Transcript We will lead the nation in improving student achievement.

11:30- 12:30
We will begin promptly at 12:30, please return on time.
“We will lead the nation in improving student achievement.”
Building the
Data Analysis
and
Probability
Strand
“We will lead the nation in improving student achievement.”
“We will lead the nation in improving student achievement.”
Data Analysis and Probability
in Middle School
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Key Ideas
Formulate questions
Collect data
Analyze data
Interpret results
Basic concepts of probability
“We will lead the nation in improving student achievement.”
Line Plots & Histograms
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A Line of Best Fit
Arm Span
Height
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• Formulate questions that can be addressed with data.
• Collect Data from a census and samples of varying size.
• Compare, analyze, and summarize data using tools such as histograms,
box-and-whisker plots, measures of central tendency, measures of
spread, and relationship models between two variables.
• Draw conclusions about data.
• Understand and apply basic concepts of probability including
experimental and theoretical probability.
“We will lead the nation in improving student achievement.”
Is this a picture graph or a pictograph?
Discuss your thinking with your neighbor.
“We will lead the nation in improving student achievement.”
It is a pictograph because…
•It uses the same symbol (s) to represent all of the
categories.
•It has a scale, each picture represents more than one item
Pictographs begin in 2nd grade.
“We will lead the nation in improving student achievement.”
•What are some things you notice
about your graph?
•How many students were surveyed?
•How did you know?
•Which had the most? What
information did you use to figure out
your answer?
•Which had the least? What
information did you use to figure out
your answer?
“We will lead the nation in improving student achievement.”
Data Grades 3-5
“We will lead the nation in improving student achievement.”
Data Analysis and Probability in High School
Key Ideas
• Outcomes of events
• Basic laws of probability
• Samples to populations
• Variability of data
• Quantifying the association between two quantitative
variables
• Differences between experimental and observational studies
“We will lead the nation in improving student achievement.”
Outcomes of Events
• Application of the addition and multiplication principles of counting
• Simple combinations and permutations
Basic Laws of Probability
• Conditional Probability
• Mutually exclusive and dependent events
• Expected Value
“We will lead the nation in improving student achievement.”
Samples to Populations & Variability of Data
• Summary Statistics
• Random Sample
• Mean Absolute Deviation (MAD)
• Population means and deviations
• Normal distribution
• Probability histograms
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Quantifying the association between two quantitative
variables:
• Model data with linear and quadratic functions
• Examine curve fitting using median-median line and ‘eyeballing’
• Model data using linear and quadratic regression
Differences between experimental and observational studies
“We will lead the nation in improving student achievement.”
Building the
Algebra
Strand
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“We will lead the nation in improving student achievement.”
Algebra Grades 3-5
Number and Operations
“We will lead the nation in improving student achievement.”
Algebra Grades 3-5
Number and Operations
67 60 + 7
x 83 x 80 + 3
4800 4800
560
560
180
180
21
21
5561 5561
Students were introduced to the Distributive
Property in Grade 3. They should understand
that 67 x 83 is the same as 80(60 + 7) + 3(60 +
7). This is a great opportunity to expand the
concept of this important property.
“We will lead the nation in improving student achievement.”
Algebra Grades 3-5
Number and Operations
If the company can produce
4,092 pieces of Juicy
Watermelon Gum per minute,
how many 12-piece packs can
they produce in one minute?
“We will lead the nation in improving student achievement.”
Algebra Grades 3-5
Number and Operations
“We will lead the nation in improving student achievement.”
My Growing
Puppy
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My Growing
Puppy
“We will lead the nation in improving student achievement.”
Algebra Grades 3-5
“We will lead the nation in improving student achievement.”
Number Sense
K-2
5, 10
16 + 27 =
4,296
“We will lead the nation in improving student achievement.”
“We will lead the nation in improving student achievement.”
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“We will lead the nation in improving student achievement.”
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Tecumseh-Harrison School Interim!
Vincennes, IN
Brevig Mission Schooll Alaska
http://brevig.bssd.org/?tag=valentine
http://www.vcsc.k12.in.us/th/interim/PatterningActivities.htm
“We will lead the nation in improving student achievement.”
Problem Solving
• Actively looking for relationships.
• Analyzing patterns.
• Analyzing methods.
• Justifying and questioning solutions.
• Extending their knowledge to new situations.
“We will lead the nation in improving student achievement.”
Algebra in Middle School
Key Ideas
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Relationships between two quantities
Rates of change
Linear Relationships
Fundamental algebraic concepts
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Cara’s
Candles
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Cara’s
Candles
Time
(hr)
Height
(16 cm
candle)
Height
(12 cm
candle)
0
16
12
1
13.5
10.5
2
11
9
3
8.5
7.5
4
6
6
5
3.5
4.5
16 cm Candle
h = 16 - 2.5t
16
cm
12
cm
or
h = -2.5t + 16
12 cm Candle
h = 12 - 1.5t
or
h = -1.5t + 12
“We will lead the nation in improving student achievement.”
