High Data Analysis MASSI
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'''MODEL THE PROCESS: First we will work on how to find the range. Range is the difference between the highest and lowest values in a data set. Let's all say it together. Range is the difference between the highest and lowest values in a data set. '''Students who are unable to respond vocally can use a voice output device to respond. Show students the rainfall/temperature table and range equation. '''Here is an equation to show how to calculate range. It says highest value minus lowest value equals range. Now look at the data for the average temperature by month. Watch me as I fill out the equation and calculate the range. First, I find the highest value, 89, and I write it here. Then I find the lowest value, 51, and I write it here. Now I solve the equation to find the value, 38. ''' | '''MODEL THE PROCESS: First we will work on how to find the range. Range is the difference between the highest and lowest values in a data set. Let's all say it together. Range is the difference between the highest and lowest values in a data set. '''Students who are unable to respond vocally can use a voice output device to respond. Show students the rainfall/temperature table and range equation. '''Here is an equation to show how to calculate range. It says highest value minus lowest value equals range. Now look at the data for the average temperature by month. Watch me as I fill out the equation and calculate the range. First, I find the highest value, 89, and I write it here. Then I find the lowest value, 51, and I write it here. Now I solve the equation to find the value, 38. ''' | ||
− | + | [[File:StudentPractice.jpg]]''' STUDENT PRACTICE: '''Give each student the rainfall/temperature table and range equation.''' Now it's your turn. Look at the table and use it to calculate the range for total rainfall and average temperature. '''Use LEAST INTRUSIVE PROMPTS script as needed to help students with each step. | |
− | + | **Note: Have the students write the numbers into the formula, but do not score writing ability. If students are unable to write the number, they can use number stamps or direct the teacher to write it for them. | |
− | + | **Note: In the following problem, students are required to subtract. If students are unable to subtract independently, it is ok to provide them with a calculator or other visual, however they must do the work independently. Be consistent with the type of accommodation provided here. | |
CHECK AND SCORE | CHECK AND SCORE | ||
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'''MODEL THE PROCESS: Now we need to learn to calculate the average, or mean, of a data set. The average/mean is one way to describe the middle of a data set. The average is the sum of the data divided by the total number of values. Let's say that together. The average is the sum of the data divided by the total number of values. '''Students who are unable to respond vocally can use a voice output device to respond. Show students the monthly rainfall/temperature table and mean/average equation. '''Let's practice finding the average high temperature for the year by using this data set '''(point to right column with "average high temperature")'''. We will use our calculator to calculate our answer. First, I add up all of the data to get the sum. So to find the average temperature for the year, I add 51 + 55 + 63 + 72 + 79 + 86 + 89 + 88 + 81 + 72 + 62 + 53 = 851. Next I need to divide 851 by the total number of values. To find that number I just count the number of months, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. We have 12 total values, or months of data. Now I divide 851 ÷ 12 = 70.9. The mean or average high temperature for the year is 70.9 degrees. ''' | '''MODEL THE PROCESS: Now we need to learn to calculate the average, or mean, of a data set. The average/mean is one way to describe the middle of a data set. The average is the sum of the data divided by the total number of values. Let's say that together. The average is the sum of the data divided by the total number of values. '''Students who are unable to respond vocally can use a voice output device to respond. Show students the monthly rainfall/temperature table and mean/average equation. '''Let's practice finding the average high temperature for the year by using this data set '''(point to right column with "average high temperature")'''. We will use our calculator to calculate our answer. First, I add up all of the data to get the sum. So to find the average temperature for the year, I add 51 + 55 + 63 + 72 + 79 + 86 + 89 + 88 + 81 + 72 + 62 + 53 = 851. Next I need to divide 851 by the total number of values. To find that number I just count the number of months, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. We have 12 total values, or months of data. Now I divide 851 ÷ 12 = 70.9. The mean or average high temperature for the year is 70.9 degrees. ''' | ||
