College and Career-Readiness ConferenceSummer

2015

STATS STANDARDS

FOR ALGEBRA 1 TEACHERS

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)

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.

OUTCOME 1

Participants will:1. Review the instructional shift of

COHERENCE.

COHERENCE

GRADE-TO-GRADE COHERENCE

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.

PARCC Model Content FrameworkAlgebra 1

PARCC Model Content FrameworkAlgebra 2

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?

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

OUTCOME 2

Participants will:2. Take an in-depth look at the

S-ID standards taught in Algebra 1

HS.S.ID.A.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).

HS.S.ID.AStandard 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).

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?

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 L13. “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 column2. Highlight the cell below the data3. Choose the “Formula” tab4. 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

HS.S.ID.B.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.

HS.S.ID.BStandard 6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are relateda. 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

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?

HS.S.ID.C.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.

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?

1. Highlight both columns of data2. Insert Scatterplot3. Add a trendline (more options!)4. In 3rd column “=slope*A2 + y-int”5. Copy and paste formula for column6. In 4th column “=A2 – A3”7. Highlight 1st and 4th columns8. Insert Scatterplot

Residual Plots on Excel

1. Enter data and create regression line equation

2. Hit “2nd” “Y=“ to access StatPlot3. For x’s use L14. For y’s, hit “2nd” “Stat” and arrow down

to “Resid”5. When graphing, use ZOOM9 for

automatic fit to the residual plot

Residual Plots on TI calculators

What makes a bad residual plot? Pattern

0 1 2 3 4 5 6 7 8 9

-0.8-0.6-0.4-0.2

00.20.40.60.8

1

Input (x-value)

Residual

What makes a bad residual plot? Pattern

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

What have you done that works?

Best Practices

Additional Resources

Illustrative Mathematics PARCC Practice Test (go to Algebra 1

Item 20) Engage NY Module Mathematics Vision Project (Module 8 is

Data)

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!

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