Dina Baccoli
Risa Henkel
Jodi Goldstein
Kevin Smith
Christian Bowen
Jill Gierasch
Tonight’s Agenda
Algebra topics to date & upcoming Midterm
Gap‐closing Sessions
2nd Semester Topics
CC Algebra 1 Regents
Integrated Algebra Regents
Resources
Algebra I Topics Covered to Mid‐term
 Algebraic Modeling and Unit Analysis
 Linear Equations and Inequalities
 Systems of Equations and Inequalities
 Exponential Functions
 Absolute Value and Piecewise Functions
Algebraic Modeling and Unit Analysis
 Properties
 Translating Verbal Phrases into Equations and I
Inequalities
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 Ex. The quotient of x and 3 is equal to 8.
 Function, Interval and Set‐builder Notation are F
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 Ex: f(x) = y; ; [2,6]
Equations & Inequalities
1. 
7
6
2 x  1   23
1
2
1
2
x2
2. 6v  5  4  5  4  3v 
1
6
 
11
4
x x
3
2
System of Equations:
Algebraically: Graphically:
 [x + 2y = 2]
 [7x + 4y = ‐16]
Word problem:
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Janus' school is selling tickets to a spring musical. On the first day of ticket sales the school sold 6 senior citizen tickets and 13 student tickets k
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k
for a total of $176. The school took in $176 on the second day by selling 12 senior citizen tickets and 4 student tickets. Find the price of a senior k d h f citizen ticket and the price of a student ticket.
Various Functions
Various Functions
 Inverse
 Piecewise
 Exponential
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 Absolute Value
Format of Mid‐Term
 Part I: 25 multiple choice (2 points each)
 Part II: 8 constructed response questions (3 points each) h)  Part III: 4 application questions (5 points each)
 Part IV: 1 analysis question (6 points)
P IV l i i (6 i )
Gap Closing Sessions
 Teachers will be running gap‐closing sessions to support the students in transitioning to the Common Core.
Core
 We are running 4 “Gap closing” sessions to further cover these topics and to make sure every student has cover these topics, and to make sure every student has all of the skills needed to be successful on the Common Core Algebra Regents.  Scheduled to take place during February and early March
 Based on student interest and teacher availability.
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Gap Closing Sessions
Operations with Fractions, Decimals, & Percents
2. Solving Equations & Inequalities
3. Graphing
4. Miscellaneous – based on feedback
1.
Session 1: Ope
at o s t
act o s, ec a s, & e ce ts
Operations with Fractions, Decimals, & Percents
 Adding and subtracting
 Multiplying and dividing
 Equivalent Fractions
 Converting
Co ve t g
Th i
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The importance of fractions…
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 “The coherence and sequential nature of mathematics dictate the foundational skills that are necessary for the learning of algebra. The most important foundational skill not presently developed appears to be proficiency with fractions (including decimals, percents, and negative fractions). The teaching of fractions must be acknowledged as critically important and improved before an increase in student achievement in algebra can be expected.”
•Final Report of the National Mathematics Advisory Panel (2008 p 18) Panel (2008,p. 18) Session 2:
Session 2: Solving Equations & Inequalities
 With a focus on fractions, decimals, and negatives
Required Fluencies in the Common Core State S
Standards for Mathematics
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Session 3: Graphing
 Strengthen understanding of the links between an equation, table of values, and graphs.
 Function representation and manipulation
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 Use of the graphing calculator
A Common Core Fluency for Algebra I
 Solving characteristic problems involving the analytic S l i h
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l i th l ti geometry of lines, including, writing the equation of a line given a point and a slope.
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Session 4: Miscellaneous
 Based on feedback from survey
 Revisit some of the earlier sessions
 Based on data from Midterm and assessments
Second Semester Focus Areas
 Polynomials
 Factoring
 Quadratic Graphs
 Statistics
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 Review for Common Core Regents
 Review for Integrated Algebra Regents
Polynomials
 Operations with monomials
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 Operations with polynomials
 Ex. The shaded area represents the deck around a swimming pool. Express as a polynomial in simplest form:
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a) The area of the swimming pool.
b) The total area of the swimming pool and deck.
a) The area of the deck.
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Factoring
 Greatest Common Factor (GCF)
 Difference of Two Perfect Squares (DOTS)
 Trinomials
 Completing the Square
 Operations with Roots
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 Solving Quadratic Equations
 Ex. The height of a flare fired from the deck of a ship in distress can be modeled by h = ‐16t2 + 104t + 56, where h is the height in feet of the flare above water and t is the time in seconds. Find the time it takes the flare to hi h hit the water. Quadratic Graphs
Quadratic Graphs
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 Graphs of Quadratics
 Transformations of Quadratic Equations
 Quadratic‐Linear Systems
 Solving Quadratics and Quadratic‐Linear S t
Systems Graphically
G hi ll
 Ex. Let f(x) = x2 + 1. Find the vertex of the function. Then identify the values of x for which f(x) is a decreasing function and the values of x for which f(x) is an increasing function.
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Statistics




