DIFFERENTIATED LESSON PLAN Suggested Components Name: Rodriquez/Smith Subject: Math 7 Date(s): 2-4 days (depending on block schedule) Lesson Topic: Data Analysis Review Within Unit on: Measures of Central Tendency and Box Plots Unit Essential Question(s): How do I summarize and display data using the measures of central tendency and box and whisker plots? Time Frame for Lesson: Lesson Generalization(s): Measures of central tendency are used in real life in different situations. Lesson Essential Question(s): How do the measures of central tendency compare and differ? How do measures of central tendency relate to real life? Why do we have different measures and how do you decide which measure of central tendency to use for a given situation? Additional Questions What are the measures of central tendency, their definitions, how do you calculate each? How can you create a box and whisker plot and what does it illustrate? CCSS/Objectives for the Lesson: Essential Standards: 4.01 Collect, organize, analyze, and display data (including box plots and histograms) to solve problems. 4.02 Calculate, use, and interpret the mean, median, mode, range, frequency distribution, and inter-quartile range for a set of data. KNOW UNDERSTAND DO Definitions of measures of central tendency How to calculate mean, median, mode, and range The importance of using the appropriate measures of central tendency. The similarities and differences between Collect Organize Analyze Display Solve Calculate Interpret
Transcript
DIFFERENTIATED LESSON PLANSuggested Components
Name: Rodriquez/Smith Subject: Math 7 Date(s): 2-4 days (depending on block schedule)
Lesson Topic: Data Analysis ReviewWithin Unit on: Measures of Central Tendency and Box Plots Unit Essential Question(s): How do I summarize and display data using the measures of central tendency and box and whisker plots? Time Frame for Lesson: Lesson Generalization(s): Measures of central tendency are used in real life in different situations. Lesson Essential Question(s): How do the measures of central tendency compare and differ?How do measures of central tendency relate to real life?Why do we have different measures and how do you decide which measure of central tendency to use for a given situation?
Additional QuestionsWhat are the measures of central tendency, their definitions, how do you calculate each?How can you create a box and whisker plot and what does it illustrate?
CCSS/Objectives for the Lesson:Essential Standards: 4.01 Collect, organize, analyze, and display data (including box plots and histograms) to solve problems.4.02 Calculate, use, and interpret the mean, median, mode, range, frequency distribution, and inter-quartile range for a set of data.
KNOW UNDERSTAND DODefinitions of measures of central tendency
How to calculate mean, median, mode, and range
How to create a box and whisker plot
The importance of using the appropriate measures of central tendency.
The similarities and differences between mean, median and mode.
The process of constructing a box and whisker plot and how the box and whisker plot represents the data given any central tendency.
Interdisciplinary Connections: Ideas: SS: discuss statistics of causalitiesPhy Ed: average amount of free throws in basketball for famous basketball players
Knowledge of Students: There are a wide range of mixed abilities (EOG scores range from 2-4). I gave a learning styles
test that showed all styles of learning (visual, kinesthetic, and auditory). 18 are visual, 7 are kinesthetic, and 2 are predominantly auditory. The majority of students are visual so I make sure I write the things I say. I also have students repeat directions and processes for the auditory learners. I encourage group discussion for the auditory learners as well. The majority of students like to work in a group; I know this from a ticket out. There are 3 students that do not like working in a group. I do not force them when the activity isn’t meant to be a group effort. English is a native language except for 2 students. I pair these students together that speak Spanish. I also have a student that is bilingual. She likes to help so I often pair them together to help communicate. In addition, I use the Spanish English translation on notes and when possible.
20 out of the 27 like sports, 15 out of 27 were interested in music and 4 were into cars. 13 out of 27 were into animals.
Two students have 504 plans for ADHD and preferential seating. Susan is one these students. I intentionally seat her in the front of the room next to a high performing student to help her focus. I know these two students would get along well because they are both on the swim team and are friends. Susan commented in her learning log that she likes working with her partner, Mary, because it helps her to learn better. Mary, a good teacher and listener, enjoys helping others.
Time Activating Strategy/Link to Prior Knowledge/Warm-up:
10 min Students will complete a word splash for box and whisker plots and measures of central tendency. Students will use 8 out of 14 words to determine the relationship between the terms in 1-3 paragraphs. Words for the Splash: upper quartile, range, median, mode, upper extreme, whiskers, interquartile range, data set, lower extreme, mean, divide , lower quartile, sum, average
Word Splash is a teaching strategy that makes vocabulary acquisition easier for elementary school students. Before beginning a new unit of study, a teacher will determine the most important vocabulary words for the topic. These words are then splashed, or displayed, in the classroom at the start of the unit.
