• ALGEBRA SEQUENCE FOR COMMON CORE
    1. NUMBER THEORY
    2. POLYNOMIALS
    3. FUNCTIONS
    4. TRANSFORMATIONS
    5. WORD PROBLEMS
    6. STATISTICS
    7. SERIES AND SEQUENCES
    8. RATIONAL EXPRESSIONS ?? NOT IN CCNY BUT IN OURS
    **8th ACCEL ALG KIDS – GEOMETRY UNIT AS WELL
     
     
    ALGEBRA 1
     
    Number Theory
    1. Sets, union, intersection, complements
    2. Laws and Properties
     
    Exponents
    1. Rules of exponents (zero, negative, rational)
    2. Change radicals to rational exponent form
    3. Evaluating rational exponents
    4. Change of base
    5. Scientific Notation
     
    Polynomials
    1. Definition
    2. Leading term, leading coefficient, degree
    3. End behavior
    4. Even/odd
    5. Operations
      1. **know how to square a binomial, cube a binomial and multiply conjugates
    6. Factoring
      1. greatest common factor, difference between squares, trinomials, sum and difference of cubes, grouping
     
    Functions
    1. 1. Basic function properties
      1. a. Definitions
      2. b. Determining a function given coordinates, mapping, graphs
      3. or equations
      4. c. Domain and range
    2. Set notation, interval notation
    3. d. f(x) notation
    4. e. Piecewise
    5. 2. Linear
    6. a. solving including literal
    7. b. solving systems
    8. c. graphing
    9. d. graphing systems
    10. e. writing equations
    11. f. study of rate
    12. 3. Inequalities
    13. a. sets of answers
    14. b. solving
    15. c. expressing solutions on a number lone, in set notation and in interval
    16. notation
    17. d. systems
    18. 4. Absolute value
    19. a. solving algebraically
    20. b. solving graphically
    21. c. inequalities
    22. 5. Radicals
    23. a. simplifying
    24. b. operations
    25. c. rationalizing
    26. d. solving algebraically
    27. e. solving graphically
    28. 6. Quadratics
    29. a. equations
    30. standard form and vertex form
    31. b. finding things
    32. 1. axis of symmetry
    33. 2. vertex
    34. 3. roots
    35. a. factor
    36. b. complete the square
    37. c. quadratic formula
    38. d. technology
    39. 4. graphing
    40. 5. solving systems algebraically and graphically
    41. 6. complex roots
    42. 7. Higher Order Polynomials
    43. a. finding zeros
    44. b. end behavior
    45. c. graphing
    46. 8. Exponentials
    47. a. the graph
    48. b. change of base
    49. c. A=P(1+(r/n))nt
    Transformations
    1. 1. reflections, rotations, translations
    2. 2. effect on functions
    Word Problems
    1. 1. vocabulary
    2. 2. translating into algebraic expressions
    3. 3. basic unknowns
    4. 4. consecutive integers
    5. 5. percent
    6. 6. ratio and proportion
    7. 7. perimeter, volume and area
    8. 8. mixture
    9. a. one variable
    10. b. systems
    11. 9. distance = rate x time
    12. 10. quadratic versions
    13. 11. growth and decay
    Statistics
    1. 1. measure of central tendency and applicable graphs
    2. 2. measures of dispersion and applicable graphs
    3. 3. bivariate data
    4. 4. scatter plots, best fit, correlation coefficient, residual
    5. summarize data in two-way frequency tables and interpret in the context of data
    6. including joint, marginal and conditional frequencies.
    7. 5. distinguish between correlation and causation
    Sequences and Series
    1. 1. Arithmetic
    2. 2. Geometric
    Rational Expressions
    1. 1. when zero, defined, undefined (domain)
    2. 2. reducing
    3. 3. multiplying and dividing
    4. 4. combining with a common denominator
    5. 5. combining without a common denominator
    6. 6. multiple operations
    7. 7. solving fractional equations
    Geometry (accelerated 8th graders - *musts for 8th grade test)
    1. definitions
    2. angles
      1. types
      2. naming and marking
      3. pairs of angles
          1. complements
          2. supplements
          3. vertical
          4. angles formed by parallel lines
          5. basic polygons
          6. triangles
    3. a. basic triangle properties
    4. 1. categorizing by sides and angle measure
    5. 2. angles of the triangle and word problems
    6. 3. determining possible number of sides of a triangle
    7. b. isosceles triangle
    8. c. right triangle
    9. a. Pythagorean thm
    10. b. trigonometry
    11. 5. quadrilaterals
    12. a. family tree
    13. b. properties of each
    14. *6. area, perimeter, volume, surface area
    15. *7. shaded area
    16. *8. error in measurement
     
