MAT Science and Mathematics : 2012

Wednesday, September 12, 2012

Tuesday, September 11, 2012

Lesson Plan Template

Lesson Plan Template

Teacher Candidate________________________ Lesson Topic________________________ Date_________________ Grade Level_______ Approximate Time ____________________
Stage 1 – Desired Results
National Standards: Georgia Performance Standards:
Essential Question:
Stage 2 – Assessment Evidence
Performance Tasks:	Other Evidence
Stage 3 – Learning Plan
Materials and Resources (Attach all templates.):
Technology (If no technology is used in this lesson, provide a justification for choosing not to use technology.)
Activating Thinking Strategies :(KWL, Questions, PBL, Word Splash, Concept Attainment Activities, Anticipatory Guide…):
Teaching Strategies (whole group, small group, active engagement of ALL students):
Evidence of Differentiated Instruction (Content, Process, and Product: MI, Learning Styles, Flexible Grouping, Stations, etc.):
Modifications for Special Needs Students: (IEPs, etc.)
Summarizing (List higher order thinking questions to determine what students have learned; Students answer essential question):
Stage 4 - Reflections
Pre- Teaching Reflection: (Assessed on the Lesson Plan Evaluation Rubric) The teacher candidate reflects upon the context of the lesson in terms of the students’ prior knowledge and other topics they have been studying. The teacher candidate reflects upon modifications and adaptations planned for the lesson and articulates rationales for planning decisions, e.g., why technology is or is not included in the lesson, etc. Using specific descriptors described by James Beane below as a guide, the pre-teaching reflection must include a discussion of how this lesson relates to the department’s conceptual framework. While not all descriptors are applicable to every lesson, this portion of the pre-teaching reflection is intended to encourage you to think about the proposed instruction through a guided process based on our conceptual framework. James Beane (2005) provides nine characteristics that a critical constructivist would find useful when assessing a teacher candidate’s instruction: germane, crucial and vital, calls for creativity, application of knowledge, coherent, democratic, sociopolitical consciousness, agency and problem posing. Thus, we seek evidence to show that our candidates are presenting material in a way that is relevant to students (germane), that what is being taught is very important (crucial and vital), students must be creative in thinking of possible solutions (calls for creativity), activities ask students to reflect on how the lesson can be used in their daily lives (requires application of knowledge), the lesson is presented in an easy-to-follow format, and it flows from one stage to another smoothly (coherent), the topic of the lesson is a social problem that needs our attention (social problem focus), the lesson provides students an opportunity to learn and apply knowledge of democratic processes (democratic), students have an opportunity to see the relationship between social and political perspectives (sociopolitical consciousness), the instruction provides pathways for power to affect change (agency) and that the lesson encourages looking at a topic from a multiple perspective viewpoint (problem posing). Post- Teaching Reflection: (Assessed on the TPOI Rubric) The teacher candidate… · Provides thoughtful assessment of the lesson’s effectiveness and the extent to which the lesson achieved its goals by citing examples from the lesson. · Identifies strengths and weaknesses of the lesson; provides specific suggestions for improving areas of weakness. · Provides appropriate explanation of why a lesson would or would not be changed for future instruction. · Reflects upon interactions with parents, students, and others to improve practice.

Lesson Plan Example Math

Lesson Plan #4

Teacher Candidate: Shayna Chapman Lesson Topic: Math

Date: March 24, 2011 Grade Level: 4^th Approximate Time: 45 minutes

Stage 1 – Desired Results

National Standards:

Grades 3–5 Expectations: In grades 3–5 all students should–

design investigations to address a question and consider how data-collection methods affect the nature of the data set;

collect data using observations, surveys, and experiments

Select and use appropriate statistical methods to analyze data

describe the shape and important features of a set of data and compare related data sets, with an emphasis on how the data are distributed;
use measures of center, focusing on the median, and understand what each does and does not indicate about the data set;
compare different representations of the same data and evaluate how well each representation shows important aspects of the data

Georgia Performance Standards:

.M4D1. Students will gather, organize, and display data according to the situation

and compare related features.

a. Construct and interpret line graphs, line plot graphs, pictographs, Venn

diagrams, and bar graphs.

c. Compare different graphical representations for a given set of data.

e. Determine and justify the range, mode, and median of a set of data.

