1. College and Career-Readiness Conference Summer 2015 FOR ALGEBRA 1 TEACHERS

2. Introductions  Mike Parker – Algebra & Stats Teacher at Patterson Mill High School (Harford County)  Brett Parker – Algebra & Geometry Teacher at C. Milton Wright High School (Harford County)

3. TODAY’S OUTCOMES Participants will: 1.Briefly review the instructional shift, COHERENCE. Examine how coherence is displayed in PARCC model content framework. 2.Take an in-depth look at the S-ID standards taught in Algebra 1. 3.Share best practices and identify muddy points.

4. OUTCOME 1 Participants will: 1. Review the instructional shift of COHERENCE.

6. In what grade does each standard fall? SP.A: Investigate patterns of association in bivariate data. SP.B: Draw informal comparative inferences about two populations. SP.B: Summarize and describe distributions. 6.SP.B: Summarize and describe distributions. 7.SP.B: Draw informal comparative inferences about two populations. 8.SP.A: Investigate patterns of association in bivariate data.

7. PARCC Model Content Framework Algebra 1

8. PARCC Model Content Framework Algebra 2

9. Problem Sort  For each problem, decide which level PARCC assessment it came from Grade 6, 7, 8, or Algebra I  You can use the Claims Documents to guide your choices ​  As your group is finishing sorting, answer the following: ​  How do these problems illustrate the instructional shift of COHERENCE? ​  What Standards for Mathematical Practice would students use to solve these problems?

10. Answer Key and Notes  Problem A – Grade 7  Problem B – Grade 8  Problem C – Grade 6  Problem D – Grade 8  Problem E – Grade 7  Problem F – Algebra I  Problem G – Grade 7  Problem H – Grade 6

11. OUTCOME 2 Participants will: 2. Take an in-depth look at the S-ID standards taught in Algebra 1

12. Cluster A. Summarize, represent, and interpret data on single count or measurable variable. Standard 1. Represent data with plots on the real number line (dot plots, histograms, and box plots).

13. Standard 2. Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (IQR, standard deviation) of two or more different data sets. Standard 3. Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

14. PARCC/HSA Comparison On the left is a PARCC problem, on the right is an HSA problem. What are the key differences that you see? What’s new compared to HSA? How will these differences impact instruction and instructional activities?

15. Teaching Standard Deviation  Introduce the concept of deviations from the mean and their effect on spread.  Explain how to calculate standard deviation using the formula. *Students should not be assessed on calculating by hand! Show them so they understand what the concept is.  Use technology to calculate standard deviation and discuss the need for precision.

16. Calculating Standard Deviation (Calculator) 1. “Stat” “Edit” 2. Enter data in L1 3. “Stat” “Calc” “1-var stats” 4. Standard Deviation is Sx The starting salaries (in thousands) at a company are given below, calculate the standard deviation. 18, 55, 65, 45, 43, 67, 88, 54

17. Calculating Standard Deviation (Spreadsheet) 1. Enter data in a column 2. Highlight the cell below the data 3. Choose the “Formula” tab 4. Insert “STDEV” 5. Select the cells that have the data The starting salaries (in thousands) at a company are given below, calculate the standard deviation. 18, 55, 65, 45, 43, 67, 88, 54

18. Cluster B. Summarize, represent, and interpret data on two categorical or quantitative variables. Standard 5. Summarize categorical data for two categories in two-way frequency tables, interpret relative frequencies in the context of the data. Recognize possible associations and trends in the data.

19. Standard 6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related a.Fit a function to the data; use the function to solve problems in the context of the data b.Informally asses the fit of a function by plotting and analyzing residuals c.Fit a linear function for a scatter plot that suggests a linear association

20. PARCC/HSA Comparison On the left is a PARCC problem, on the right is an HSA problem. What are the key differences that you see? What’s new compared to HSA? How will these differences impact instruction and instructional activities?

21. Cluster C. Interpret Linear Models. Standard 7. Interpret the slope and the intercept of a linear model in context of the data. Standard 8. Compute, using technology, and interpret the correlation coefficient of a linear fit. Standard 9. Distinguish between correlation and causation.

22. PARCC/HSA Comparison On the left is a PARCC problem, on the right is an HSA problem. What are the key differences that you see? What’s new compared to HSA? How will these differences impact instruction and instructional activities?

23. 1. Highlight both columns of data 2. Insert Scatterplot 3. Add a trendline (more options!) 4. In 3 rd column “=slope*A2 + y-int” 5. Copy and paste formula for column 6. In 4 th column “=A2 – A3” 7. Highlight 1 st and 4 th columns 8. Insert Scatterplot Residual Plots on Excel

24. 1. Enter data and create regression line equation 2. Hit “2 nd ” “Y=“ to access StatPlot 3. For x’s use L1 4. For y’s, hit “2 nd ” “Stat” and arrow down to “Resid” 5. When graphing, use ZOOM9 for automatic fit to the residual plot Residual Plots on TI calculators

25. What makes a bad residual plot?  Pattern

26. What makes a bad residual plot?  Pattern

27. What makes a good residual plot?  Randomness (no patterns)  Close to 0

28. What have you done that works? Best Practices

29. Additional Resources  Illustrative Mathematics Illustrative Mathematics  PARCC Practice Test (go to Algebra 1 Item 20) PARCC Practice Test  Engage NY Module Engage NY Module  Mathematics Vision Project (Module 8 is Data) Mathematics Vision Project

30. What are the muddiest points? Record any question you still have after today’s presentation on your post-it note. Please provide your name and email address. Stick your post-it on the door as you leave today, and we will respond. Thank you!

31. Teaching the Common Core content using the Standards for Mathematical Practice to reach progressively higher levels of proficiency attains mathematical rigor. -Hull, Balka, and Harbin Miles