FOR
ALGEBRA 1 TEACHERS
Summer 2015
College and Career-Readiness Conference
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.
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 Framework
Algebra 1
PARCC Model Content Framework
Algebra 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
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).
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).
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.
2.
3.
4.
“Stat” “Edit”
Enter data in L1
“Stat” “Calc” “1-var stats”
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.
2.
3.
4.
5.
Enter data in a column
Highlight the cell below the data
Choose the “Formula” tab
Insert “STDEV”
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
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.
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
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?
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?
Residual Plots on Excel
1.
2.
3.
4.
5.
6.
7.
8.
Highlight both columns of data
Insert Scatterplot
Add a trendline (more options!)
In 3rd column “=slope*A2 + y-int”
Copy and paste formula for column
In 4th column “=A2 – A3”
Highlight 1st and 4th columns
Insert Scatterplot
Residual Plots on TI calculators
1.
2.
3.
4.
5.
Enter data and create regression line equation
Hit “2nd” “Y=“ to access StatPlot
For x’s use L1
For y’s, hit “2nd” “Stat” and arrow down to “Resid”
When graphing, use ZOOM9 for automatic fit to
the residual plot
What makes a bad residual plot?

Pattern
R
e
s
i
d
u
a
l
1
0.8
0.6
0.4
0.2
0
-0.2 0
-0.4
-0.6
-0.8
2
4
6
Input (x-value)
8
10
What makes a bad residual plot?

Pattern
What makes a good residual plot?


Randomness (no patterns)
Close to 0
Best Practices
What have you done that works?
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