Valley Stream Central High School District Algebra 1 Scope and Sequence (Common Core) September 2013 MODULE 1: Relationships Between Quantities and Reasoning with Equations 32 Days Sub-Topics Specific Topics Common Core Resources Number of Days The Structure of Expressions Algebraic Expressions – The distributive property Algebraic Expressions – The commutative and associative properties Adding and subtracting polynomials Multiplying polynomials A.SSE.2 A-APR.1 Module 1 Lessons 6 – 9 B p. 848 - 849 B p. 715 – 720 B p. 732 C p. 167 – 185 Additional Resources 3 days Factoring Using a GCF (with a monomial and a binomial) B p. 732 Additional Resources 2 days Introduction to Functions Graphs of piecewise-defined linear functions Graphs of quadratic functions Graphs of exponential functions Analyzing graphs (water usage during a typical day at school) Two graphing stories N-Q.1 N-Q.2 N-Q.3 A-CED.2 Module 1 Lessons 1 – 5 A p. 11 – 16, 67, 68, 71 D p. 94 – 97 C p. 392 B p. 964 - 965 5 days Review and Test (2 days) Marking Period 1 Test #1 – Total 12 days
MODULE 2: Descriptive Statistics 24 Days Sub-Topics Specific Topics Common Core Resources Number of Days Shapes and Centers of Distributions Distributions and their shapes Describing the center of a distribution Estimating centers and interpreting the mean as a balance point S-ID.1 S-ID.2 S-ID.3 Module 2 Lessons 1 – 3 B p. 456 - 520 3 days Describing Variability and Comparing Distributions Summarizing deviations from the mean Measuring variability for symmetrical distributions Interpreting the standard deviation Measuring variability for skewed distributions (Interquartile Range) Comparing distributions S-ID.1 S-ID.2 S-ID.3 Module 2 Lessons 4 – 8 B p. 479 - 520 5 days Review and Test – 2 days Marking Period 1 Quarterly Total 10 days Categorical Data on Two Variables Summarizing bivariate categorical data Summarizing bivariate categorical data with relative frequencies Conditional relative frequencies and association S-ID.5 S-ID.9 Module 2 Lessons 9 – 11 B p. 577 – 614 D p. 174 - 177 3 days Numerical Data on Two Variables Relationships between two numerical variables (2 days) Modeling relationships with a line Interpreting residuals from a line More on modeling relationships with a line Analyzing residuals (2 days) Interpreting correlation Analyzing data collected on two variables S-ID.6 S-ID.7 S-ID.8 S-ID.9 Module 2 Lessons 12 - 20 D p. 162 – 173 B p. 541 - 575 9 days Review and Test – 2 days Marking Period 2 Test #1 – Total 14 days
Note: ** At the time this scope and sequence was created. Modules 3 – 5 were not available. These are subject to revision once they become available from the state. ** MODULE 3 Linear and Exponential Relationships 40 Days Sub-Topics Specific Topics Common Core Resources Number of Days Solve Systems of Equations Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. A-REI.5 A-REI.6 A p. 377 – 407 D p. 62 – 71 2 days Represent and Solve Equations and Inequalities Graphically Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line) A-REI.10 A-REI.11 A-REI.12 A p. 368 – 376 D p. 56 – 61 2 days Understand the Concept of a Function and Use Function Notation Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, the f(x) denotes the output of f corresponding the input x. The graph of f is the graph of the equation y = f (x) Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. F-IF.1 F-IF.2 F-IF.3 A p. 18 -34 D p. 78 – 81 A p. 66 A p. 235 - 250 6 days Quarterly 2 Cutoff
Build a Function that Models a Relationship Between Two Quantities Write a function that describes a relationship between two quantities F-BF.1 A Chapter 4 2 days Build New Functions from Existing Functions Identify the effect on the graph of replacing f(x) by f(x) +k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. F-BF.3 E p.395 - 407 2 days Construct and Compare Linear, Quadratic, and Exponential Models and Solve Problems Distinguish between situations that can be modeled with linear functions and with exponential functions. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (including reading these from a table) Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. F-LE.1 F-LE.2 F-LE.3 A Chapter 4.4 and 4.5 E p. 369 - 379 6 days Interpret Expressions for Functions in Terms of the Situation They Model Interpret the parameters in a linear or exponential function in terms of a context F-LE.5 E p. 381 - 394 2 days Review – 3 days Tests – 3 days
MODULE 4: Expressions and Equations 30 Days Sub-Topics Specific Topics Common Core Resources Number of Days Interpret the Structure of Expressions Interpret expressions that represent a quantity in terms of its context Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2) Factoring A-SSE.1 A-SSE.2 B. p. 645, 701 – 707, 731 - 742 C p. 95 -97, 168 – 172 5 days Write Expressions in Equivalent Forms to Solve Problems Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. A-SSE.3 B – p. 743 – 760, 771 – 778 C – p. 176 2 days Perform Arithmetic Operations on Polynomials Understand that polynomials from a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract and multiply polynomials. A-APR.1 B – p. 717 – 730 C – p. 181 - 186 2 days Understand the Relationship between Zeros and Factors of Polynomials Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. (ex: find the zeros of (x-2)(x2 – 9)) A-APR.3 B - p. 743 – 750 C – p. 503 - 508 2 days
Quarterly 3 Cutoff Sub-Topics Specific Topics Common Core Number of Days Create Equations that Describe Numbers or Relationships 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. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. (For ex, rearrange Ohm’s law V=IR to highlight R) A-CED.1 A-CED.2 A-CED.4 A – p. 71 – 122 Chapter 3 and 5 B Chapter 11 C p. 89 – 94 Chapter 4 6 days Solve Equations and Inequalities in One Variable Solve quadratic equations in one variable. (Complete the square to transform any quadratic into the form (x – p)2=q that has the same solutions. Derive quadratic formula from this form) A-REI.4 B – Chapter 12 C – Chapter 13 7 days Review – 3 days Tests – 3 days