Students understand symmetry through reflection of light waves.

Using a mira, students draw symmetrical pictures and then explain how the mira works using what they know about reflection and the eye.

15 minutes

Materials: Drawing paper, symmetrical magazine photos cut on the line of symmetry, or printed images cut on the line of symmetry, etc. for students to choose and play with. Miras for student pairs.

Connecting math and science is a great way to kill two birds with one stone! I opened the lesson today with the Driving Question: What is reflection? How can we use mathematics to explain it?

I asked my students to get their science notebook out and find a blank page on the right to write the Driving Question on the right side at the top. I asked them to develop a KLEWS Chart on the page by turning the page horizontally. I directed them to fill in the K by answering what they think they know about reflection. Then, I asked them to try to answer the second question.

I roved the classroom and examined some of their answers to get an understanding of how students perceived reflection.

We shared our thinking together by a whole class quick share. They needed to listen because the rules were that no one could say the same thing. I filled out our KLEWS chart for the classroom on my whiteboard.

When we were finished, I moved to the next part of the lesson, by writing the word "symmetry" on the board.

10 minutes

I asked students to also fill out the K part of their chart explaining what they know about symmetry. I roved the classroom and quickly scanned what they understood. I asked for three quick shares and then added to the classroom KLEWS chart.

I decided to simply show students this clever rap to reinforce their understanding of symmetry so that there would be no misunderstandings of one line of symmetry. The goal today would be to connect reflection with symmetry and I knew I needed them to be clear in their understanding before they could connect the science to the math.

20 minutes

Students were given paper and Miras to work with. *(A Mira is a reflective geometry tool that can be purchased.)* They were allowed to choose magazine photos I had carefully clipped out. Photos were cut straight through the line of symmetry and each group were allowed one. I explained that they needed to coach each other through this complex task and it wasn't going to be easy.

I told them that they needed to find the line of symmetry like they had seen in the rap video and then sketch the object on the other side to match what they saw identically. As they began, I stopped them along the way and asked them to fill in their KLEWS chart: I coached them to be sure to seek the answer to the Driving Question, take turns sketching their objects and observe each other as they drew. When one draws the other filled in the chart. At this point in the lesson, they were still absorbed with the Mira itself. They had never seen one or used one! No one was drawing yet! They spent time figuring out how to look through it, around it, over it under it, above it and all over the place! My patience was key at this point! I know that discovery based science needs to be coached and not herded. I refrained! I did NOT instruct them how to use it! This was going to be tough. I began to make myself mobile between groups, not spending too long with them so I wouldn't be tempted to show them how it should be done!

I realized that I needed to clarify the task again and again because the thinking about how the Mira worked was overtaking the focus of the lesson. They were struggling to connect the paper and drawing to how the image would be reflected. I had to show them to use the paper in some instances. I could feel myself needing to coach more carefully without giving in. I began asking questions like, what if you set it down? That was safe enough! It prodded a little, without giving it away. Then, I asked, what happens if you move it a little? This helped them see they were on the right track, but guided them to fully see the line of symmetry and reflection as a whole. The struggle to find the symmetry line continued and I needed to continually rove and talk them through, but not give it away.

And then it happened! I couldn't stand it anymore with one group! I realized they were using refraction and used the opportunity to review. Then, I helped and realized the discovery through coaching too much took away some of the joy of figuring it out themselves.

Then, suddenly, they did it! One group finally got it. As they were drawing the lighthouse students who struggled started to gather around them. They were learning from each other and the full circle of inquiry, discovery and joy of learning from one another came full circle.

This is what NGSS is about! Hands on! For me? Hands off!

20 minutes

As we started to conclude, I drew their attention on the whiteboard where the Driving Questions were written. How are you proving that reflection is responsible for that image? How is math involved? What is your evidence? What do you see? What are you learning by moving the Mira around until it works? How do you know?

The puzzled looks on their faces told me that the KLEWS chart was difficult for them. These questions helped support the driving question as they worked to fill in their questions and wonders. As they asked about the Scientific Phenomena section, I told them to connect their vocabulary. What did we learn about reflection here today? Suddenly I heard words like, "light bounces!" I told them to write it down! And the process of the chart slowly filled in as they got more comfortable with thinking and writing about a complex task they had just experienced.

As tough as this struggle of thinking is for them, the reality that this is the best thing that science brings to our students was revealed throughout. This is how life is grappled with. No one gives us answers.

I closed with asking them if they liked the lesson? They did. They really did!