Essential Question:

How can the mean, median, mode and range be used to analyze a given set of data?

Stage 2 – Assessment Evidence

Performance Tasks:

Students will determine the mean, median, mode and range for sets of data and use the info to answer questions.

Other Evidence

Students will use activates for the quick comprehension quiz which will provide teacher with printable data (informal assessment).
The teacher will monitor the room to check the group’s work. In addition, the groups will turn in their data forms.

**Early finishers: Students/groups who finish early will be able to visit the website http://www.bbc.co.uk/schools/ks2bitesize/maths/data/mode_median_mean/play.shtml

Stage 3 – Learning Plan

Materials and Resources (Attach all templates.):

Computer

Promethean board

Activotes

Flipchart

Desks/chairs

Data Graphic Organizer (reproducible)

Notebook paper

Pencils

Shoes

Websites used: http://www.bbc.co.uk/schools/ks2bitesize/maths/data/mode_median_mean/play.shtml

or http://www.bbc.com.uk/education.mathfile/shockwave/games/train.html

Technology (If no technology is used in this lesson, provide a justification for choosing not to use technology.)

This lesson relies heavily on the use of technology. To begin this lesson, the teacher will use the promethean board and computer to project the lesson’s flipchart. During the later portion of the lesson, students will use the activotes to check their knowledge by completing an interactive quiz.

Activating Thinking Strategies :(KWL, Questions, PBL, Word Splash, Concept Attainment Activities, Anticipatory Guide…):

To begin this lesson, students will be asked to complete a short “Dear Teacher” letter. During this activity, students will use a piece of notebook paper and pencil and will write a short letter to Ms. Chapman in which they will write on the one of the following prompts:

Option 1: What are you still having trouble understanding- mean, median, mode and range?

Option 2: If you feel you have mean, median, mode and range under your belt, explain how you can use these in everyday life.

Teaching Strategies (whole group, small group, active engagement of ALL students):

This lesson will begin with the students as a whole group as they complete the activating strategy, “Dear Teacher.” During this writing exercise, each student will write about what they do not understand about the concept or how they can use the concepts in everyday life. This activity should take the students 5-7 mins.

After the students write their letters, the teaher will collect them and the class will proceed to cover the MMMR flipchart on the promethean board. This flip chart will contain the standards, essential question, and everyday life examples. After the flipchart has been covered, students will be divided into mixed ability groups (small groups) in which they will be asked to find the mean, median, mode and range of their groups shoe sizes and family sizes. They will be asked to complete the given MMMR data sheet and the groups will compare their data with others when they finish.

To conclude the lesson, students will be given a short quiz in which they will use the activotes to project their answers. By using the activotes, data will be shown right away and the teacher will be able to make further explanations if need be. Students will then be asked a series of higher level thinking questions and then be dismissed.

Evidence of Differentiated Instruction (Content, Process, and Product: MI, Learning Styles, Flexible Grouping, Stations, etc.):

For this lesson, flexible groups will be used as students complete the lesson’s interactive portion. These groups have been made based on the student’s Benchmark test scores. This week, I gathered the student’s scores and made the groups to have a student (or two) who is higher so that he/she would be able to lead the group (if need be). In addition, I kept in mind similar personalities and tried to make the groups have ones that would work well together.

Although each child has a different learning style, this lesson will meet each student style in the following ways:

· Visual Learner: These students will enjoy the flipchart and the graphs that they will find as they collect their data. In addition, these students will find that the quiz is helpful because it is presented in a very pleasing manner.

· Auditory Learner: These students will enjoy listening to the teacher and group members as the concepts are explored.

· Kinesthetic Learner: These students will love working with the groups and getting to hold a voter for their quiz. I think that these students will have the most fun with this activity because it is very hands on!

Modifications for Special Needs Students: (IEPs, etc.)

Since I will be teaching this lesson to all of the fourth graders at one point during the day, I will have several students who have special needs. As best I can, I will address each specific need presented in my classroom:

Visual and auditory impairments: These students will sit in the front of the classroom so that they are in close proximity to the teacher. In addition, students who have auditory impairments will wear their hearing headphones as the teacher uses the microphone.

