## Desired Results

Too often we see something beautiful and we admire its beauty, but never think about the deeper meaning. Where did it get its beauty? How did it come to be? My job as a teacher is to teach my students skills to be able to use in the outside world. Specifically, as a math teacher, I continuously teach my students mathematics that they will need in their everyday lives. This time around, I want to show my students the mathematics that they visually see that is in the outside world. My big idea is for my students to see math in nature, culture, and in themselves. First, we will look into the beauty of nature and how mathematics is involved in creating the distinct beauty it holds. Then we will look into culture and discover how nature and mathematics help influence culture. Finally, we will look at ourselves and how mathematics makes up our bodies. We will tie it all together and look at how mathematics influences us in our everyday lives. What do we see in our day-to-day interactions that has mathematics behind them? At the end, the students should be able to see and explain the mathematics behind nature and culture. They should also be able to explain how this influences them.

## Evidence

There will be formative and summative assessments throughout the course of the year. The students will complete a formative assessment after each day the Big Idea is taught. The students will fill out a journal page. This journal page will explain what part of the big idea was discovered for the day. They will draw a picture and explain what this means to them. The teacher will collect each page and at the end of the year the students will form a book with all of the pages that they have filled out over the school. The teacher will review the pages as they care collected and correct and misconceptions. The students will also complete three summative assessments throughout the year. The first summative assessment will be to grow a plant as this will reflect the nature part of the Big Idea. As the students grow their plants, they will identify what mathematic concepts describe what they see as the plant grows. The second summative assessment will require the students to paint a picture that is inspired through mathematics. This piece will reflect their knowledge of how mathematics influences culture. The last summative project will require the students to create a collage of how mathematics influences the students. They will create a collage that will reflect the vision of mathematics through their eyes. They will show through their collage where they see math in their everyday lives.

## Instruction

I will be teaching my Big Idea to my sixth grade students. Since I am a mathematics teacher, I am required to cover all mathematical standards that are required from common core and make sure students are adequately prepared for NWEA and PARCC testing. With that in mind, my Big Idea lessons will be incorporated into strategically chosen time throughout each week with about an hour spent each week on my Big Idea. Each student will have their own lap top that they will be allowed to use. I will also have an ELMO and projector that I will be able to use. In order to highlight the mathematics in nature, culture, and the student, I have chosen the following mathematical concepts: tessellations, golden ratio (golden spiral), Voronoi patterns, fractals, Turing’s equations, and symmetry. We will visit these concepts and how they relate in all three forms, nature, culture, and self. Some of these mathematical concepts may be a little difficult for sixth grade students to understand, so I will need to focus on bring the content down to their level so that they can understand the mathematics. For example, Turing’s equations explain how animal’s spots or stripes form. The equation is very complex, so I will need to come up with a way to make it understandable to my students. For each lesson of my Big Idea, I have decided to start with some sort of question that will be based off of nature, culture, or self. For example, why do hexagons form a pattern for honeycomb? We will then do an activity that will help the students to discover the mathematics behind the question. Students will be given 20 circles, 20 triangles, 20 hexagons, 20 diamonds, and 20 ovals. They will also be given a sheet of paper. Which shape can take up the most space on the sheet of paper? Which shape would ultimately hold the most honey? We will then discover the mathematical concept behind the activity as in this case it would be tessellations. Students will then complete a journal entry to describe the knowledge that they have just discovered. Each lesson will be set up in the same manner. A question, an activity to help discover the answer to the question, and a discussion about the discovery. For technology, I will require a lot of art supplies. The students will be using art supplies to create things and complete activities. Students will use lap tops from time to time to complete online field trips.

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