College and Career-Readiness Conference Summer 2015 FOR ALGEBRA TEACHERS

TODAY’S OUTCOMES Participants will: 1.Briefly review the instructional shift, COHERENCE 2.Examine MD College And Career-Ready Standards and their relationship to PARCC assessment items 3.Identify important concepts and vocabulary associated with specific statistics standards 4.Share best practices and identify muddy points

Mike Parker – Patterson Mill HS, Harford County Brett Parker (no relation other than being two ridiculously good looking guys) – C. Milton Wright HS, Harford County

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

A purposeful placement of standards to create logical sequences of content topics that bridge across the grades and courses, as well as across standards within each grade/course.

Coherence across the grades What does solving the equation (x – 5) 2 = 36 have to do with geometry?

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).

Standard 4 Use data from a sample survey to estimate a population mean or proportion Standard 5 Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant

OUTCOME 2 Participants will: 2.Look at the PARCC model content framework for the high school statistics and probability standards.

PARCC Model Content Framework Algebra 1

PARCC Model Content Framework Algebra 2

Algebra I & II Problem Sort  For each problem, decide which level PARCC assessment it came from: Middle Grades, Algebra I or Algebra II.  You can use the Combined Claims Document 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?

Answer Key and Notes  Problem A – Grade 7  Problem B – Algebra 2  Problem C – Algebra 2  Problem D – Algebra 1  Problem E – Algebra 2

OUTCOME 3 Participants will: Identify important concepts and vocabulary associated with specific statistics standards by completing a rigorous activity

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. 3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

4 Use data from a sample survey to estimate a population mean or proportion 5 Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant

What's New? - Problems D & E Shape, Center and Spread - Shape - Skewed left/right, approximately normal, uniformly distributed, mode, outlier Center - Mean, median Spread - Range, interquartile range, standard deviation

Write down two things you notice and two things that you wonder about the data in front of you.

Pick two classes to compare using the following questions: 1. Which class did better? Why did your group decide that? 2. Which class was more consistent? Why did your group decide that? 3. Which class has the highest standard of deviation? 4. Are there any students that affected your answers?

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.

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

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

A Fit a function to the data; use functions fitted to data to solve problems in the context of the data B Informally assess the fit of a function by plotting and analyzing residuals C Fit a linear function for a scatter plot that suggests a linear association

What's New? - Regression Algebra I students will be required to make linear, exponential and quadratic modeling equations. These models may be created without regression as well, for example by estimation or by recognizing a pattern based on the points. Ex: Write an exponential model that contains the points (0, 6) and (1, 18).

What's New? - Residuals Interpreting residuals - "Analysis of residuals may include the identification of a pattern in a residual plot as an indication of a poor fit." - PARCC Claims Document for Algebra I EOY

Residuals  Defined as the prediction error  Smaller values = better fit  Residual plots show the relationship between an x value and the corresponding residual value  Technology should be used to create residual plots  A residual plot showing random points is linear while a residual plot showing a curved pattern is non-linear  A scatter plot that appears linear may not be when looking at the residual plot with an exaggerated y- axis

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

Anscombe!  With your group (or partner or by yourself) do the following to your data set:  A. Find the standard deviation of the x-variables  B. Find the equation and correlation coefficient for the line of best fit  C. Create a residual plot

Based on the residual plots, which equation gives the better fit to the data? How do you know it's better?

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 _

Share Out  Pick a task that aligns to one or more of the following: S.ID.2, S.ID.3, S.ID.6, S.IC.4 or S.IC.5, then do the following:  Share what elements of the task differ from Maryland's previous curriculum (what shifts will have to occur?)  What Standards for Mathematical Practice are involved?  What previous knowledge/courses will be helpful? How does this prepare students for "the next level"? _

What have you done that works? Best Practices

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 address. Stick your post-it on the door as you leave today, and we will respond. Thank you!