Manchester University



Causes of Development: War Lesson Plan #1by Karla ConradLesson: Mean Median and Mode Length: 45 mins Age or Grade Level Intended: Pre-AlgebraAcademic Standard(s):8.6 Students collect, organize, represent, and interpret relationships in data sets that have one or more variables. They determine probabilities and use them to make predictions about events. Performance Objective(s):At their seats students will independently be able to calculate the mean, median, and mode of their data set with 100% accuracy. Students will explain with 100% accuracy what the different means tell us regarding the question of if the amount of troops was increasing or decreasing between 2003 and 2008.Students will find the range and affect of outliers with 100% accuracy.Student will complete their homework with 85% accuracy. Assessment: While student are working on the mean, median, and mode independently at their seat, I will circulate the room to make sure they are being done correctly. While facilitating a discussion about the means and what they tell us, I will make sure all students are participating and conveying to me that they understand the relationship. While going through two homework problems that find the range and effect of outliers, I will circulate the room and make sure all students are finding these calculations correctly. I will grade the homework the next day.Advance Preparation by Teacher: Have a data set; using number of troops in Iraq for this lesson. (see attached)Procedure:Introduction/Motivation:Ask students what country they learned about in Mr. Kunze’s class. Let them talk about the Iraq area and maybe a few things they learned in that class. (only about 5 minutes spent on this) Hand out the troop statistics and have the students look at the numbers for a while. Now ask them to hypothesize whether they think the amount of troops has been increasing or decreasing since the war started? (Bloom’s: Analysis) Step-by-Step Plan:Tell the students we are going to calculate the mean, median, and mode of the data in order to help justify our hypothesis. Have the class turn to pg 412 in their books. Read out loud the definition of mean. (Gardner: Verbal-Linguistic)Ask the students if there are any questions about the example of finding mean.Repeat this with median and mode. (This should all be review, but needed to continue further with this standard) Have the students count off by sixes. Have them write down their number on the top of the statistics handout.Explain that the 1’s are going to find the mean, median, and mode of the number of troops in 2003. The 2’s will find it for 2004, 3’s 2005 and so on. During this time I will circulate the room an make sure calculations are being done correctly. (Gardner: Intrapersonal, Bloom’s: Application)After they independently find the mean, median and mode at their desk I will tell the students to meet with the other students that are the same number. Then all of the 1’s will compare their calculations. If there are discrepancies throughout the group they will have to help each other and recalculate to find what they think the real answer is. (Garder: Interpersonal, Bloom’s: Comprehension)Each group will then tell the group their answers.All of the students will return to their seats. I will then facilitate a short conversation about what number we should look at to see if the number of troops has increased or decreased. The students will explain what the means tell us about the data. (Bloom’s: Comprehension) I will then introduce the students to range and outliers. (pg 413) I will then give them their homework assignment pg. 415 7,8,11-16As a class go through number 7 and 13 to find the range and the effect of an outlier on the mean. I will circulate the room as we go through the problem to make sure students are calculating correctly. Make sure and direct the student’s attention to the directions on each section. Read them aloud and make sure they know what to do.Closure: Through this activity we learned a way to analyze data and draw conclusions from numbers. Tomorrow we will learn how to put numbers into graphs that will aid people in reading the data.Adaptations/Enrichment: For learning disabled students I would form the groups a bit different and make sure they were with students that would treat them with respect and help them understand the material. For students with intellectual disabilities doing two of the homework problems together will help because it simplifies the assignment a bit, but I would also take off one of the word problems from their assignment because that is not a top priority with this lesson.For ADHD students, after addressing the whole class about directions I would make a point before they leave to one-on-one tell this student the directions. Also during the first part of the lesson I would make sure they are making eye contact with me and see if they could repeat back the directions to me. For a student with a communication disorder I could tell them before the discussion to write down on paper what the means tell us about the data. Then when they are ready to share that information to raise their hand. While reading their thoughts I will not finish the students sentence for them and make sure they can take the time that they need to express their idea. Self-Reflection: 1. Did the students in the same groups come up with many different answers? 