use their previous knowledge to come up with the symmetry index on their own. It will be interesting to see what methods they devise.