ADHD: Children that are ADHD will also sit close to the teacher. These students will also find that there will be little clutter on the desks when they work on their activities (which will help their attention levels). These students will enjoy working in groups (which they have been previously placed).

*All students who have a special need (learning disability) will be placed in a group/pair which will have a student who is of a higher academic level. This way, these students can learn not only from the activities, but also from the surrounding students.

Summarizing (List higher order thinking questions to determine what students have learned; Students answer essential question):

To conclude the lesson, the students will be asked a series of higher level thinking questions. These questions include:

· How can I use M,M,M, and R in my everyday life?

· Which concept do you think we use more than the others? Give an example.

· How can the mean, median, mode and range be used to analyze a given set of data?

Stage 4 - Reflections

Pre- Teaching Reflection:

I am looking forward to teaching this lesson because these students really struggle with the chosen concepts. I think that this lesson is germane in that it presents students with material that can be seen in their everyday life (germane) as well as the lesson is very active. Students will enjoy working in groups and they will remain active from the beginning of the lesson until the end. While the material does cover the GA standards, it is very crucial and vital that students be able to understand and apply these concepts to their everyday lives and it is preparing them for their CRCT which is in a few weeks. I think that by using different resources (Promethean board and interactive quiz, graphic organizer and groups) I think students will form a better understanding of the concepts. I also feel that this lesson is presented in a coherent fashion as well as it encourages creativity and overall a positive learning environment. Not only does this lesson meet a majority of the Beane characteristics, it also helps children to reflect and realize how they encounter mean, median, mode and range problems every day. I think my students will thoroughly enjoy this lesson and I look forward to their responses!