− | + | [[File:StudentPractice.jpg]]''' STUDENT PRACTICE: '''Give each student the rainfall/temperature table, mean equation, and a calculator.''' Now it's your turn. Look at the table and use it to calculate the average/mean. '''Use LEAST INTRUSIVE PROMPTS script as needed to help students with each step. | |
− | + | **Note: Have the students write the numbers into the formula, but do not score writing ability. If students are unable to write the number, they can use number stamps or direct the teacher to write it for them. | |
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− | + | [[File:StudentPractice.jpg]]''' STUDENT PRACTICE: '''Give each student the rainfall/temperature table.''' Now it's your turn. Look at the table and use it to find the mode. '''Use LEAST INTRUSIVE PROMPTS script as needed to help students with each step. | |
CHECK AND SCORE | CHECK AND SCORE | ||
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'''MODEL THE PROCESS: Now we are going to learn about how to find the median of the data. The median is the number that is in the middle of a data set after you put the numbers in order. Say it with me. The median is the number that is in the middle of a data set after you put the numbers in order. '''Students who are unable to respond vocally can use a voice output device to respond. Show students the rainfall/temperature table. '''Let's look at the data for average temperature. We are going to look at the data for fall only. The fall months are September, October, and November '''(point to months)'''. They are shown with a brown background in the table. The first thing I'm going to do is write all the numbers in order from least to greatest. Watch me write 62, 72, 81. There are three numbers here, so the middle is the second number. Count two numbers in one, two, '''(while pointing to 62, 72)'''. The middle number is 72°, so the median is 72°. ''' | '''MODEL THE PROCESS: Now we are going to learn about how to find the median of the data. The median is the number that is in the middle of a data set after you put the numbers in order. Say it with me. The median is the number that is in the middle of a data set after you put the numbers in order. '''Students who are unable to respond vocally can use a voice output device to respond. Show students the rainfall/temperature table. '''Let's look at the data for average temperature. We are going to look at the data for fall only. The fall months are September, October, and November '''(point to months)'''. They are shown with a brown background in the table. The first thing I'm going to do is write all the numbers in order from least to greatest. Watch me write 62, 72, 81. There are three numbers here, so the middle is the second number. Count two numbers in one, two, '''(while pointing to 62, 72)'''. The middle number is 72°, so the median is 72°. ''' | ||
− | + | [[File:StudentPractice.jpg]]'''STUDENT PRACTICE: '''Give each student the monthly rainfall/temperature table.''' Now it's your turn. Look at the table and use it to find the median. '''Use LEAST INTRUSIVE PROMPTS script as needed to help students with each step. | |
− | + | **Note: Have the students write the numbers, but do not score writing ability. If students are unable to write the number, they can use number stamps or direct the teacher to write it for them. | |
CHECK AND SCORE | CHECK AND SCORE | ||
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− | + | [[File:StudentPractice.jpg]]''' STUDENT PRACTICE: '''Give each student the monthly rainfall/temperature table for steps 50 & 51, and the Tuscan rainfall table and line graph for steps 52-54.''' Now it's your turn. Look at the table and see if you see any outliers. '''Use LEAST INTRUSIVE PROMPTS script as needed to help students with each step. | |
CHECK AND SCORE | CHECK AND SCORE | ||
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− | + | [[File:StopSign.jpg]] This is the end of the lesson. Have the student analyze the local weather patterns. They can either take data by reading a thermometer and tracking rainfall, or lookup the information online. They can then graph the data in scatterplots and line graphs to identify outliers or patterns in the data. Then, have students find the descriptive statistics using the data set. Graphing and descriptive statistics can be done using Microsoft® Excel. There is a generalization worksheet with this level. You can use this for additional guided practice or to send home as homework. | |
− | + | {| | |
− | '''INDEPENDENT PRACTICE: Data Analysis Skills Test''' | + | |rowspan=2|'''INDEPENDENT PRACTICE: Data Analysis Skills Test''' |
− | '''Teacher Says/Does''' | + | ||'''Teacher Says/Does''' |
− | '''Student Response''' | + | ||'''Student Response''' |
− | '''Error Correction''' | + | ||'''Error Correction''' |
− | + | |- | |