2.Were the students able to work as a team to come up with the final answer? 3. Were the students able to infer things from the mean? 4. Was the homework objective met? Iraq War FactsNumber of troops in IraqMar-2003175,000?Apr-2003175,000?May-2003172,500?Jun-2003176,250?Jul-2003178,750?Aug-2003172,500?Sep-2003160,000?Oct-2003167,500?Nov-2003160,000?Dec-2003152,500?Jan-2004155,000?Feb-2004138,000?Mar-2004147,500?Apr-2004160,000?May-2004170,000?Jun-2004172,500?Jul-2004167,500?Aug-2004175,000?Sep-2004160,000?Oct-2004166,000?Nov-2004172,500?Dec-2004183,000?Jan-2005180,000?Feb-2005175,000?Mar-2005168,500?Apr-2005168,000?May-2005168,000?Jun-2005168,000?Jul-2005168,000?Aug-2005168,000?Sep-2005175,000?Oct-2005185,000?Nov-2005190,000?Dec-2005190,000?Jan-2006185,000?Feb-2006168,000?Mar-2006168,000?Apr-2006168,000?May-2006168,000?Jun-2006162,000?Jul-2006162,000?Aug-2006173,000?Sep-2006173,000?Oct-2006173,000?Nov-2006187,000?Dec-2006175,000?Jan-2007162,000?Feb-2007167,000?Mar-2007172,000?Apr-2007180,000?May-2007185,000?Jun-2007192,000?Jul-2007194,000?Aug-2007196,000?Sep-2007198,000?Oct-2007198,000?Nov-2007198,000?Dec-2007190,000?Jan-2008190,000?Feb-2008185,000?Mar-2008180,000?Apr-2008175,000?May-2008170,000?Jun-2008165,000?Jul-2008162,000?Causes of Development: War Lesson Plan #2by Karla ConradLesson: Displaying Frequency and Histograms Length: 45 mins Age or Grade Level Intended: Pre-AlgebraAcademic Standard(s):8.6 Students collect, organize, represent, and interpret relationships in data sets that have one or more variables. They determine probabilities and use them to make predictions about events. Performance Objective(s):The students will create a line plot and find the mean, median, and mode of the data with 100% accuracy. Students will create a histogram with 100% accuracy. Student will complete their homework with 85% accuracy. Assessment: While student are working on the line plot, mean, median, and mode independently at their seat I will circulate the room to make sure they are being done correctly. I will circulate the room checking the students’ histograms.I will grade the homework the next day.Advance Preparation by Teacher: N/AProcedure:Introduction/Motivation:Our Unit theme involves us having a Penny War between all the homerooms. The math classes are going to be keeping track of who is winning on a day to day basis and who the overall winner will be. In order for us to be good at tracking this data we need to learn some different types of charts. Step-by-Step Plan:The first type of chart is a line plot. This plot keeps track of frequency. Frequency is the number of times a data item occurs. For example after the Penny Wars are over we may want to know who won the most individual days of the war. We will not be able to make our Penny War line plot till the war is over so for now we will practice with some different data.Let’s look at the body temperature of cats. A vet takes the temperature of 12 cats as they come in for checkups. The temperatures are as follows: 101,102,101,100,102,103,102,101,101,104,101,104. (Put these on the board)We now want to put these numbers in a line plot to see how many times each temperature appears. We must come up with a scale for our plot. What is the lowest temperature? (100) What is the highest temperature? (104)1257300461010So our scale is 100-104. Above each number we will put an X above it for each time a cat had that temperature. Go through the data points and end up with an image like this on the board: (Gardner: Visual-Spatial)From this type of chart we can easily find the mean, median, and mode like we did yesterday.Who can explain how to find the mode of this data? (Blooms: Application; Gardner: Linguistic)Who can explain how to find the median of this data? (Blooms: Application; Gardner: Linguistic)How did we find the mean yesterday? (Blooms: Knowledge)There is a shortcut when using frequency tables, instead of adding all the values up. We can use multiplication. How would this look? (Blooms: Analysis) : (100 *1) + (101*5) + (102*4) + (103*1) + (104*1)/ all the X’sTurn to pg. 420 and make a line plot of hours spent on homework. At your seat find the mean, median, and mode of this data. (Blooms: Comprehension; Gardner: Intrapersonal)After everyone has finished move on to explain a histogram.This line plot can also be turned into something called a histogram. Instead of having X’s tell us how many times that number occurs there will be a bar and frequency will be on the Y axis. For the number of hours spent on homework the histogram will look like this: (Gardner: Visual-Spatial)At your seat make a histogram for the cat temperature. (Blooms: Comprehension)Assign homework problems: pg. 420 5, 7, 8,13,14Closure: Tomorrow we will see how you can apply math to social studies as we look more at War and how it creates development. Adaptations/Enrichment: For learning disabled and ADHD students I could create X’s and numbers out of paper so they could create their line plots on their desks by actually moving the pieces around. This hands on activity would help them retain the information and stay engaged in the lesson. For students with intellectual disabilities I could do one of the homework problems together. It would help simplify the assignment a bit and it would help them understand the directions for the problems to come. For gifted and talented students I could change two of the review homework problems to story problems involving data. This would add some challenge to the assignment, but it would not give them additional work to do. For intellectual disability students I could have the cat temperature data and the hours spent on homework data already printed out on a sheet of paper. They could then draw the plots on the paper. This would decrease the amount of note taking and writing they would need to do during the lesson, which can sometimes be very time consuming. Self-Reflection: 1. Were the students able to apply the last lesson on mean, median, and mode to this lesson?2. Did the students meet the in-class objectives?3. Did the students follow the two examples or were more examples needed? 