Evidence 1. Graphing Linear Inequalities Lesson PlanThis lesson plan was written and implemented for an Algebra 1 Part 1 class. I collaborated with my cooperating teacher to design and prepare for the lesson and I led the class. The student work is images of the graphs students worked on in their assigned groups from both of the class sections. I led this lesson twice, for two separate classes, and made some adjustments between classes based on how it went in the previous class. During this lesson, students were in small groups and were first given a linear inequality to graph on large poster paper and then were given an ordered pair. They went to every single graph in the room, in a gallery walk format, to determine if their given point was a solution to the linear inequality.
This lesson relates to Standard 8, Instructional Strategies, because I used a variety of instructional strategies to help my students develop a deep understanding of content areas and their connections. Throughout the lesson, I included whole-class discussions, direct instruction, a gallery walk with group work, and an individual assignment. This shows that I develop a variety of clear, accurate presentations of content, along with a variety of instructional strategies. In addition, during the gallery walk, groups were each assigned one of ten different linear inequalities. Then, they were each assigned a different ordered pair to test with each of the ten graphs. By the end of the activity, there were ten graphs of linear inequalities around the classroom with ten ordered pairs on each graph. This provided students with a variety of representations of finding solutions to linear inequalities graphically, showing that I develop a variety of clear, accurate representations of concepts. Students were also expected to make connections between the inequalities and solutions to determine rules for identifying solutions of linear inequalities. A typical lesson for this class included notes and individual practice. This task was very different from the regular schedule of activities my students did, and they handled the challenge extremely well. This also shows my ability to use a variety of instructional strategies in the classroom. After the first lesson, I reflected on how each activity went. I used my observations from monitoring the class to evaluate what needed to change. I determined that the engagement was not as interesting as I had hoped for students. In the second class, I adjusted my line of questioning by using popsicle sticks with the students’ names to determine which student would be called on next. This kept their attention better and more of them were contributing to the class discussion. Also, in both classes I adjusted the pacing of the lesson to provide more time for students to complete the gallery walk. This shows that I monitor and adjust strategies in response to learner feedback. The group work students were assigned in this lesson required them to discuss their ideas with one another. I circulated the room providing guided questions to groups who needed more support. I encouraged groups to develop their problem-solving skills by asking them questions instead of giving them a straight answer. This also communicated to them that I wanted them to do mathematical thinking for themselves. In addition, I chose to ask specific students in the group questions to encourage independent thinking despite it being a group activity. This shows that I encourage and guide the development of problem-solving skills and independent thinking in students. This evidence is important to me because it shows that I plan flexibly for a lesson and I have the ability to adjust instructional strategies both during class and for future lessons. The planning I did ahead of time to assign groups had to be adjusted on the spot when students were absent and I had multiple activities planned for the end of class, each with a different time requirement to allow students as much time as they needed on the gallery walk. This lesson also shows that I understand the importance of providing a variety of ways to learn throughout a class period to keep students engaged with mathematics. |
Evidence 2. Quadratics Desmos Lesson PlanThis lesson was an introductory lesson to start off a unit on quadratics in an advanced Algebra I class. I modified an investigation from my cooperating teacher by turning it into a Desmos activity for the class to do. Students started off the class by drawing the motion of objects that travel in a parabola and we discussed the shape and where those appear in real-life. Then, we moved on to discussing how each coefficient in the standard form of a quadratic equation (a, b, and c in ax2+bx+c=0) impacts the shape and location of the graph.
This relates to Standard 8 because it shows that I use a variety of instructional strategies to encourage learners to build skills to apply knowledge in meaningful ways. Throughout the Desmos activity, students had to draw pictures, make real-world connections, and compare various scenarios to find relationships. All of these were done through the online platform and students had their own worksheets that followed along with the activity, since that was how they were used to taking notes on new material. The worksheet had questions that required students to investigate various quadratic equations and develop their own conclusions. This shows I provide students with materials and media that are appropriate and challenging for their instructional levels. This lesson was given to me by my cooperating teacher and I chose to modify it. The original lesson was on paper and used graphing calculators, which students no longer use. By changing the lesson into a Desmos activity, which is a system they are familiar with, I was able to get more whole-class engagement with drawing pictures at the beginning of the lesson because they could see each other’s drawings and compare them. This shows that I evaluate curricular materials for accuracy, currency, and student interest because I modified a lesson to make it relevant and engaging for students. This evidence is important to me because I had a lot of fun teaching it to the students. Right from the start of the lesson, I could tell students were engaged. I was able to pull up all of their drawings on my own screen and share them with the rest of the class. We talked about which were realistic and how each of the drawings were related (they were all parabolas). I could tell that certain aspects of the lesson were challenging for students but they did a great job staying on task and asking each other questions. The students really did teach themselves the concepts by making connections and working with their table partners, so I really did not have to do much during the lesson. It was very rewarding to see them building new skills throughout the class. |
Evidence 3. "In Whose Best Interest Is Interest?" Lesson PlanThis lesson was written for a Math 8 class. I implemented this lesson in three separate classes, two of which also have a special education co-teacher. In this lesson, students are practicing their new knowledge on simple interest by exploring practical applications. Students worked in groups based on ability level and the assignment was modified for each group. Every single student was still working toward the learning goal: I can apply my knowledge of simple interest to a practical situation. Students first were given information on various Certificates of Deposit from two different banks. They were asked to compare the rates and determine which CD would be the best deal for the customer and the bank. The highest level group also compared different car down payments and interest rates to determine which deal to accept.
This relates to Standard 8 because it shows that I understand and use a variety of instructional strategies to encourage learners to develop deep understanding of content areas and their connections. In this lesson, the goal was for students to apply their knowledge of simple interest. Every single group accomplished this goal. Students were given information on a variety of Certificates of Deposits from two banks. This shows that I develop a variety of clear, accurate presentations and representations of concepts. Students were asked to compare the rates to determine which was the best deal. To do so, students had to take into account interest rates, length of the terms, and the minimum balance (or principal). Some of the questions they had to answer left room for interpretation. There was not one right answer, but the accuracy of their answer depended on the reasoning students provided. This shows that I encourage and guide the development of problem-solving skills and independent thinking in students. This evidence is important to me because it shows my ability to develop lessons that apply content to real world situations in a way that is engaging and beneficial to students. The most challenging part of this lesson was deciding how to change the types of questions each group received. I wanted to make sure that every group was still investigating and working on a high cognitive demand task while providing students with the support they needed. I think that the groups my cooperating teacher and I chose really helped students to support one another on the task. I was proud of the connections the students made and the reasoning they used to answer the questions. |