− | + | ||Give each student the ''''Data Analysis Skills Test 2''''.''' Read directions for each problem and have student select response. Record whether response is correct or incorrect.''' | |
− | Give each student the ''''Data Analysis Skills Test 2''''.''' Read directions for each problem and have student select response. Record whether response is correct or incorrect.''' | + | ||Only provide praise for completing assessment (if student needs encouragement). Do not provide specific praise for correct answers while student is testing. |
− | Only provide praise for completing assessment (if student needs encouragement). Do not provide specific praise for correct answers while student is testing. | + | ||Once the student has completed the test, review missed problems with the student. |
− | Once the student has completed the test, review missed problems with the student. | + | |} |
− | + | ||
'''Troubleshooting and Data-Based Decision Making for Data Analysis Skills Test:''' | '''Troubleshooting and Data-Based Decision Making for Data Analysis Skills Test:''' | ||
If student is unable to complete any items on the data analysis test independently and correctly, go back and teach one problem step-by-step. | If student is unable to complete any items on the data analysis test independently and correctly, go back and teach one problem step-by-step. | ||
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Revision as of 11:41, 20 August 2013
MASSI: Math Activities with Scripted Systematic Instruction
Activity: Analyzing Weather Patterns
Grade Band: High School Concept: Data Analysis |
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Common Core State Standard | Core Content Connectors | MASSI OBJECTIVES |
S-ID.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. | HS HS.DPS.1c1 Use descriptive stats; range, median, mode, mean, outliers/gaps to describe the data set | Identify Range, Mean/Average, Median, Mode, and Outliers/Gaps |
S-ID.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. |
Teaching Materials: Rainfall Scatterplot, Monthly Rainfall/Temperature Table, Annual Rainfall Line Graph, Annual High Temperature Line Graph, Equations for Range and Mean/Average, Table and Line Graph for Tuscan Total Rainfall
Other Materials: Rainfall Scatterplot, Monthly Rainfall/Temperature Table, Annual Rainfall Line Graph, Annual High Temperature Line Graph, Equations for Range and Mean/Average, Table and Line Graph for Tuscan Total Rainfall
Worksheets: There are student worksheets to review each component of the lesson
Assessments: Progress Monitoring for taking data during the lesson; Skills Test
TEACHING OVERVIEW: The first section of the MASSI provides remedial practice on identifying outliers in a data set, and reading tables and graphs. Students will then learn to use descriptive statistics (range, mean/average, median, mode, and outliers/gaps) in a data set.
SCRIPT FOR LESSON
MASSI CULMINATING ACTIVITY: Have the student analyze the local weather patterns. They can either take data by reading a thermometer and tracking rainfall, or lookup the information online. They can then graph the data in scatterplots and line graphs to identify outliers or patterns in the data. Then have students complete descriptive statistics on the data. Students can track other relevant weather data as well.
BUILD TOWARDS FULL GRADE LEVEL COMPETENCE
Here are ideas to build competence towards the full grade level competence using this same activity. See the unit plan and talk with the general education teacher for more ideas.
Component | Activity | What Student Does | Generalization/ Fluency |
Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. | Students will enter a data set (e.g., average high and low temperatures across a year for a specific location) into an appropriate graphing calculator or computer program to fit into a normal distribution. Students then evaluate the area of normal curves. | Decides if data set is appropriate for distribution analysis. Enters data into graphing calculator (or other appropriate computer program) to run descriptive statistics and fit a normal distribution. Evaluates the area of normal curves. | Have students complete data analysis across different data sets (e.g., different years, different locations, etc.). |
Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. | Creates two way frequency data tables (showing a relationship between two categorical variables). Have students create a table analyzing students' participation in sports vs. other extracurricular activities, also showing men vs. women's participation. Interpret relative frequencies and analyze for associations and trends. | Students create tables reflecting categorical data with at least two types of variables. Students then analyze the data looking for associations and trends. | Present as many types of categorical data sets as possible, with multiple categories. |