4. Did the majority of class have a question while working independently or were they able to do it without help?Causes of Development: War Lesson Plan #3by Karla ConradLesson: Stem-and-Leaf Plots Length: 45 mins Age or Grade Level Intended: Pre-AlgebraAcademic Standard(s):8th grade Math8.6 Students collect, organize, represent, and interpret relationships in data sets that have one or more variables. They determine probabilities and use them to make predictions about events. 8th grade World Geography4.11 Compare the levels of economic development of countries of the world in terms of Gross Domestic Product per capita and key demographic and social indicators. Map and summarize the results. Performance Objective(s):Student will explain the steps of creating a stem-and-leaf plot with 100% accuracy.Students will use the information from a histogram or line plot to create a stem-and-leaf plot with 100% accuracy.Assessment: The student will walk me through how to make a stem-and-leaf plot as I prompt them with questions. Through the example I will make sure the students are able to read the data and then turn it into a stem leaf plot. Advance Preparation by Teacher: Search for websites that have good GDP data for Iraq and the United States. find things that look like:Procedure:Introduction/Motivation:We have already looked at line plots and histograms that can organize data. Can someone summarize how we create a histogram? (Blooms: Knowledge) We will now look at another type: stem-and-leaf plots. I am first going to give an introduction to these charts and then tomorrow you are going to get in groups and apply this technique to data you find using the internet. Step-by-Step Plan:Introduce the vocabulary of stem and leaf. Show that the plot is made up of numbers and a single line. Explain that a stem is a number to the left of the line drawn. The leaf is then located to the right. Leaves are always single numbers. (Gardner: Verbal-Linguistic)Have the class turn to page 433 and find the data set that is the prices of digital music players. Walk them through the process to turn this into a stem-and-leaf plot. Reminders that the data must always be presented in numerical order. (Gardner: Logical-Mathematical)The first step is to choose the stems. Since the numbers are three digit numbers the stem must be 2 digits, leaving 1 for the leaf.The stems must be writing on the left side of a line, in numerical order.The leaves are them filled in, also in numerical order. At the bottom there must be a key. This one would read Key: 19| 2 means $192The result should look like the plot on page 433.The students will now walk me through creating a stem-and-leaf plot using the high temperatures data on page 433. (Gardner: Visual-Spatial)What will be my stems from this data?, Where should I write them?, How do I determine my leaves? (Gardner: Verbal-Linguistic; Blooms: Application)Why is it important that the leaves are only one digit numbers? (Blooms: Analysis)Handout an example of a Gross Domestic Product graph. Give a brief explanation to what this graph represents for a country and how it is calculated. Overall state that this can be looked at to establish the economic standing of a country. It is based on the amount of goods and services that are in the country, as well as involving imports and exports. Ask the students what they know about goods and services, as well as imports and exports. (Blooms: Knowledge) These are things that have been covered in history class or could come from general knowledge. This can turn into a discussion involving GDP.Lead a brief discussion about how GDP can change throughout a conflicting period like war. (Blooms: Evaluation) Closure: Tomorrow we are going to look at GDP of different places and summarize the data in a new form: a box-and-whisker plot. This plot helps summarize the GDP of countries in order for us to gather information from it. Adaptations/Enrichment: For learning disabled students I would have them write down their thoughts before asking them questions in front of the whole class. This will give them extra time to pinpoint ideas. For students with intellectual disabilities I would provide them with some problems worked out the will help them with tomorrows assignment. Having more examples to follow will allow them to get a grasp on the material. For ADHD students, during the first part of the lesson I would make sure they are making eye contact with me. Throughout the lesson I will continually keep their attention to the front of the board by using proximity and eye contact. I would also allow them to have a stress ball to squeeze during the lesson. This can sometimes keep their body busy, but allow them to better concentrate on the lesson. For a student with a visual impairment, I would find a line plot or histogram in brail so that they can read the data off the charts. Without this the student would feel disconnected from the task at hand. I would also make sure to give the students notes from class in brail or enlarged print. Self-Reflection: 1. Did the students follow the first example? 