When the students enter the classroom and see the new words, their interest is peaked and they are motivated to learn what they mean and why they are there. The teacher then invites them to try and read the words and guess what they mean. These predictions help their brains to organize and assimilate the new vocabulary.
As the students read and learn about the content area topic, they add pictures to the vocabulary words that represent their definitions. Students can also create their own word splashes on the front of their folders or notebooks with definitions and illustrations of the vocabulary terms. The word splash can then be used as a study aid to help students interact with and recall the words.
For a video that includes examples of different types of word splashes: http://www.youtube.com/watch?v=IxS1buOWgbw
Other types of Hooks/Activating Strategies for the following days:1. Playing Jeopardy in groups, boys versus girls. A fun way to get them going. We would not play Jeopardy very often in order to keep it unique and more of a
special activity.2. Bringing in a guest speaker, a mathematician or someone from the real world who works with statistics (i.e. the business world). Speaker will be directly related with the topic at hand.
Differentiated Activating Strategy
The word splash is differentiated through tiering the assignment. The Lower Level students will complete a matching with definitions and words. They will then receive a fill in the blank to understand how the words connect. There will be space provided for students to write additional thoughts about how the words connect.The On Grade students will complete the assignment listed above (8 out of 14 words).The Above Grade students will use all 14 words to write 1-3 paragraphs about how the words connect.
Other types of Hooks/Activating Strategies:Adding games is an element of fun which is a predictor of motivation. The majority of students like to play games so we may try this tomorrow. Inviting a speaker provides for a real world connection and piques interest.
Time Lesson/ Content/ Process Activity
15 min Students read different articles based on readiness and interest that include the words from the word splash. Some articles are about: baseball, football, and animals. Teachers use the knowledge of students to pick articles.
10 min
Go over the Task 1 choice board with the students to make sure that they understand the requirements and the expectations. Students will choose 3 in a row to complete. A rubric is assigned to set guidelines and set expectations. (Task 1 and rubric is included after the lesson plan.)
40-80 min Allow time for students to get started with the choice board activities. Decide how much time should be allotted per task and if the tasks take more than one day.
40-50 min
Task 2: Students choose the interest that best fits: sports, music, or cars. Then students complete the task(s) that follow in pairs. Regardless of the interest chosen, students will make charts, graph results, calculate measures of central tendency and the range, gather all their information and present to class their findings briefly.
Assignment will be started in class and completed at home if need be. Presentations will begin the next day. Reflections will be due the day following the last presentation.
(Task 2 and rubric is included after the lesson plan.)
30-40min Task 3: Students calculate mean, median, mode and range using M&M’s. In pairs using bags of M & M’s, students calculate the measures of central tendency. The following directions apply for all.1. Calculate the mean number of M & M’s in each bag (total).2. Calculate the mean number of each color of M & M’s in each bag.3. Calculate the median number of M & M’s based on color totals.4. Calculate the mode for the M & M’s based on color.5. Calculate the range of M & M’s.
Green Groups: Students are obligated to use regular, peanut, and crispy M & M’s.Red Groups: Students are obligated to use regular and peanut M & M’s.Blue Groups: Students are obligated to use regular M & M’s.
After making calculations, work with other members of your color to combine your answers and get final number for each. Each group will then have a final set of numbers which will be presented to the class as a whole. The teacher will then tally the total numbers together on the Smart Board to see the differences.
(Task 3 and rubric is included after the lesson plan.)
10 min Allow students to present their rap, poem or song. (Voluntary)
Differentiated Content
Task 2 The content is differentiated by interests: sports, music or cars. In addition, Task 2 is differentiated by content by students using the internet or reference books provided by the teacher for homeruns, hits, RBI’s, and batting average information.
Task 3 The process is the same in this activity. However, the content is differentiated by readiness because students are using more than one kind of M&M. (The more choices of M&M’s the more difficult it is to calculate.)
Differentiated Process
Task 1 The choice board is designed on the teachers’ knowledge of students and is differentiated by readiness and multiple intelligences. Students have the choice to complete three tasks in a row on the Tic-Tac-Toe choice board. The sections on the board are differentiated based on Bloom’s Taxonomy. There is a rubric included. The teacher can appropriately challenge certain students by guiding them to complete particular tasks.