     
    Algebra 1 Modules
     
    Module 1: Relationships Between Quantities and Reasoning with Equations and Their Graphs
     
    In this module students analyze and explain precisely the process of solving an equation. Through repeated reasoning, students develop fluency in writing, interpreting, and translating between various forms of linear equations and inequalities and make conjectures about the form that a linear equation might take in a solution to a problem. They reason abstractly and quantitatively by choosing and interpreting units in the context of creating
    equations in two variables to represent relationships between quantities. They master the solution of linear equations and apply related solution techniques and the properties of exponents to the creation and solution of simple exponential equations. They learn the terminology specific to polynomials and understand that polynomials form a system analogous to the integers.
     
    N.Q .1: Use units as a way to understand problems and to guide the solution of multi-step problems; choose and
    interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
    N.Q .2: Define appropriate quantities for the purpose of descriptive modeling.
    N.Q .3: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
     
    Module 2: Descriptive Statistics
     
    In this module, students reconnect with and deepen their understanding of statistics and probability concepts first introduced in Grades 6, 7, and 8. Students develop a set of tools for understanding and interpreting variability in data, and begin to make more informed decisions from data. They work with data distributions of various shapes, centers, and spreads. Students build on their experience with bivariate quantitative data from Grade 8. This module sets the stage for more extensive work with sampling and inference in later grades.
     
    S.ID.1: Represent data with plots on the real number line (dot plots, histograms, and box plots).
    S.ID.2: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread
    (interquartile range, standard deviation) of two or more different data sets.
    S.ID.3: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible
    effects of extreme data points (outliers).
     
    Module 3: Linear and Exponential Functions
     
    In earlier grades, students define, evaluate, and compare functions and use them to model relationships between quantities. In this module, students extend their study of functions to include function notation and the concepts of domain and range. They explore many examples of functions and their graphs, focusing on the contrast between linear and exponential functions. They interpret functions given graphically, numerically, symbolically, and verbally; translate between representations; and understand the limitations of various representations.
     
    A.SSE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
    A.CED.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
    A.REI.11: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
     
    Module 4: Polynomial and Quadratic Expressions, Equations, and Functions
     
    In earlier modules, students analyze the process of solving equations and developing fluency in writing, interpreting, and translating between various forms of linear equations (Module 1) and linear and exponential functions (Module 3). These experiences combined with modeling with data (Module 2), set the stage for Module 4. Here students continue to interpret expressions, create equations, rewrite equations and functions in different but equivalent forms, and graph and interpret funcions, but this time using polynomial functions, and more specifically quadratic functions, as well as square root and cube root functions.
     
    N.RN.3: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an
    irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
    A.SSE.1: Interpret expressions that represent a quantity in terms of its context.
    A.SSE.2: Use the structure of an expression to identify ways to rewrite it.
     
    Module 5: A Synthesis of Modeling with Equations and Functions
     
    In Module 5, students synthesize what they have learned during the year about functions to select the correct function type in a series of modeling problems. Students no longer have the benefit of a module or lesson title that includes function type to guide them in their choices. Skills and knowledge from the previous modules will support the requirements of this module, including writing, rewriting, comparing, and graphing functions and interpretation of the parameters of an equation. Students must also draw on their study of statistics in Module 2, using graphs and functions to model a context presented with data and/or tables of values. In this module, the modeling cycle is used as the organizing structure, rather than function type.
     
    8.F.4: Construct a function to model a linear relationship between two quantities. Determine the rate of change and
    initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a
    table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it
    models, and in terms of its graph or a table of values.
    8.F.5: Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the
    function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a
    function that has been described verbally.
    N.Q .2: Define appropriate quantities for the purpose of descriptive modeling.