16 cm Candle
h = 16 - 2.5t
12 cm Candle
or
h = -2.5t + 16
h = 12 - 1.5t
h = -1.5t + 12
or
Cara's Candles
Height Height
(16 cm (12 cm
candle) candle)
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16
12
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10.5
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Height (cm)
Time
(hr)
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16
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12
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8
6
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16
13.5
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10.5
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1
0
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Time (hours)
16 cm Candle
6
12 cm Candle
“We will lead the nation in improving student achievement.”
8
• Generalize patterns using multiple representations.
• Use proportional reasoning to solve problems including direct
and inverse proportions.
• Investigate how change in one variable affects the other
variable: constant of proportionality, constant rate of change,
and slope.
• Investigate linear relationships including linear functions and
inequalities and systems of linear equations and inequalities.
“We will lead the nation in improving student achievement.”
Algebra in High School
Key Ideas
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Family of functions, characteristics
Simplifying expressions
Solving equations and inequalities
Inverse
Matrices and linear programming
Sequences and series
“We will lead the nation in improving student achievement.”
Functions and their Characteristics
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Basic functions: f(x) = xn (n=1,2,3), √x, |x|, and 1/x
Step and piecewise functions
Exponential functions
Quadratic functions in standard and vertex forms
Polynomial functions
Logarithmic functions
“We will lead the nation in improving student achievement.”
Simplifying Expressions
 Simplify simple radical expressions; radical expressions which require
operations with sq roots
 Simplify polynomial expressions
 Expand binomials using the Binomial Theorem
 Simplify rational expressions
 Factor expressions
 Simplify expressions involving complex numbers
“We will lead the nation in improving student achievement.”
Solving Equations and Inequalities
 Solve quadratic equations in the form ax² + bx + c = 0,
where a = 1
 Solve equations such as √x + b = c
 Solve rational equations
 Solve quadratic equations and inequalities in one
variable
 Solve polynomial, exponential, and logarithmic
equations and inequalities
“We will lead the nation in improving student achievement.”
Inverse
• Explore inverses of functions
• Use composition to verify that functions are inverses of
each other
• Define logarithmic functions as inverses of exponential
functions
“We will lead the nation in improving student achievement.”
Matrices and Linear Programming
• Basic operations
• Use matrices to formulate and solve problems
• Solve linear programming problems in two variables
• Understand and apply matrix representations of vertex-edge
graphs
“We will lead the nation in improving student achievement.”
Sequences and Series
• Recognize sequences as functions with whole number
domains
• Explore arithmetic series and various ways of computing their
sums
Sequence A: 5 , 8 , 11 , 14 , 17 , ...
Sequence B: 26 , 31 , 36 , 41 , 46 , ...
Sequence C: 20 , 18 , 16 , 14 , 12 , ...
“We will lead the nation in improving student achievement.”
How is the Georgia Department of Education
supporting teachers?
 Learning Village website
GeorgiaStandards.org
 Standards and Frameworks
Classroom Videos
 Parent Letters
 CRCT/EOCT Student Guides
 Communication with GaDOE Mathematics Team
“We will lead the nation in improving student achievement.”
Go to www.georgiastandards.org and click on the
link for Learning Village
“We will lead the nation in improving student achievement.”
You will be directed to the Learning Village information page. Click on the
Learning Village link again.
“We will lead the nation in improving student achievement.”
A log-in window will pop up. Click on the link to “Sign up for an
account”
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Click on the
folder for
appropriate
grade levels
csources …
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Check out other resources available on
Learning Village.
“We will lead the nation in improving student achievement.”
Check out other resources available on
Learning Village.
“We will lead the nation in improving student achievement.”
Change is good.
You go first.
-Dilbert
(As quoted by former Secretary of Education and Governor of South Carolina
Richard Riley on
March 26, 2009)
“We will lead the nation in improving student achievement.”
DOE Mathematics Team
Janet Davis
Program Manager
(404) 463-1736 [email protected]
Sandi Woodall
Sharon Hooper
Secondary Mathematics
Program Specialist
Elementary Mathematics
Program Specialist
Sharquinta Tuggle
Jessica Jetton
(404) 463-6924
[email protected]
Secondary Mathematics
Teacher on Assignment
(404) 463-0634
[email protected]
(404) 651-7272
[email protected]
Elementary Mathematics
Teacher on Assignment
(404) 463-0734
[email protected]
“We will lead the nation in improving student achievement.”