## Lesson Study Summary

### Monday - Friday, July 1 - 5, 2013

Monday

We briefly discussed what lesson study is before deciding on a topic/goal of the lesson. We contacted our partner summer school teacher in order to figure out what the students in her class knew and what preferences she might have with respect to their learning. She requested we teach students how to use matrices to transform figures on the coordinate plane as a way to review multiplying and adding matrices before their final exam 2 days after our lesson. We used the rest of this session to refresh our background knowledge and begin to brainstorm ideas for tasks:

• Roving food truck application?
• Use the idea of a scaled version of something else (shape, picture)
• Creating a mural for a wall (blown-up version)
• Have students discover the translation matrix on their own
• Given a diagram on a grid and blank grid, transform this however they want. Then determine matrix expression. Give partner original image and math and have them do transformation. Do final images match up?
• Jennifer's Brilliant Idea: Transformation Battleship!
• Carl's game: Carl transforms a shape. Mary guesses transformation. Points given based on how close guess is to Carl's shape. 3 guess per turn.

Tuesday

In order to understand our teaching environment for the lesson (space, posters, materials, seating, etc...) we visited Brittanie Goff's classroom at Park City High School. We met Ms. Goff and the 6 students we would be teaching. We found the school to be well stocked with rulers, markers, electronic equipment, and anything else we might need. The students seemed generally upbeat for a summer school class; this could have been in part because this is a bridge class from the regular track to the honors track.

Ms. Goff gave us the task she would have used had we not offered to teach this class. This task was limited to translations, reflections, and rotations. We completed the task as a group and analyzed the positives and negatives of the task. Generally, we believed the task to be too leading and "cookbookish". We spent some time looking through other textbook tasks while sharing more other ideas for tasks.

The question of how to assess students during this lesson arose before we left.

Wednesday

We set up a timeline for our task/lesson design:

• Friday (7/5): Planning
• Monday (7/8): Planning
• Tuesday (7/9): Planning, Practice
• Wednesday (7/10): Present at PCHS
• Thursday (7/11): Reflect and revise
• Friday (7/12): Present portion to PCMI HS students 1-2pm; 1/2 day
• 3rd Week: Reflect. Create new lesson.

We split up into groups to design intro of lesson came back to discuss both ideas.

Group 1:
Give students a map of Park City and tracing paper. Have them plot 3 port-a-potties in places on the map important to them (needed because a flood destroyed infrastructure). Use tracing paper to model transformations. Have students use the transformations to make image matrix and pre-image matrix. Use these matrices to have students attempt to find transformation matrices.

Group 2:
Guide students through transformations using Patty Paper.

We decided to go with the Group 1's opener and use it as the basis for the lesson.

Friday

Using GeoGebra we applied a grid to a map of park city. We made the handout for the introduction and began scripting the lesson. We also began to match tasks to mathematical practices.

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This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.