MAT Science and Mathematics : Lesson Plan Example Math

Lesson Plan Template

Teacher Candidate: Barry Rollins Lesson Topic: Distance Formula Date: 5-11-2011 Grade Level: 9th Approximate Time: 55 Minutes
Stage 1 – Desired Results
National Standards: Using the Common Core Standards: · 8.G.8. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. Georgia Performance Standards: MM1G1a. a. Determine the distance between two points.
Essential Question: How can we find distance using the knowledge we have already gained? Is there an easier way?
Stage 2 – Assessment Evidence
Performance Tasks: Group Work on Distance (Includes all files attached except for Distance Formula Notes)	Other Evidence Math 1 Final (not attached, two questions will concern distance)
Stage 3 – Learning Plan
Materials and Resources (Attach all templates.): Activator Distance Intro Grid Practice Distance on a plane Plane practice Distance Formula Notes
Technology (If no technology is used in this lesson, provide a justification for choosing not to use technology.) For this lesson I am not using technology. I am a major advocate of technology, especially since the arrival of my Promethean board, and had initially planned to use a flipchart to assist with this lesson. During the last week the motherboard has been replaced, and as of today (May 9^th) a pen has gone bad and my laptop will no longer work with the system. This may be fixed by the time of the lesson, in which event I may display some of the attachments to use as a template for teaching. I have decided it would be prudent to prepare for complications and this seemed the best way to ensure the lesson would be presented effectively without concern.
Activating Thinking Strategies LKWL, Questions, PBL, Word Splash, Concept Attainment Activities, Anticipatory Guide…): To begin the lesson I will allow the class to divide into their own groups. This is an advanced group of students and I have been grouping them all year, so I have decided it will be interesting to see what choices they make when left to make their own decisions. The activator worksheet will then be handed out, and includes a review of the Pythagorean Theorem. The activator has two purposes. First, the use of the Theorem is important to the lesson and the skill needs reviewing as they have not used it since the beginning of the year. Second, the Theorem is essential to derive the distance formula, and hopefully the activator will assist the students with making the connection on their own, rather than have me present the formula to them.
Teaching Strategies (whole group, small group, active engagement of ALL students): Once the activator is complete students will work on the Distance Intro worksheet in groups. The questions are designed to initially have them consider distance based on Taxicab Geometry (which may come up in discussion), which assists in creating the right triangle. This leads into a discussion of straight line distance and hopefully they will connect the Pythagorean Theorem with finding this distance. The grid practice document then provides practice for the students and an opportunity for me to monitor their work and look for misconceptions. The Distance on a plane document uses questioning in an attempt to have the students derive the distance formula on their own, although guided questioning and direct instruction may be needed at this point. This is followed by plane practice, which once again offers me the opportunity to monitor the students as they work and look for misconceptions. The bottom of this document asks for students to answer the essential questions, and this section will likely be used to lead a class discussion of the topic.
Evidence of Differentiated Instruction (Content, Process, and Product: MI, Learning Styles, Flexible Grouping, Stations, etc.): The lesson combines different styles of content and process within the delivery. There are sections where the content is higher level, usually along with a process of discussion and making connections to previous material. Examples of this would be realizing the use of the Pythagorean Theorem to find distance, and also connecting this concept to derive the distance formula. There are also sections which offer opportunity for practice and direct instruction in groups as needed, such as the grid and plane practice documents, which may assist students who learn math better as a “skill and drill” process. This is as flexible as my grouping has ever been, as I am allowing the students to choose their groups were I would normally divide them based on their abilities or personalities. Hopefully this will produce an interesting dynamic as groups attempt to progress with the assistance of their partners, and likely their friends. I believe technology would have assisted in making the concepts more visual, but hopefully the design of the documents and progression of the lesson will assist in making the concepts coherent.
Modifications for Special Needs Students: (IEPs, etc.) There are no special needs students in the class being observed, but the same lesson will be used earlier in the day for a collaborative Math 1 class. The students will be given the distance formula notes document, which not only explains the topic, but also explains some common misconceptions and mistakes students make with the formula. Grouping will be designed in this class, and will be done in mixed ability groups. There will also be an increased amount of direct instruction and guided questioning during the lesson. If any students have issues with reading they will be paired with other students for assistance, and they may also use their notes handout to assist when completing the practice sections of the lesson.