Lesson Plan Example Grammar Review

Teacher Candidate Kim F. Patton Lesson Topic_CRCT Grammar Review__ Date March 14, 2010 Grade Level 8th Approximate Time 55 minutes
Stage 1 – Desired Results
National Standards: 2. Students apply a wide range of strategies to comprehend, interpret, evaluate, and appreciate texts. They draw on their prior experience, their interactions with other readers and writers, their knowledge of word meaning and of other texts, their word identification strategies, and their understanding of textual features (e.g., sound-letter correspondence, sentence structure, context, graphics). 6. Students apply knowledge of language structure, language conventions (e.g., spelling and punctuation), media techniques, figurative language, and genre to create, critique, and discuss print and non-print texts. Georgia Performance Standards: ELA8R1. The student demonstrates comprehension and shows evidence of a warranted and responsible explanation of a variety of literary and informational texts. For literary texts, the student identifies the characteristics of various genres and produces evidence of reading that: Compares and contrasts genre characteristics from two or more selections of literature. Analyzes a character’s traits, emotions, or motivations and gives supporting evidence from the text(s). g. Analyzes and evaluates the effects of sound, form, figurative language, and graphics in order to uncover meaning in literature: i. Sound (e.g., alliteration, onomatopoeia, internal rhyme, rhyme scheme, meter) ii. Figurative language (e.g., simile, metaphor, personification, hyperbole, symbolism, imagery). h. Analyzes and evaluates how an author’s use of words creates tone and mood and provides supporting details from text. ELA8C1 The student demonstrates understanding and control of the rules of the English language, realizing that usage involves the appropriate application of conventions and grammar in both written and spoken formats. The student a. Declines pronouns by gender and case, and demonstrates correct usage in sentences. b. Analyzes and uses simple, compound, complex, and compound-complex sentences correctly, punctuates properly, and avoids fragments and run-ons. c. Revises sentences by correcting misplaced and dangling modifiers. d. Revises sentences by correcting errors in usage. e. Demonstrates appropriate comma and semicolon usage (compound, complex, and compound-complex sentences, split dialogue, and for clarity). f. Analyzes the structure of a sentence (basic sentence parts, noun-adjective, adverb clauses and phrases). g. Produces final drafts/presentations that demonstrate accurate spelling and the correct use of punctuation and capitalization.
Essential Question: Can you successfully answer all review questions correctly?
Stage 2 – Assessment Evidence
Performance Tasks: Review: Jeopardy game	Other Evidence CRCT practice review book – Answer Sheet p161 CRCT on April 20,2010
Stage 3 – Learning Plan
Materials and Resources (Attach all templates.): Jeopardy Review PowerPoint Word Splash – Review words Computer/Screen/Elmo CRCT Review books and answer guide
Technology: PowerPoint – Jeopardy CRCT Review Game
Activating Thinking Strategies: CRCT is in FOUR days Word Splash – <On PowerPoint> What are your struggles? List out ANYTHING you still have questions about and we will review.
Teaching Strategies: Whole Group: Jeopardy game for CRCT review. My general purpose in creating and executing this game is to have a fun, collaborative, and creative way to review grammar rules and usage in our classroom, and for students to experience the challenge and higher level thinking required to master the CRCT. If the students play the game and put in a maximum effort, their retention of the review material will be strengthened. Individual: After we play the game, the class will work independently in their CRCT workbooks (pages 137-152).
Evidence of Differentiated Instruction: Flexible grouping is consistently used. I will conduct whole-class introductory discussion for Grammar Review for the CRCT. We will play a game with the entire class. I will divide the class into teams based on ability. After the game, we will follow-up with independent work in their CRCT workbooks. By using multiple ways of presenting the material, the students will have a diverse sampling of questions as they may appear on the CRCT. For students with physical or cognitive disabilities, such a diversity of examples may be vital in order for them to access the concept being taught. Other students may benefit from the same multiple examples by obtaining a perspective that they otherwise might not.
Modifications for Special Needs Students: (IEPs, etc.) I do not currently have any IEPs. · Provided written individual instructional guides to insure that students stay focused and on task · Provided visual aids to accompany the lesson objectives
Summarizing: Ticket out the Door: Answer Sheet Page 161
Stage 4 - Reflections
Pre- Teaching Reflection: Two weeks ago the eighth grade took a benchmark to show the progress they have made this year in ELA. My cooperating teacher took the scores from that test and found areas that they are weak in. I focused this lesson on several of those elements. The quickest way to test their knowledge is to review with a game (germane). I took all of the questionable areas and made a review game. All of the questions came from other CRCT review test (coherent). I feel good about the wording of the questions. Often times the student will be familiar with the concept, but the wording of the test question will confuse them. Jeopardy game for CRCT review. My general purpose in creating and executing this game is to have a fun, collaborative, and creative way to review grammar rules and usage in our classroom, and for students to experience the challenge and higher level thinking required to master the CRCT (democratic). If the students play the game and put in a maximum effort, their retention of the review material will be strengthened. We have not used the CRCT test prep booklets and the students need to be familiar with the test questions. The review in the workbook will add to this review. POST-Teaching Reflection: This lesson went well, even though we had a fire drill during the middle of the class period. Fortunately I was prepared and was able to show my classroom management skills. At the beginning of the class, I had the students write down anything they felt they were still having trouble with. I had them continue to write of this sheet during the review game of any item they felt they needed practice on. I was very pleased to have such high participation. The review game of Jeopardy went very well. The students were able to see the screen and all of the components worked wonderfully! I have a fear of everything going wrong on observation day, but it went well. I am very happy with the participation from the game. I think I will break them into smaller groups next time so I can hear more of the students answer and be able to get feedback from more of them. When they had a question or I could hear that they were going to answer wrong, I asked several questions before going on to the next screen. By discussing it, I felt they were catching on to the right answer. I had made the review game based on the Benchmark test and feel I did a good job. A couple of questions stumped them and it was good to talk them out. Overall I feel the game was very productive in achieving a good review for the CRCT. I just love it when things work they way they are supposed to! Besides the fire drill, it was a great lesson!

Lesson Plan History

Teacher Candidate: J.J. Martone Lesson Topic: World History/Columbian Exchange

Date: November 15 2011 Grade Level: 9^th Approximate Time: 55 minutes

Stage 1 – Desired Results

National Standards: A. Thematic Standard 2:Time, Continuity, and Change

Georgia Performance Standards: SSWH10 The student will analyze the impact of the age of discovery and expansion into the Americas, Africa, and Asia

b. Define the Columbian Exchange and its global economic and cultural impact.

