Unit Week Day CCSS Standards Mathematical Practices Objective I Can Statements 3 – Modeling Linear Data 8 Data to Functions 36 CCSS.MATH.CONTENT.HSS.ID.B.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. CCSS.MATH.CONTENT.HSS.ID.B.6.A Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. CCSS.MATH.CONTENT.HSS.ID.B.6.B Informally assess the fit of a function by plotting and analyzing residuals. CCSS.MATH.CONTENT.HSS.ID.B.6.C Fit a linear function for a scatter plot that suggests a linear association. Make sense of problems and persevere in solving them. Model with mathematics. Students will be able to make predictions using a trend line from a scatter plot. I can make predictions a trend line from a scatter plot. 3 – Modeling Linear Data 8 Data to Functions 37 CCSS.MATH.CONTENT.HSN.Q.A.2 Define appropriate quantities for the purpose of descriptive modeling. Attend to precision. Look for and make use of structure. Students will be able to fit a linear function (trend line) to a scatter plot with and without technology. I can fit a linear function line) to a scatter plot with and without technology. 3 – Modeling Linear Data 8 Data to Functions 38 CCSS.MATH.CONTENT.HSS.ID.B.6.A Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Attend to precision. Look for and make use of structure. Students will be able to create a scatter plot of bivariate data and estimate a linear function that fits the data and use this function to problems in the context of the data. I can create a scatter plot of data and estimate a linear function that fits the data and use this function to solve problems in the context of the data.
3 – Modeling Linear Data 9 – Functions 43 CCSS.MATH.CONTENT.HSS.ID.C.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. CCSS.MATH.CONTENT.HSS.ID.C.8 Compute (using technology) and interpret the correlation coefficient of a linear fit. Use appropriate tools strategically. Look for and make use of structure. The student can compute the correlation coefficient of a set of linearly related data using Microsoft Excel. I can compute the correlation coefficient of a set of linearly related data using Microsoft Excel. 3 – Modeling Linear Data 9 – Functions 44 CCSS.MATH.CONTENT.HSS.ID.C.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. CCSS.MATH.CONTENT.HSS.ID.C.8 Compute (using technology) and interpret the correlation coefficient of a linear fit. Use appropriate tools strategically. Look for and make use of structure. The student can compute the correlation coefficient of a set of linearly related data using technology. I can compute the correlation coefficient of a set of linearly related data using technology. 3 – Modeling Linear Data 9 – Functions 45 CCSS.MATH.CONTENT.HSF.BF.B.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x),f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an ex Attend to precision. Look for and make use of structure. The student can use the computations of the cerrelation coefficient to answer questions and make predictions. I can use the computations of the correlation coefficient to answer questions and make predictions. 3 – Modeling Linear Data 10 – Cause and Effect 46 CCSS.MATH.CONTENT.HSS.ID.C.9 Distinguish between correlation and causation. Construct viable arguments and critique the reasoning of others. The student will be able to understand the difference between correlation and causation. I can understand the difference between correlation and causation.
3 – Modeling Linear Data 10 – Cause and Effect 47 CCSS.MATH.CONTENT.HSS.ID.C.9 Distinguish between correlation and causation. Reason abstractly and quantitatively. The student will be able to understand the difference between correlation and causation. I can understand the difference between correlation and causation. 3 – Modeling Linear Data 10 – Cause and Effect 48 CCSS.MATH.CONTENT.HSS.ID.C.9 Distinguish between correlation and causation. Reason abstractly and quantitatively. The student will be able to understand and explain that a strong correlation does not mean causation. I can understand and explain that a strong correlation does not mean causation. 3 – Modeling Linear Data 10 – Cause and Effect 49 CCSS.MATH.CONTENT.HSS.ID.C.9 Distinguish between correlation and causation. Reason abstractly and quantitatively. The student will be able to understand and explain that a strong correlation does not mean causation. I can understand and explain that a strong correlation does not mean causation. 3 – Modeling Linear Data 10 – Cause and Effect 50 Assessment Assessment Assessment Assessment
