Algebra 1 Correlation to Common Core- Transition Document
SC Indicators(2007 Elementary Algebra Standards)
/ Common Core Standards / Notes
CC Extensions or
Just Looking through a Different Lens
Rows highlighted in yellow indicate standards that will no longer be included in Algebra 1 after transition to Common Core is complete.
Rows highlighted in light blue indicate standards that are new CC Algebra 1 standards. These standards will be added to the Algebra 1 curriculum during the transition period (2012-2015).
Rows that are not highlighted contain current Algebra 1 standards that are a close match to a corresponding CC Algebra 1 standard. These standards will remain in the Algebra 1 curriculum with possible extensions as required by CC.
EA-2
Through the process standards the student will demonstrate an understanding of the real number system and operations involving exponents, matrices, and algebraic expressions.
EA-2.1 / Exemplify elements of the real number system, including integers, rational numbers, and irrational numbers. / Under CC, students must understand integers, rational, and irrational numbers over the course of the 3 years in middle school.
EA-2.2 / Apply the laws of exponents and roots to solve problems. / CC has moved this to grade 8.
8.EE.1 and 8.EE.2
EA-2.3 / Carry out a procedure to perform operations (including multiplication and division) with numbers written in scientific notation. / CC has moved this to grade 8.
8.EE.3 and 8.EE.4
EA-2.4 / Use dimensional analysis to convert units of measure within a system. / 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. / Dimensional analysis is also addressed in grades 7 and 8. (8-5.6) The intent of the CC standard here is broader than the intent of the SC standard. Although there is a minimal match, dimensional analysis will move to grade 6 under CC.
EA-2.5 / Carry out a procedure using the properties of real numbers (including commutative, associative, and distributive) to simplify expressions. / A.REI.1 - Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. / Not a direct match, but using properties of operations to simplify would be used. However the properties of equality would also be used. See page 90 in CC standards.
EA-2.6 / Carry out a procedure to evaluate an expression by substituting a value for the variable. / CC has moved this to grade 6.
6.EE.1 and 6.EE.2c
EA-2.7 / Carry out a procedure (including addition, subtraction, multiplication, and division by a monomial) to simplify polynomial expressions. / A.APR.1 - Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. / The focus of this CC standard is closure on the set of polynomials under the operations of addition, subtraction, and multiplication. However the student’s ability to perform these operations is implied in this standard.
Operations with polynomials is also addressed in SC Algebra 2 standards.
EA-2.8 / Carry out a procedure to factor binomials, trinomials, and polynomials using various techniques including expressions with a greatest common factor, difference between two squares, and quadratic trinomials. / A.SSE.2 - Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2). / This CC standard is much broader than the match to this one standard. The CC intent is to use structure to identify ways to rewrite a variety of expressions to put them in amore useful form for a specific purpose.
EA-2.9 / Carry out a procedure to perform operations with matrices including addition, subtraction, and scalar multiplication. / CC has moved this topic to a 4th year course.
N.VM.7 and N.VM.8
EA-2.10 / Represent applied problems using matrices. / CC has moved this topic to a 4th year course.
N.VM.6
EA-3
Through the process standards the student will demonstrate an understanding of relations and functions.
EA-3.1 / Classify a relationship as being either a function or not a function from data presented through a table, set of ordered pairs, or graph. / 8.F.1 - Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
F.IF.1 - 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, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). / CC will initially address this concept in grade 8.
EA-3.2 / Use function notation to represent functional relationships. / F.IF.1 - 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, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
F.IF.2 - Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. / The CC standard extends the SC standard to interpreting the notation in the context of a problem situation.
EA-3.3 / Carry out a procedure to evaluate a function for a given element in the domain. / F.IF.2 - Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. / The CC standard extends the SC standard to using and interpreting the notation in the context of a problem situation.
EA-3.4 / Analyze the graph of a continuous function to determine the domain and range of the function. / F.IF.1 - 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, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
F.IF.5 – Relate the domain of a function to its graphand, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of persona-hours it takes to assemble n engines in a factory, then the positive integers would be appropriate domain for the function. / This SC standard emphasizes identifying the domain and range based on an analysis of the graph. The CC extension includes determining the domain by analyzing quantities appropriate to the problem context. SC standards address this part of the standard in EA-5.10.
EA-3.5 / Carry out a procedure to graph parent functions
(including y = x, y = x2, y = , y = , and y = / F.IF.7b - Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★
b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. / Partial Match-Note that CC also includes cube root, step and piecewise functions.
EA-3.6 / Classify a variation as direct or inverse. / Currently this is also addressed in SC standards in grade 7. The closest match seems to be 7.RP2a and c and 8.EE.5
EA-3.7 / Carry out a procedure to solve literal equations for a specified variable. / A.CED.4 - Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V =IR to highlight resistance R.
A.REI.3 - Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. / A.REI.3 includes solving inequalities where coefficients are represented by letters.
EA-3.8 / Apply proportional reasoning to solve problems. / This standard is addressed thoroughly under CC in grades 6, 7, and 8.
6RP3, 7.RP 3, and 8.EE.5,
(Also currently addressed in grades 6, 7, and 8 under SC standards.)
EA-4
Through the process standards the student will demonstrate an understanding of writing and solving linear equations.
EA-4.1 / Carry out a procedure to write an equation of a line with a given slope and a y-intercept. / F.IF.8 - Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. / Parts a and b (not shown) of this CC standard focus more on quadratic and exponential functions. The beginning part of the standard stated at left also addresses linear functions-thus the correlation. In grade 8, CC expects students to construct linear functions from a variety of types of given information although CC does not specify exactly what information may be given.