Essential Question: Why is chocolate milk a sweet example of the Columbian Exchange?

Stage 2 – Assessment Evidence

Lesson Plan Template

Performance Tasks:

I will ask the students the following questions:

-Why did different crops grow in different areas?

-What are some important foods that would have been missing from your area before 1492?

-What changed in 1492 that enabled foods to travel to different areas?

Other Evidence: Asking the students to identify the regions of the world where the ingredients to the chocolate milk originated

Stage 3 – Learning Plan

Materials and Resources (Attach all templates.):

-Columbian exchange chart

-Blank world map from http://www.studentsfriend.com/aids/curraids/maps/sfworldp.pdf

-world map (see PowerPoint)

-colored pencils

-chocolate milk (only if students want some and if they are not allergic)

Technology (If no technology is used in this lesson, provide a justification for choosing not to use technology.)

blank world map from internet

world map with countries listed from internet

constructed the Columbian Exchange Chart in a Word document

PowerPoint slide show

Activating Thinking Strategies :(KWL, Questions, PBL, Word Splash, Concept Attainment Activities, Anticipatory Guide…):

As the students walk into class, I will have projected from the projected the following: “write down some of your favorite breakfast, lunch, and dinner foods”. I will give them about 5 minutes to do this and then go into my lesson.

Teaching Strategies (whole group, small group, active engagement of ALL students):

- I will write the following quote on the board: “Before 1492, there were no tomatoes in Italy, no pineapples in Hawaii, no potatoes in Ireland, no oranges in Florida, and no cattle in Texas.”

- I will call on an individual student to read the quote to the class

- I will then divide students into pairs and ask them to answer the following question on a blank sheet of notebook paper: “Why were these important food crops missing in these areas before 1492?”

- I will give students background information on the Columbian Exchange in my PowerPoint.

- I’ll pass out the Columbian Exchange charts and blank world maps to each student in the class

- I’ll instruct students to examine the Columbian Exchange chart and the world map. Ill asked them to find the country of origin for each of the major food crops of the Columbian exchange. I’ll instruct the students to create a key and color and put a symbol of each plant and animal in the nation of origin.

- The students will answer the following questions presented on my PowerPoint:

Why did different crops grow in different areas? What are some important foods that would have been missing from your area before 1492? What changed in 1492 that enabled foods to travel to different areas?

- I’ll then inform the students that they are about to taste an example of the Columbian Exchange by passing out a small sample of chocolate milk to every student in the class that would like some along with a d list of chocolate milks ingredients on the PowerPoint.

- I’ll then ask the students to look for familiar ingredients in the product and make a list of the familiar ingredients on the PowerPoint.

- I’ll then ask the students to identify the regions of the world where the ingredients to the chocolate milk originated and discuss the Aztec Chocolate Drink.

- Then go into my summarizing activity, “Why is chocolate milk a sweet example of the Columbian Exchange?”

Evidence of Differentiated Instruction (Content, Process, and Product: MI, Learning Styles, Flexible Grouping, Stations, etc.):

Visual- seeing the questions

Auditory-hearing them being read off

Taste- drinking the chocolate milk

Flexible grouping- putting them into groups to help with the sharing of color pencils

Modifications for Special Needs Students: (IEPs, etc.)

Gifted Student- To challenge a gifted student would ask them the question “what happened if Columbus never landed in the Americas, would another ‘Columbian Exchange have happen? Would a different person/group have started a trade between the Old and New Worlds? Would the foods have ended up in different places than during the Columbian Exchange?”

Could also have a gifted student find out where the food was found of their favorite meal (breakfast, lunch, or dinner). Could also tie in the different thanksgiving foods since thanksgiving is coming up.

Summarizing (List higher order thinking questions to determine what students have learned; Students answer essential question): Have them answer the question “Why is chocolate milk a sweet example of the Columbian Exchange?” and “What was the impact of the Columbian exchange economically and culturally?” on a piece of paper.