2. Were the students able to walk me through the steps of making the plot after only seeing one other example? 3. Were the students able to understand GDP?4. Were the students about to have a conversation about GDP, imports, exports and then connect it with conflict/war? 5. Was everyone participating in the discussion?Causes of Development: War Lesson Plan #4by Karla ConradLesson: Stem-and-Leaf Plots Length: 45 mins Age or Grade Level Intended: Pre-AlgebraAcademic Standard(s):8th grade Math8.6 Students collect, organize, represent, and interpret relationships in data sets that have one or more variables. They determine probabilities and use them to make predictions about events. 8th grade World GeographyCompare the levels of economic development of countries of the world in terms of Gross Domestic Product per capita and key demographic and social indicators. Map and summarize the results. Performance Objective(s):Student will explain the steps of creating a stem-and-leaf plot with 100% accuracy.Students will use the information from a histogram or line plot to create a stem-and-leaf plot with 100% accuracy.Assessment: The student will walk me through how to make a stem-and-leaf plot as I prompt them with questions. I will grade the project and be able to see if they read the data correctly and if they made the stem leaf plot correctly.I will grade the homework the next day. Advance Preparation by Teacher: N/AProcedure:Introduction/Motivation: We are going to use what we know about stem leaf plots and apply real life GDP data to the type of plot. In order to do this we will be going to the computer lab to research the data going to be used in the stem leaf plot. Review an example of a stem leaf plot done the previous day.Step-by-Step Plan:After creating that stem-and-leaf plot, give students instructions on the group project they are going to do: (Gardner: Interpersonal) They are going to use the internet to find data on the Gross Domestic Product (GDP) of Iraq and the United States. Remind them that GDP is something they have talked about in their history or geography classes. Can anyone summarize what we defined the GDP was yesterday during our conversation? (Blooms: Knowledge; Gardner: Verbal-Linguistic) They will need to find a line graph or a histogram that has this data. They will then create a stem-and-leaf plot by reading the data off of the graph shown. They will turn in both their created plot and the one from the internet. (Blooms: Comprehension, Application; Gardner: Logical-Mathematical) Tell the students to get into pairs. As a group they will need paper, a pencil, and one book for them to use as a guide.Take the class to the computer lab.Give them some links where they can easily find the data wanted so that the research does not consume their time.Have the students print off the graph and hand in their plots. After the students have finished, return to the room. Get the students attention and give them their homework assignment: pg 435-6 2-6, 7, 10,11Go over the directions for the problems. Walk them through number two to get them started. Closure: You have now created a plot that can easily read by people who want to study the GDP. We will review the material we have gone over in the past couple days including mean, median, mode, histograms, and the stem leaf plots tomorrow. We will not be doing it in a traditional manner, but instead do it in a class wide competition. Adaptations/Enrichment: For a class with multiple learning disabled students I would form the groups a bit different and make sure they were with students that would treat them with respect and help them understand the material. For students with intellectual disabilities doing two of the homework problems together will help because it simplifies the assignment a bit, but I would also take off one of the word problems from their assignment because that is not a top priority with this lesson.For ADHD students, after addressing the whole class about directions for the group project I would make a point while they are walking to the computer lab to one-on-one tell this student the directions. Also during the first part of the lesson I would make sure they are making eye contact with me. For a student with a visual impairment, I would make sure this student was in a group that worked well together and was willing to take the time to make sure the visual impaired student participated just as much as everyone else. Self-Reflection:Were the students able to remember stem and leaf plots from the previous day?Did the students follow the directions of the project easily?Did all students participate in the group project?Did the students seem to enjoy this activity?ResourcesGross domestic product. (2010, November 24). Retrieved from publicdata? ds=wb-wdi&met =ny_gdp_mktp_cd&idim=country:IRQ&dl=en&hl =en&q=gdp+graph+of+IraqIraq war in figures. (2010, September 1). Retrieved from ................
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