Task 3 is tiered by ability. The green group is more challenging because they have to compare between three types of M&M’s.
Adaptations for Inclusion: Students are allowed to complete any 3 sections on the board. They do not have to be in a row.
Time Summarizing Activity/Closure (each day if lesson extends more than one day)
10 min 3-2-1 – Students will write 3 things that they found out, 2 interesting things and 1 question that they have about measures of central tendency and/or box and whisker plots.
Differentiated Summarizing Activity/Closure
Products/Assessment:Tiered by Choice - Students will provide all answers and assignments from the Tic-Tac-Toe choice boards for Task 1
For task 2, Multimedia presentation choice such as Smart board, PowerPoint, or handouts
Differentiated Products
Materials and Resource: Word Splash wordsTic-Tac-Toe BoardsRap/Poem/Song RubricVocabulary Terms
Reflection/Notes:
Task 1:Choose any three activities below. Make sure that you get three in a row, column, or diagonal to successfully complete this task! (Hint: measures are defined as mean, median, and/ or mode.) You must use all three of the central tendencies by the end of the three choices.
Choose one of the measures and write a poem which would help to explain them to a non-math
person.
Choose one of the measures and make a drawing or cartoon identifying the measure you chose to a non-math person.
Choose one of the measures and depict it using a slogan
Choose 2 measures and create a story (written or verbal) with any
differences and similarities.
Choose 2 measures and create a poster about the similarities and
differences.
Choose 2 measures and create a rap or song about them and
compares the similarities and differences.
Using all 3 measures, debate which is the best for measuring
central tendency within your group.
Using all 3 measures, go online and use the Smart
Board to present the class w/ real life stats and their measures of
central tendency.
Using all 3 measures, create an interview in which one person
plays the role of an interviewer, and the other is a measure of
central tendency.
Task 1: Mean, Median, and Mode RubricStudent Name: ________________________________________
CATEGORY 4 3 2 1MathematicalConcepts
Explanation shows complete understanding of the mathematical concepts used to solve the problem(s).
Explanationshowssubstantialunderstanding of the mathematical concepts used to solve the problem(s).
Explanationshows someunderstandingof themathematicalconcepts needed to solve the problem(s).
Explanationshows verylimitedunderstandingof theunderlyingconceptsneeded to solvethe problem(s)OR is not written.
Explanation Explanation is detailed and clear.
Explanation is clear.
Explanation is a little difficult to understand, but includes critical components.
Explanation is difficult to understand and is missing several components OR was not included.
Working withOthers
Student was an engaged partner, listening to suggestions of others and working cooperatively throughout lesson.
Student was an engaged partner but had trouble listening to others and/or working cooperatively.
Student cooperated with others, but needed prompting to stay on-task.
Student did not work effectively with others.
Completion All measures are used.
All but 1 of the measures are used.
All but 2 of the measures are used.
None of the measures are used.
Creativity Showed a high level of creativity.
Showed some level of creativity.
Showed a limited level of creativity.
Showed nolevel of creativity.
Task 1 Anchor Activity: Create challenge questions of varying degrees of toughness. They must be associated with the concepts of mean, median, or mode. They will be used for class review before the unit exam. Review will consist of typical review and the possibility of a few rounds of Math Millionaire.
Task 2: Choose the interest that best fits you: sports, music, or cars! Then complete the task(s) that follow in pairs. Assignment will be started in class and completed at home if need be. Presentations will begin the next day. Reflections will be due the day following the last presentation.
Sports: Teacher will provide a list of the top players in baseball over the last few years. Students will choose two baseball players of their choice. Students will access their statistics from the past 6 years (via the internet:
http://sports.yahoo.com/mlb/stats or reference books provided by the teacher depending on number of available computers/availability of computer lab), more specifically homeruns, hits, RBI’s, and batting average.
Students will make charts of each player, year, and stats. Students will graph results on the same graph for each stat, using different colors to
differentiate between the two players. Students will calculate measures of central tendency. Students will calculate the range for each player’s stats for that period of time. Students will gather all their information and present to class their findings briefly. Students will briefly present their findings to the entire class. They will discuss:
o The players they chose, the references used.o The statistics.o The charts and the graphs.o Their calculations of central tendency and range.o Their conclusions (i.e. forecast of future)
Students will also comment on any reasons for discrepancies in the numbers. Students are required to present and encouraged to do a multimedia presentation.
o In the case of the sports interest group, the student will assume the role of a sportscaster to deliver his stats, results, conclusions, etc. to the class.
o They may use also the Smart board, PowerPoint, handouts, or any way they feel comfortable presenting.