Summarizing (List higher order thinking questions to determine what students have learned; Students answer essential question): The summarizer for the lesson is included with the last practice document, which asks students to answer the essential questions for the lesson. This will be done as a discussion, and hopefully will lead to an understanding first of how to apply the Pythagorean Theorem to find the distance between two points. Also, this is designed to assist students in realizing the distance formula is basically a shortcut to solve the problem, and that it can be useful with more difficult problems where side lengths may be difficult to find as they are not integers, and also create more accurate answers by avoiding rounding during the process.
Stage 4 – Reflections
Pre- Teaching Reflection: The lesson is tied directly to other topics the students have studied, namely the Pythagorean Theorem. It was introduced during their eighth grade year, and extended this year to include the converse of the theorem and triangle classification. The activator is designed to assist them in revisiting this knowledge, with remediation if needed, and also to assist in making the connection to the Distance formula. I have mentioned why the technology will not be in use. Currently the board is working again, although there are still some issues with the pens and not everything has been worked out to my satisfaction. Considering modifications, I think the guided notes will be very useful for many of my students. In my collaborative class I plan to go through the process of labeling the points and plugging them into the formula thoroughly, as the formula is provided for their end of course test. The first handout is designed to have students consider Taxicab Geometry initially, only using avenues and streets to reach their destination. This should assist them in seeing the right triangle that is formed when working in this manner, and hopefully the connection to the Pythagorean Theorem and the hypotenuse being the missing length will be made without too much guidance. The grid practice document offers more practice wherein hopefully students who understand the concept can assist others in their group, and also I will have an opportunity to monitor the students as they work as well. The concept is then applied to the coordinate plane with the next handout, and it is assumed students will use the same method to find the missing distance. At the bottom of this document I attempt to use leading questions again, hopefully assisting the students in realizing shortcuts to find the distance, and possibly even to derive the distance formula itself. If time permits at this point I may go into a discussion of the formula, labeling points, and working out the calculations. The class observed has many advanced students, and many will have made this connection for themselves. Again, I will focus on that part in some of the other classes where it will be needed. The lesson is summarized with the essential questions, and the connection to the Pythagorean Theorem should be first identified as the method already learned which can assist in calculating this distance, as well as the use of the Distance Formula to assist in making the process easier and faster. I believe this lesson to be crucial and vital, considering the topic of the lesson to be the Distance Formula and the connection with the Pythagorean Theorem. The Theorem is one of the most important to Geometry in my opinion, and the many applications of the Theorem are very useful in everyday life for the students. Not to mention the variety of proofs of the Theorem and their worth in modeling this important process. The Formula also provides a method of calculating distance which can be applied in many jobs as well as daily life. Another standard in this unit is quadrilateral properties in the coordinate plane, and the Formula is essential in finding side and diagonal lengths to prove these properties. The lesson also calls for creativity. I think the concept is often taught by introducing the formula, how to label points, and how to work out the math. Honestly when I taught Geometry my first year that is exactly how I did it. This lesson makes the connection to the Pythagorean Theorem, and then allows students the freedom to make their own connection to the Formula and even attempt to derive it for themselves. Students can now be creative in coming with solutions for the Taxicab problem initially posed, as well as applying the Theorem and trying to derive the Formula. Finally, I believe the lesson to be coherent. The activator reintroduces the Theorem and allows students a chance to practice it, as well as allows me the chance to remediate if needed. The introduction of Taxicab Geometry forces students to look at the distance using a 90 degree angle, and should lead to the discovery of the right triangle and possible use of the Pythagorean Theorem to find the missing length. The questions then guide the students towards this knowledge, followed by time to practice the new skill. Once this is done the knowledge is applied to the coordinate plane, and questions again guide the students towards the Distance Formula. At this time I can remediate and focus on the basic skill if needed, or save the time for the final discussion of the essential question if the class is doing well with the concept. Overall I must say I will miss my technology, but that I believe the lesson should go well without it if things go as planned. Post- Teaching Reflection: (Assessed on the TPOI Rubric) The main goal of this lesson was to have students make the connection between the Pythagorean Theorem and the Distance Formula, and I think the lesson was effective in this respect. The initial activator allowed students the time to practice, and while many solved