Content to Be Added to Algebra I to Ensure Full Alignment to the CCSS

ALGEBRA I

Content to be Added to Algebra I to Ensure Full Alignment to the CCSS

N-RN.1 (2012-2013)

Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.

N-RN.3 (2012-2013)

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.

N-Q.2 (2012-2013)

Define appropriate quantities for the purpose of descriptive modeling.

A-SSE.1 (2012-2013)

Interpret expressions that represent a quantity in terms of its context.

A-SSE.2 (2013-2014)

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).

A-CED.4 (2013-2014)

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.1 (2012-2013)

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.

A-REI.3 (2014-2015)

Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

A-REI.4 (2013-2014)

Solve quadratic equations in one variable.

a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from this form.

b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as bi for real numbers a and b.

A-REI.5 (2012-2013)

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.7 (2014-2015)

Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x2 + y2 = 3.

F-LE.5 (2012-2013)

Interpret the parameters in a linear or exponential function in terms of a context.

S-ID.1 (2014-2015)

Represent data with plots on the real number line (dot plots, histograms, and box plots).

S-ID.2 (2013-2014)

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.7 (2012-2013)

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

S-ID.9 (2013-2014)

Distinguish between correlation and causation.

While the CommonCoreState Standards below match the indicated GLEs at this grade level, the highlighted text indicates additional content requirements of the CCSS, which are to be taught beginning in 2012-13. The GLE text is listed in Table 3, Content that will Remain the Same.

A-APR.1 (2012-2013)

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.

A-CED.1 (2012-2013)

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-CED.2 (2012-2013)

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

A-CED.3 (2012-2013)

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

A-REI.10 (2012-2013)

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).

F-LE.2 (2012-2013)

Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

S-ID.6 (2012-2013)

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

F-LE.1 (2012-2013)

Distinguish between situations that can be modeled with linear functions and with exponential functions.

Content that Will Remain the Same through the Transitional Years in Algebra I

GLE # M.9.4

Matching CCSS N-Q.3

Distinguish between an exact and an approximate answer, and recognize errors introduced by the use of approximate numbers with technology

GLE # M.9.8

Matching CCSS A-SSE.3 /A-APR.1

Use order of operations to simplify or rewrite variable expressions

GLE # M.9.9

Matching CCSS A-CED.1/A-CED.2 /A-CED.3

Model real-life situations using linear expressions, equations, and inequalities

GLE # M.9.11

Matching CCSS A-CED.1

Use equivalent forms of equations and inequalities to solve real-life problems

GLE # M.9.13

Matching CCSS A-REI.10

Translate between the characteristics defining a line (i.e., slope, intercepts, points) and both its equation and graph

GLE # M.9.14

Matching CCSS A-REI.12 /A-CED.3

Graph and interpret linear inequalities in one or two variables and systems of linear inequalities

GLE # M.9.15

Matching CCSS F-LE.2 /A-CED.2 /F-IF.7

Translate among tabular, graphical, and algebraic representations of functions and real-life situations

GLE # M.9.16

Matching CCSS A-REI.6 /A-REI.8 /A-REI.9 /A-CED.3

Interpret and solve systems of linear equations using graphing, substitution, elimination, with and without technology, and matrices using technology

GLE # M.9.19

Matching CCSS N-Q.3

Use significant digits in computational problems (Not in MyMathLab)

GLE # M.9.20

Matching CCSS N-Q.3

Demonstrate and explain how relative measurement error is compounded when determining absolute error (Not in MyMathLab)

GLE # M.9.21

Matching CCSS N-Q.1

Determine appropriate units and scales to use when solving measurement problems

GLE # M.9.28

Matching CCSS S-ID.3

Identify trends in data and support conclusions by using distribution characteristics such as patterns, clusters, and outliers

GLE # M.9.29

Matching CCSS S-ID.6

Create a scatter plot from a set of data and determine if the relationship is linear or nonlinear

GLE # M.9.30

Matching CCSS S-IC.2

Use simulations to estimate probabilities

GLE # M.9.31

Matching CCSS S-IC.1

Define probability in terms of sample spaces, outcomes, and events

GLE # M.9.35

Matching CCSS F-IF.1

Determine if a relation is a function and use appropriate function notation

GLE # M.9.36

Matching CCSS F-IF.1 /F-IF.5

Identify the domain and range of functions

GLE # M.9.37

Matching CCSS F-IF.1

Analyze real-life relationships that can be modeled by linear functions

The GLEs below do not match a Common Core State Standard at this grade level; however, they will continue to be taught through the transitional years (2012-13 and 2013-14) to decrease the possibility that the transition process will create curricular gaps.

GLE # M.9.1

Moved to grade 8

Identify and describe differences among natural numbers, whole numbers, integers, rational numbers, and irrational numbers

GLE # M.9.2

Moved to grade 8

Evaluate and write numerical expressions involving integer exponents

GLE # M.9.5

Moved to grade 7

Demonstrate computational fluency with all rational numbers (e.g., estimation, mental math, technology, and paper/pencil)

GLE # M.9.24

Relates to GLE 13 & 15

Graph a line when the slope and a point or when two points are known

GLE # M.9.25

Moved to grade 8

Explain slope as a representation of “rate of change”

GLE # M.9.32

Needed for later grade

Compute probabilities using geometric models and basic counting techniques such as combinations and permutations

GLE # M.9.35

Moved to grade 8

Identify and describe the characteristics of families of linear functions, with and without technology

GLE # M.9.36

Moved to grade 8

Compare and contrast linear functions algebraically in terms of their rates of change and intercepts

Note: All Standards must include teacher instruction to insure understanding and ability to demonstrate application.