EA-4.2 / Carry out a procedure to write an equation of a line with a given slope passing through a given point. / F.IF.8 - Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. / See note on EA-4.1.
EA-4.3 / Carry out a procedure to write an equation of a line passing through two given points. / F.IF.8 - Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. / See note on EA-4.1
EA-4.4 / Use a procedure to write an equation of a trend line from a given scatter plot. / S.ID.6 – Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
a. Fit a function to the data, use functions fitted to data to solve problems in the context of the data.
c. Fit a linear function for a scatter plot that suggests a linear association. / CC also includes additional standards that require students to use more formal methods to assess how a model fits data. Students will use residuals to analyze the goodness of fit. They will use graphical representations and knowledge of the context to make judgments about the appropriateness of linear models.
EA-4.5 / Analyze a scatter plot to make predictions. / S.ID.6 – Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
a. Fit a function to the data, use functions fitted to data to solve problems in the context of the data. / See note above.
EA-4.6 / Represent linear equations in multiple forms including point-slope, slope-intercept, and standard. / F.IF.8 - Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
7.EE.2 - Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. / Parts a and b (not shown) of F.IF.8 focus more on quadratic and exponential function. The beginning part of the standard stated at left also addresses linear functions-thus the correlation.
EA-4.7 / Carry out procedures to solve linear equations in one variable algebraically. / A.REI.3- Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
7.EE.4 - Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraicsolution to an arithmetic solution, identifying the sequence of theoperations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
b. Solve word problems leading to inequalities of the form px + q r or px + q r, where p, q, and r are specific rational numbers. Graphthe solution set of the inequality and interpret it in the context ofthe problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.
8.EE.7 - Solve linear equations in one variable.
a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. / In both SC and CC standards, students in grades 6, 7, and 8 solve linear equations and inequalities in one variable with rational number coefficients and constants.
EA-4.8 / Carry out procedures to solve linear inequalities in one variable algebraically and graph the solution. / A.REI.3 - Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
See 7.EE.4 above. / In both SC and CC standards students in grades 6, 7, and 8 solve linear equations and inequalities in one variable with rational number coefficients and constants.
EA-4.9 / Carry out a procedure to solve systems of two linear equations graphically. / 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.★
A.REI.6 – Solve systems of linear equations exactly and approximately (e.g. with graphs), focusing on pairs of linear equations in two variables
8.EE.8:Analyze and solve pairs of simultaneous linear equations.
a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
b. Solve systems of two linear equations in two variables algebraically and estimate solutions by graphing the equations.Solve simple cases by inspection.For example, 3x + 2y = 5 and 3x +2y = 6 have no solution because 3x + 2y cannot simultaneously be 5and 6.
c. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for twopairs of points, determine whether the line through the first pair ofpoints intersects the line through the second pair. / For A.REI.11, CC requires students in Algebra 1 to focus on linear and exponential and to learn the general principle of solving f(x) = g(x).
EA-4.10 / Carry out a procedure to solve systems of two linear equations algebraically. / A.REI.5 – 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.6 – Solve systems of linear equations exactly and approximately (e.g. with graphs), focusing on pairs of linear equations in two variables
See 8EE.8 above. / A.REI.5 is only minimally aligned. ‘Note that it uses the verb “prove”.
EA-5
Through the process standards the student will demonstrate an understanding of the graphs and characteristics of linear equations.
EA-5.1 / Carry out a procedure to graph a line given the equation of the line. / F.IF.7a- Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★
a. Graph linear and quadratic functions and show intercepts, maxima, and minima. / Note that CC includes graphing quadratic functions expressed symbolically.
EA-5.2 / Analyze the effects of changes in the slope, m, and the y-intercept, b, on the graph of y = mx + b. / F.BF.3 - 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.
F.IF.4 - For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where thefunction is increasing, decreasing, positive, or negative; relative maximumsand minimums; symmetries; end behavior; and periodicity.★
F.LE.5 - Interpret the parameters in a linear or exponential function in terms of a context. / CC notes that Algebra 1 students should focus on vertical translation for linear and exponential functions. Students can also focus on vertical stretches and reflections for linear functions.
EA-5.3 / Carry out a procedure to graph the line with a given slope and a y-intercept. / F.IF.7a - Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★
a. Graph linear and quadratic functions and show intercepts, maxima, and minima. / Note that CC includes graphing quadratic functions expressed symbolically.
EA-5.4 / Carry out a procedure to graph the line with a given slope passing through a given point. / F.IF.7a - Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★
a. Graph linear and quadratic functions and show intercepts, maxima, and minima. / Note that CC includes graphing quadratic functions expressed symbolically.
EA-5.5 / Carry out a procedure to determine the x-intercept and y-intercept of lines from data given tabularly, graphically, symbolically, and verbally. / F.IF.4 - For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where thefunction is increasing, decreasing, positive, or negative; relative maximumsand minimums; symmetries; end behavior; and periodicity.★
F.IF.7a - Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★
a. Graph linear and quadratic functions and show intercepts, maxima, and minima. / F.IF.4 includes determining features of both quadratic and exponential functions as well as linear ones.
EA-5.6 / Carry out a procedure to determine the slope of a line from data given tabularly, graphically, symbolically, and verbally. / F.IF.6 – Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
8.F.4 – Construct a function to model linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship of from two (x, y) values including reading these from a table or from a graph. Interpret the rate of change and initial value for a linear function in terms of the situation it models, and in terms of its graph or a table of values. / Finding slope is addressed in CC in middle school.