the problems without issue, I was able to assist some students with misconceptions. The most common misconception was labeling the hypotenuse incorrectly, and also some students would forget to take the square root to complete the problem. The initial Taxicab Geometry sheet worked well, and most students made the connection to the Theorem and solved the problems. A few realized we were working towards the Distance Formula as they had been exposed to it in their support class, and one student even mentioned liking to draw the triangle and use the Theorem better. Most students had little issue with the grid practice, as well as applying the knowledge to the coordinate plane. I noticed deriving the formula was a challenge for many of the students, although they were really using it in their computations without realizing it. One student said the formula was too hard so I asked him how he did the problem. As he described each step I would explain which part of the formula he was completing, and by the time he was done we arrived at the same answer. I am not sure if this helped him or not, but I think it helped put the Formula more in the terms that students would use and may have been helpful to others. I think the lesson had several strengths, most of which have been mentioned above. The guided questioning was useful to help students create connections of their own. I think putting these on the papers also allowed faster students to work ahead and make this connection, without stating it before other students were able to come to their own conclusions. The practice also worked well in solidifying the concept for many of the students. Finally, the flexible time I was using for either extra work labeling points and using the formula or discussing the essential question worked fairly well, although time was somewhat constraining. While the lesson had many strengths, there were more weaknesses than just the time constraint I ran into. The main weakness was in the Distance on a plane document. As mentioned before, students found it very challenging to derive the formula on their own. This may have been due to lack of prior experience isolating variables within equations, or possibly more guidance as needed for the process. Either way I found this to be the biggest weakness of the lesson. To solve these issues in the future, I would first address the time constraints. I think the activator would be the best way to resolve this issue, as it involves several problems using the Pythagorean Theorem. My initial thought was that more students would try the work in the groups as there were a similar number of problems to the number of students in the group, but if I cut this down to two problems (one to find a leg and one a hypotenuse) I believe it would still serve the purpose intended and allow me more time later in the lesson on the current topic. As for the major weakness in the Formula derivation, I think using some of the comments made by my student may be effective. I could use more guiding questions, and describe the steps of the Formula in terms similar to the student. I could also fill in some of the structure of the Formula for students who find this more challenging, to assist them in completing the task for themselves as well as to help model variable isolation from the Theorem. While this was not stated directly as a weakness or issue, my final change would be the use of technology. I could easily use visuals of taxi cabs to assist students in finding the right triangle, and could use coordinate planes to assist with this visual as well. There is good chance that with full use of my Promethean board the concepts of this lesson would remain unchanged, but the delivery would take a much stronger presence. I think the students took the lesson well, and judging from their comments during the lesson I believe the topic was understood by most. I know I will likely need to spend time on the subject tomorrow in my collaborative class, and reinforce the connections as well as labeling of points and use of the Formula. It was also interesting and refreshing to hear students mention prior knowledge from their support class, and I think this assisted many of them with their confidence levels and resulted in better work during the task. Considering conversations with others, the majority of this lesson is a work in progress and is the result of conversations with other teachers. As I mentioned before I initially began instructing students by providing the Formula and showing them how to plug in the coordinates and solve for the distance. It was my department head who first mentioned using the Theorem to introduce the concept, and I tried this last year for the first time. Before I began to write this particular lesson, I looked online and reviewed Power Points and lecture motes from some other schools and colleges. I then found the idea for the Taxicab Geometry, and created the guided questions to assist the students. I have not discussed this lesson specifically with any parents, although I have often discussed the class and my teaching method with parents. I believe the majority of students enjoy my class, and most are also successful. Two of my coworkers have daughters who are in ninth grade this year, and they were asking me which classes I would have to try and get them into the ones I would teach. I am now getting similar questions as to whether I will move up to Math 2 along with this class of students, but my Principal has a daughter who will be entering the ninth grade. I hope to be asked to teach this course again, as assignment of another teacher to the course might infer I was not as prepared to teach the class. I believe I will have the class again, however, and have even talked some with the Principal about the Department Head position. Keeping my fingers crossed.