Unit 3 – Modeling Linear Data Course: Algebra 1 8 Data to Functions Day: 37 Common Core State Standard: CCSS.MATH.CONTENT.HSN.Q.A.2 Define appropriate quantities for the purpose of descriptive modeling. Mathematical Practice: CCSS.MATH.PRACTICE.MP6 Attend to precision. CCSS.MATH.PRACTICE.MP7 Look for and make use of structure. Objective: Students will be able to fit a linear function line) to a scatter plot with and without technology. I can statement: I can fit a linear function (trend line) to a scatter plot with and without technology. Procedures: 1. Students will complete the Week 8 Bellringer (Day 37). 2. Students will work with partners and complete the Beginners guide to line of best fit and Gapminder line of best fit . 3. The Day-37-Presentation- Beginner line of best fit will be used to look for misconceptions and encourage discussion. 4. Students will complete Week 8 Exit Slip (Day 37) before leaving for the day. 5. Use the Day-37-Practice- Beginner line of best fit as individual practice or homework. Materials: Week 8 Bellringer (Day 37) Gapminder Line of Best Fit Beginners guide to line of best fit Day-37-Presentation- Beginner line of best fit Week 8 Exit Slip (Day 37) Day-37-Practice- Beginner line of best fit Accommodations/Special Circumstances: Technology: Gapminder Create Scatter Plot in Reflection: Extra/Additional Resources:
Unit 3 – Modeling Linear Data Course: Algebra 1 Topic: 9 – Understanding Functions Day: 41 Common Core State Standard: CCSS.MATH.CONTENT.HSS.ID.C.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. CCSS.MATH.CONTENT.HSS.ID.C.8 Compute (using technology) and interpret the correlation coefficient of a linear fit. Mathematical Practice: CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically. CCSS.MATH.PRACTICE.MP7 Look for and make use of structure. Objective: The student can determine whether correlation coefficient shows a weak positive, strong positive, weak negative, strong negative, or no correlation. I can statement: I can determine whether correlation coefficient shows a weak positive, strong positive, weak negative, strong negative, or no correlation. Procedures: 1. Students will complete the Week 9 Bellringer (Day 41). 2. Students will work with partners and complete the Day-41-Activity-Correlation coefficient. 3. The will be used to look for misconceptions and encourage discussion. 4. Students will complete Week 9 Exit Slip (Day 41) before leaving for the day. 5. Use the Day-41-Practice- Correlation coefficient as individual practice or homework. Materials: Week 9 Bellringer (Day 41) Day-41-Activity-Correlation coefficient Week 9 Exit Slip (Day 41) Day-41-Practice- Correlation coefficient Accommodations/Special Circumstances: Technology: Reflection: Resources:
Unit 3 – Modeling Linear Data Course: Algebra 1 Topic: 9 – Understanding Functions Day: 43 Common Core State Standard: CCSS.MATH.CONTENT.HSS.ID.C.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. CCSS.MATH.CONTENT.HSS.ID.C.8 Compute technology) and interpret the correlation coefficient of a linear fit. Mathematical Practice: CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically. CCSS.MATH.PRACTICE.MP7 Look for and make use of structure. Objective: The student can compute the correlation coefficient of a set of linearly related data using Microsoft Excel. I can statement: I can compute the correlation coefficient of a set of linearly related data using Microsoft Excel. Procedures: 1. Students will complete the Week 9 Bellringer (Day 43). 2. Students will work with partners and complete the Day-43-Activity. 3. The Day 43 – Calculating Correlation Coefficient using Excel will be used to look for misconceptions and encourage discussion. 4. Students will complete Week 9 Exit Slip (Day 43) before leaving for the day. 5. Use the Day-43-Practice as individual practice or homework. Materials: Week 9 Bellringer (Day 43) Day-43-Activity Day 43 – Calculating Correlation Coefficient using Excel Week 9 Exit Slip (Day 43) Day-43-Practice Accommodations/Special Circumstances: Technology: Microsoft Excel Reflection: Extra/Additional Resources:
Unit 3 – Modeling Linear Data Course: Algebra 1 Topic: 10 – Cause and Effect Day: 46 Common Core State Standard: CCSS.MATH.CONTENT.HSS.ID.C.9 Distinguish between correlation and causation. Mathematical Practice: CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively. CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others. Objective: The student will be able to understand the difference between correlation and causation. I can statement: I can understand the difference between correlation and causation. Procedures: 1. Students will complete the Week 10 Bellringer (Day 46). 2. Students will work with partners and complete the Day 46 Activity-Cause and Effect. 3. The Day 46 Presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete Week 10 Exit Slip (Day 46) before leaving for the day. 5. Use the Day-46-Practice – Cause and effect day 1 as individual practice or homework. Materials: Week 10 Bellringer (Day 46) Day 46 Activity-Cause and Effect Day 46 Presentation Week 10 Exit Slip (Day 46) Day-46-Practice – Cause and effect day 1 Accommodations/Special Circumstances: Technology: Reflection: Extra/Additional Resources:
