Download Algebra 2

FOR ALGEBRA TEACHERS
Summer 2015
College and Career-Readiness Conference
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.
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
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




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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 yaxis
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
Anscombe!



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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


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Illustrative Mathematics
PARCC Practice Test (go to Algebra 1 Item 20)
Engage NY Module
_
Mathematics Vision
Project (Module 8 is Data)
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"?
Best Practices
What have you done that works?
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!