Students will begin this in class and have time to work on it today, finish at home if necessary, and be presenting it tomorrow.
A brief 1-2 paragraph reflection on another student’s presentation and what you learned, due day after presentations are complete.
Music: Teacher will provide a list of the top songs over the last few years. Students will choose at least 2 songs of their choice. Students will access the information from the past 6 years (via the internet:
http://www.billboard.com/bbcom/charts/chart_display.jsp?g=Singles&f=The+Billboard+Hot+100) more specifically number of days in the top spot, top 10, etc. and the different songs that were there.
Students will make charts of each song, with a breakdown by year.
Students will graph results on the same graph for each song, using different colors to differentiate between the two songs.
Students will calculate measures of central tendency. What was the mean number of days in the top spot, top 10, etc. What was the median, and what song was the mode.
Students will calculate the range for each songs measures for that period of time. Students will gather all their information and present to class their findings briefly. Students will briefly present their findings to the entire class. They will discuss:
o The songs they chose, the references used.o The statistics.o The charts and the graphs.o Their calculations of central tendency and range.o Their conclusions (i.e. forecast of future)
Students will also comment on any reasons for discrepancies in the numbers. Students are required to present and encouraged to do a multimedia presentation.
o In the case of the music interest group, the student will assume the role of a disc jockey to deliver his stats, results, conclusions, etc. to the class.
o They may also use the Smart board, PowerPoint, handouts, or any way they feel comfortable presenting.
Students will begin this in class and have time to work on it today, finish at home if necessary, and be presenting it tomorrow.
A brief 1-2 paragraph reflection on another student’s presentation and what you learned, due day after presentations are complete.
Cars: Teacher will provide a list of cars over the last few years. Students will choose at least 2 cars of their choice. Students will access the information from the past 6 years (via the internet:
http://www.caranddriver.com/) to gather information on the cars and their prices. Students will make charts of each car, with a breakdown by year. Students will graph results on the same graph for each car, using different colors to
differentiate between the two cars. Students will calculate measures of central tendency. Students will calculate the range for each car measured for that period of time. Students will gather all their information and present to class their findings briefly. Students will briefly present their findings to the entire class. They will discuss:
o The cars they chose, the references used.o The statistics.o The charts and the graphs.o Their calculations of central tendency and range.o Their conclusions (i.e. forecast of future)
Students will also comment on any reasons for discrepancies in the numbers. Students are required to present and encouraged to do a multimedia presentation.
o In the case of the car interest group, the student will assume the role of a car salesman to deliver his stats, results, conclusions, etc. to the class.
o They may also use the Smart board, PowerPoint, handouts, or any way they feel comfortable presenting.
Students will begin this in class and have time to work on it today, finish at home if necessary, and be presenting it tomorrow.
A brief 1-2 paragraph reflection on another student’s presentation and what you learned, due day after presentations are complete.
Task 2 Anchor Activity: Think of another interest (i.e. another sport) you may be interested in. Perform some of the same calculations and looks for trends in the numbers across different sports (i.e. players in their prime, players in contract years, etc.
Task 2 SPORTS
1. Using the handouts or the internet, pick two baseball players and locate their stats over the past 3 years. Use the chart below to organize your data.
2009 2010 2011
Homeruns
Hits
RBI
AVG
2. Then graph your results, having a separate graph for each statistic (i.e. both players homerun totals on the same graph, using different colors to tell them apart)
3. Calculate the following measures of central tendency for the statistics that you find over the past 3 years for each of the two players:
o Mean for each statistico Mode for each statistico Median for each statistico 4. Range for each statistic
4) Comment on any discrepancies in the numbers.
5) Prepare a brief presentation for tomorrow in the role of a sportscaster. You are encouraged to use multimedia equipment, but it is not required.
Task 2 CARS
1. Using the handouts or the internet, pick at least two cars and locate prices for at least 3 different years. Use the chart below to organize your data.
CARS 2009 2010 2011
Car 1
Car 2
Car 3
Car 4
2. Then graph your results, having a separate graph for each statistic (using different colors to tell them apart)
3. Calculate the following measures of central tendency for the statistics that you find over the past 3 years for each of the cars:o Mean for each statistico Mode for each statistico Median for each statistico Range for each statistic
4. Comment on any discrepancies in the numbers.5. Prepare a brief presentation for tomorrow in the role of a car salesman. You are encouraged to use multimedia equipment, but it is not required.