Stage 4 - Reflections

Pre- Teaching Reflection: (Assessed on the Lesson Plan Evaluation Rubric)

Up to this point, the students have been studying the early civilizations of the Americas and Africa, and the Age of Exploration. My lesson will be the first that the students will see about the Columbian Exchange but is almost the end of the unit. I feel that the students will enjoy this activity in class because of the coloring, the topic of food, and receiving some chocolate milk. I feel that they will find it interesting that many of the common foods today were originally from outside the United States. The information will be presented in a relevant way to the students through food (germane). The students can also use it in their daily lives by looking at the ingredients in not only chocolate milk but other foods too (requires application of knowledge). The direction of the activity has an easy to follow format and flows from one part to another (coherent). It will be great using food as a tool in teaching the Columbian Exchange because it will get the interest of the students.

Post- Teaching Reflection: (Assessed on the TPOI Rubric)

I feel as if the lesson was very effective in teaching the Columbian Exchange because the students could relate to it through food. The students enjoyed the lesson and the chocolate milk treat at the end. An example of this was when a student broke down all of the different ingredients in a hamburger and was able to point out from the map they did, where all of the ingredients came from around the world. I also walked the class through a thanksgiving dinner and dessert with where foods such as corn, turkey, and sugar originated from. Some strengths that I had during the lesson plan was the variety of differentiated instruction, enthusiasm, and my planning and preparation. I asked the students to make a key and use colors to show plants and draw a symbol to represent an animal. I had many different maps showing, the countries of the world, the triangular trade pattern, and a blank map that the students had to color and add symbols along with the triangle trade pattern routes. Another strength I mentioned was my enthusiasm. I believe that enthusiasm is a major key to teaching because the students will feed off of it and it showed especially during the lesson. My last strength I felt that really helped me was my planning and preparation I put into this lesson. Mrs. Blake gave me advice and she told me that planning and preparation is everything when it comes to teaching a lesson. It helped set a good ground for me to teach the lessons and make a few minor adjustments as the day went on. Some areas I need to work on are projecting the EQ and GPS at the start of the lesson not just for me but the students to see as well, some type of student self-assessment, and a critical thinking question that ties the lesson to the Unit EQ. Mrs. Blake already has the EQ and GPS up in the room, but I feel that it would be a great habit for me to get into by posting the EQ and GPS at the beginning of the lesson. For self assessment I could have them write down a question about something such as a term or concept that they did not understand at the end of the lesson and turn it in to me. Not only will they see what they need to study some more, but I can even use it to know what to cover with them before a quiz or test. For the critical thinking question, I tried to tie everything together at the end but I feel as if the students needed to do it. That means I need to develop a question that ties everything in the Unit together to show if the students can put things together. The only changes I would make to this lesson would be my few weaknesses that I had. I feel as if I incorporated those things into my lesson, it would have been even better than it was. Between classes, I asked Mrs. Blake how she thought the lesson was going. She thought it was going very well but pointed out a few things that I needed to try. The first being that when it came to putting them into groups, don’t let the students pick their own groups. 2^nd period was over this. I said “let’s get into groups” and sure enough they all jumped up and got together with their friends. Not that the behavior was terrible but they were the worst out of all three classes. So Mrs. Blake recommended that I put them into groups and when I did that behavior was better. My second adjustment came after 3^rd period. I noticed that it was taking the students all long time to answer the questions after they completed their maps and I needed to get to the summarizing questions. So after they completed, I had them move their desk back and complete the questions. This went so much smoother and behavior was even better. So that is how Mrs. Blake helped me with making adjustments throughout the day. I just want to point out a few things with the students. The first being a disappointment. With the map, I had feeling that they would have a hard time finding some countries so I would help them by letting them know what continent the country was from on. Well, I figured out that some students struggle with continents and could not even locate Europe and South America. These are 9^th graders and how do they not know the continents? With the disappointment out of the way I’ll go into my positive that I saw out of students. Mrs. Blake and I have discussed this student because we see his potential but you can see that he does not like school. He does not show up to class that most of the time. I can honestly say that I have only seen him about 4 times since I have been interning with Mrs. Blake this semester. During this activity, he was actually enjoying and doing the work. I am hoping that he recognizes that school can be fun and that Mrs. Blake and I care about him. He is a really smart student he just needs to put himself to the work and school.

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.