Unit 3 – Modeling Linear Data Course: Algebra 1 Topic: 10 – Cause and Effect Day: 48 Common Core State Standard: CCSS.MATH.CONTENT.HSS.ID.C.9 Distinguish between correlation and causation. Mathematical Practice: CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively. CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others. Objective: The student will be able to understand and explain that a strong correlation does not mean causation. I can statement: I can understand and explain that a strong correlation does not mean causation. Procedures: 1. Students will complete the Week 10 Bellringer (Day 48). 2. Students will work with partners and complete the Day-48-Activity- Causation. 3. The Day 48 Presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete Week 10 Exit Slip (Day 48) before leaving for the day. 5. Use the Day-48-Practice as individual practice or homework. Materials: Week 10 Bellringer (Day 48) Day-48-Activity- Causation Day 48 Presentation Week 10 Exit Slip (Day 48) Day-48-Practice Accommodations/Special Circumstances: Technology: Reflection: Resources:
Unit 3 – Modeling Linear Data Course: Algebra 1 Topic: 10 – Cause and Effect Day: 49 Common Core State Standard: CCSS.MATH.CONTENT.HSS.ID.C.9 Distinguish between correlation and causation. Mathematical Practice: CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively. CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others. Objective: The student will be able to understand and explain that a strong correlation does not mean causation. I can statement: I can understand and explain that a strong correlation does not mean causation. Procedures: 1. Students will complete the Week 10 Bellringer (Day 49). 2. Students will work with partners and complete the Is This For Real Causation vs Correlation. 3. The Day-49-Presentation- Causation and Correlation will be used to look for misconceptions and encourage discussion. 4. Students will complete Week 10 Exit Slip (Day 48) before leaving for the day. 5. Use the Day-49-Practice – Causation and Correlation as individual practice or homework. Materials: Week 10 Bellringer (Day 49) Is This For Real Causation vs Correlation Day-49-Presentation- Causation and Correlation Week 10 Exit Slip (Day 49) Day-49-Practice – Causation and Correlation Accommodations/Special Circumstances: Technology: https://www.glogster.com/Student Friendly Data & Web Resources Reflection: Extra/Additional Resources:
Line of Best Fit Classwork Linear Regression Line --- a best fitting line for a certain group of data that have been plotted. This allows you to make predictions about where other points would most likely fall. Example: Below is a table of asteroid names, their average distances from the sun (in millions of miles), and their orbital periods (the time it takes them, in years, to revolve around the sun). Question 1: About how long would it take an asteroid that is 230 million miles from the sun to make 1 revolution? Question 2: If an asteroid was discovered, and astronomers knew that its orbital period was almost exactly 4 years, about how far would you predict this asteroid to be from the sun? Asteroid Name Average Distance from the Sun Orbital Period Ceres 257.0 4.60 Pallas 257.4 4.61 Juno 247.8 4.36 Vesta 219.3 3.63 Astraea 239.3 4.14 Hebe 225.2 3.78 Iris 221.4 3.68 Flora 204.4 3.27 Metis 221.7 3.69 Hygeia 222.6 5.59 1. Make a scatterplot of the table above on your graphing calculator. 2. Graph the Linear Regression Equation in the form y = mx + b Answer to Question #1 It takes about ______ years for an asteroid that is 230 million miles from the sun to make one revolution. Answer to Question #2 above: An asteroid that has an orbital period of 4 years could be predicted to be about _______________ miles from the sun.
5 2.80 2.10 6 3.10 2.00 7 2.90 2.65 8 3.25 2.25 9 3.30 2.60 10 3.60 3.00 11 3.25 3.10 Let High School GPA be your x values (List 1) and College GPAs be your y values (List 2). 1. Make a scatterplot of the data. Here is your copy/paste: 2, 1.6 2.25, 2 2.6, 1.8 2.65, 2.8 2.8, 2.1 3.1, 2 2.9, 2.65 3.25, 2.25 3.3, 2.6 3.6, 3 3.25, 3.1 2. Find the Regression Equation in the form y = mx + b 3. Graph the Regression Equation on your scatterplot to make sure it looks like the best - fitting line. 4. a.) If you earn a 3.80 GPA in high school, predict what you would get in college for your Freshman year. Freshman year GPA would be _______. b.) If a freshman in college got a 3.60 GPA, what would she have got for her high school GPA? High School GPA would have been _______. Practice Activity #2 Chirping Frequency and Temperature for the Striped Ground Cricket
Day 42 Choose the most appropriate Correlation Coefficient 0.067 -0.012 2.1 -2 -0.08 2.1 0.9 -1 3. -2 1.2 -0.66 0.001 4. -1 -0.3 -0.001 0.11
student grades. There could be a variety of other factors that influence the student grades in addition to the weather. could be additional factors such as the activities that resulted in injury, were both groups (L & R handed) doing the same tasks, etc.