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Select two lessons taught at two different times during your field experiences. Describe each lesson and the classroom context including:

Lesson One: Rocket Man

• Grade level and curricular materials

This geometry class was a heterogeneous mix of ninth and tenth graders. Materials include handouts, rulers, popsicle sticks, calculators, smartboard, and the Problem of the Day. Our textbook was Discovering Geometry by Kendall Hunt Publishing. The class did not receive a book to bring home but could access the book online with a class username.

• Classroom

There was always an posted on the left hand side of the board for the students to follow. The students received a geometrybune every three classes so they were aware of upcoming learning objectives and assignments. There was a in the front of the room which holds rulers, protractors, and compasses. Also, there is extra graph paper and lined paper on top of the tool chest.

• Number and ability levels of students

This classroom is a heterogeneous group of twenty students. There are a few students on IEPs for Emotional Disturbances and ADD. There are visual, concrete, and kinesthetic learners.

• Point in the teaching sequence the lesson takes place

This lesson was at the end of October during the triangle unit, a month before my solo period began.

• Rationale for lesson plan

Previous to this lesson we learned the transformations: slide, rotate and reflection.  Dilations is the final lesson in transformations and similarity is the first concept in the series of Similar Triangles. In our next lesson we will use proportions to find corresponding parts of similar triangles.

• Summary of lesson, assessment(s), and student work Rocket man was a lesson aligning with Dan Meyers curriculum. We introduced the concept of similarity by showing my mentor, Rick, at the NASA space center in Florida. In the spirit of Dan Meyer's technique, the students formulate the problem in front them. They were asked what they could gather from the photo. The students created the problem of figuring out how big the rocket was by knowing Rick's height. The students got a copy of the picture and measured Rick and the rocket.  They set up a proportion to using Rick's height and their measurements to figure out how tall the rocket engine is. We checked the rocket engine's Wikipedia page to check our numbers. This hook gave the student a real life example of both similarity and dilation.   After this hook we drew a DSRP to connect dilation as our final transformation. The  diagram was a part/whole visual which models the 'system' thinking of DSRP.  Transformations are the larger 'whole' which gets put in a box. Then all the 'parts' are scattered above the box in circles. Dilations were the newest part that we learned after slides, reflections, and rotations. I then highlighted the different 'perspectives' from which you can show transformations by putting hash marks through boxed: verbally, graphically, and algebraically.

I then led ten minutes of direct instruction on the definition of scale factor and similarity. The students practiced the new concept with some dilations classwork.

At the end of class we reviewed dilations with the whiteboards. I posed a series of questions by giving them the form of a dilation and asked for the written or algebraic dilation on their whiteboard. For HW (student work) they practiced some more dilations and we reviewed the HW next class together followed by a HW check (student work).

DRAFT: This module has unpublished changes. DRAFT: This module has unpublished changes.

Lesson Two: Shadow Man

• Grade level and curricular materials

This geometry class had a mix of ninth and tenth graders. Materials include handouts, rulers, popsicle sticks, calculators, smartboard, and the Problem of the Day.  Our textbook was Discovering Geometry by Kendall Hunt Publishing. The class did not receive a book to bring home but could access the book online with a class username.

• Classroom

There is always an posted on the left hand side of the board for the students to follow. The students receive a every three classes so they are aware of upcoming learning objectives and assignments.

• Number and ability levels of students

This classroom is a heterogeneous group of twenty students. There are a couple students on IEPs for Emotional Disturbances and ADD. There are many visual and kinesthetic learners.

• Point in the teaching sequence the lesson takes place

This lesson was on November first during a unit on triangles, a few weeks before my solo period began.

• Rationale for lesson plan

In the previous two lessons we learned how to set up proportions and the similar triangle conjectures: SAS, AA, and SSS. In this lesson  we used similar triangle knowledge to solve indirect measurement problems. In the following class, the students went outside and gathered their own measurements to find the heights of: basketball hoops, buildings, trees, etc.

• Summary of lesson, assessment(s), and student work

We started the class with our routine Problem of the Day.  The problem is chosen from an assortment of old NECAP tests ranging from Functions & Algebra, Data, Geometry & Measurement, to Numbers & Operations. The students always checked their when they entered the room to collect their returned work.  After the problem of the day we reviewed the from the previous class. I always use popsicle sticks to randomly call on students when reviewing homework.  I usually get a gauge of how the students did on their HW by taking a quick assessment while they do the problem of the day.

We began the similar triangles lesson with the 'Shadow Man' hook.  This hook was modeled after Dan Meyer's technique. The students were shown a picture of fellow math teacher, Wayne, with the school's goal post. They were then asked what they can surmise from the photo Eventually they realized that given enough information they can figure out how tall the goal post is. The investigation ended with real world proof of what the students had found. In the photos we found the shadow's length and Wayne's shadow's length. We then drew two diagrams of Wayne and the goalpost.  The students then reached the conclusion that we have two similar triangles through AA; connecting to our previous lesson.  We then practiced with some similar triangle examples.

This lesson was further built upon in an indirect measurement problem solving activity (student work). The students went out to the school yard and found the height of various objects. Using similar triangles, measuring tape, their height they found the heights of trees, goalposts, lightposts, and rooflines.

The students practiced their similar triangles for HW (student work) that night. This lesson was assessed in the next class through a similar triangle HW check (student work). Through a series of three concept tests 80% of the class mastered the similar triangles concept.

DRAFT: This module has unpublished changes.