Correlation and Causation
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y
Measures of Central Tendency
Standard deviation
Graphic Representations
 Histograms
 Box and Whisker Graphs
 Ex. Emma recently purchased a new car. yp
She decided to keep track of how many gallons of gas she used on five of her business trips. The results are shown in the table to the right.
Write the linear regression equation for this data where miles driven is the hi d h il d i i h independent variable. Regents Review
 Common Core Regents Review (June 3)
(
)
 Integrated Algebra Regents Review (June 20)
 Right Triangle Trigonometry
 Algebraic Fractions
The Common Core Regents Examinations in Algebra 1
Regents Examinations comparison
The Integrated Algebra included the following types and numbers of questions: CC Algebra 1 Sample Questions
 Multiple Choice
 Open Response (2 pt)
Open Response (4 pt)
(
)
Open Response Open Response (6 pt)
(6 )
Open Response The Next Steps to prepare for Integrated Algebra
 Time between Regents Exams  CC June 3rd and Int. Alg. June 20th
 MS MS – up to 12 instructional days  *Earth Sci Reg 6/19
 HS HS – up to 9 instructional days
 Additional Review Sessions
 2 Saturday Sessions available

June 7th and 14th
 Evenings in May
Expected In School Topics
 Right Triangle Trigonometric Functions  Sine, cosine, tangent
 Inverse trig. Functions
Inverse trig Functions
 Word problems including angles of elevation and depression.
 Operations with algebraic fractions
 Finding values for which an algebraic fraction is undefined
 Simplifying fractions with polynomials in the numerator and denominator
 Adding and subtracting fractional expressions with like and unlike denominators
 Multiplying and dividing polynomials and expressing the product or quotient in simplest form
Expected Saturday Sessions
 Set Theory: Union, Intersection, Complements
 Probability: Factorials and permutations
 Plane and Solid Geometry:  Perimeter of polygons and figures composed of polygons 



and/or sectors of circles
Area of polygons and those composed of polygons and/or circles or sectors of circles, shaded regions
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Volume: cube, rectangular prism, cylinder
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Surface Area: cube, rectangular prism, cylinder
Relative Error
8th Graders during NYS Math Exam
 Three 1.5 hour sessions while the remainder of the students are taking the NYS Gr8 Math Exam
 Transformations and parallel lines cut by a transversal forming special pairs of angles.
forming special pairs of angles
What Materials Are We Using in Algebra
 Referencing EngageNY math curriculum modules
 Go Math!
 On-Core Algebra
 AMSCO
 IXL
 Mathrightnow.com
 Various Common Core math resources
Resources at Home
 www.IXL.com
 MathRightNow.com
 Go Math! student account
 LearnZillion.com
 KhanAcademy.org
 RegentsPrep.org