Task 2 MUSIC
1. Using the handouts or the internet, pick at least two popular songs and locate their stats over the past 3 years. Use the chart below to organize your data.
MUSIC:SONG “X”
2009 2010 2011
Top Song
Top 5
Top 10
Top 100
2. Then graph your results, having a separate graph for each statistic (using different colors to tell them apart)
3. Calculate the following measures of central tendency for the statistics that you find over the past 3 years for each of the songs:o Mean for each statistico Mode for each statistico Median for each statistico Range for each statistic
4. Comment on any discrepancies in the numbers.
5. Prepare a brief presentation for tomorrow in the role of a disc jockey. You are encouraged to use multimedia equipment, but it is not required.
Explanation shows complete understanding of the mathematical concepts used to solve the problem(s).
Explanationshowssubstantialunderstanding of the mathematical concepts used to solve the problem(s).
Explanationshows someunderstandingof themathematicalconcepts needed to solve the problem(s).
Explanationshows verylimitedunderstandingof theunderlyingconceptsneeded to solvethe problem(s)OR is not written.
Working withOthers
Student was an engaged partner, listening to suggestions of others and working cooperatively throughout lesson.
Student was an engaged partner but had trouble listening to others and/or working cooperatively.
Student cooperated with others, but needed prompting to stay on-task.
Student did not work effectively with others.
MathematicalErrors
90-100% of the steps and solutions have no mathematical errors.
Almost all (85-89%) of the steps andsolutions have no mathematical errors.
Most (75-84%) ofthe steps and solutions have no mathematical errors.
More than 75%of the steps andsolutions havemathematical errors.
Diagrams andSketches
Diagrams and/or sketchesare clear and greatly add to the reader's understanding of the procedure(s).
Diagrams and/or sketchesare clear and easy to understand.
Diagrams and/or sketches are somewhat difficult to understand.
Diagrams and/or sketches are difficult to understand or are not used.
Creativity Showed a high level of creativity.
Showed some level of creativity.
Showed a limited level of creativity.
Showed nolevel of creativity.
Neatness andOrganization
The work is presented in aneat, clear, organizedfashion that is easy to read.
The work is presented in a neat and organized fashion that is usually easy toread.
The work is presented in an organized fashion but may be hard to read at times.
The workappears sloppyand unorganized. It ishard to know whatinformation goes together.
Presentation The presentation is delivered entirely in saidrole with no missing components.
The presentation isDelivered somewhat in said role with 1- 2 components missing.
The presentation isdelivered in a limited said role with 3-4 components missing.
The presentationis not deliveredin said role withmore than 4 components missing.
Task 3: Mean, Median, Mode and Range with M&M’s
You will be assigned a group color. Regardless of what group color you are assigned to, use the chart similar to this to record your results.Color Regular Peanut CrispyGreenRedBlueOrangeYellowBrown
Green GroupIn pairs using the given bags of regular, peanut, and crispy M & M’s, answer the following questions:1. Calculate the mean number of M & M’s in each bag (total).2. Calculate the mean number of each color of M & M’s in each bag.3. Calculate the median number of M & M’s based on color totals.4. Calculate the mode for the M & M’s (hint: based on color).5. Calculate the range of M & M’s.
Red GroupIn pairs using the given bags of regular and peanut M & M’s, answer the following questions:1. Calculate the mean number of M & M’s in each bag (total).2. Calculate the mean number of each color of M & M’s in each bag.3. Calculate the median number of M & M’s based on color totals.4. Calculate the mode for the M & M’s (hint: based on color).5. Calculate the range of M & M’s.
Blue GroupIn pairs using the given bags of regular M & M’s, answer the following questions:1. Calculate the mean number of M & M’s in each bag (total).2. Calculate the mean number of each color of M & M’s in each bag.3. Calculate the median number of M & M’s based on color totals.4. Calculate the mode for the M & M’s (hint: based on color).5. Calculate the range of M & M’s.
Task 3 Anchor Activity:
Research M&M’s online on the website: http://www.m-ms.com/us/. See if you can find any information on how they are packaged and if there truly is a set way that the company determines how man y go in each bag, how many of each color, etc. Comment in your journals.
