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Common Core Learning Standards for Mathematics High School Algebra 1 Relationships Between Quantities and Reasoning with Equations Common Core Learning Standards Concepts Embedded Skills Reason quantitatively and use units to solve problems. Working with quantities and the relationships between them provides grounding for work with expressions, equations, and functions. N.Q.1 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. N.Q.2 Vocabulary N.Q.3 SAMPLE TASKS Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only. Common Core Learning Standards Interpret the structure of expressions. Limit to linear expressions and to exponential expressions with integer exponents. A.SSE.1 Interpret expressions that represent a quantity in terms of its context.★ a. Interpret parts of an expression, such as terms, factors, and coefficients. b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P. Concepts Identify terms and coefficients in an algebraic expression Identify parts of multi term expressions and formulas by breaking them up into their parts Embedded Skills A.SSE.1 Identify parts of an expression, including its terms, factors and coefficients. Identify the factors within a term Identify the difference between monomials, binomials, trinomials, and polynomials Vocabulary Terms Expression Monomial Binomial Trinomial Polynomial Factor Coefficient Translate a complex expression by dissecting it into its individual parts SAMPLE TASKS Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only. Common Core Learning Standards Concepts Embedded Skills Create equations that describe numbers or relationships. Limit A.CED.1 and A.CED.2 to linear and exponential equations, and, in the case of exponential equations, limit to situations requiring evaluation of exponential functions at integer inputs. Limit A.CED.3 to linear equations and inequalities. Limit A.CED.4 to formulas which are linear in the variable of interest. Creating equations, inequalities, quadratic, and exponential equations A.CED.1 create a linear equation or inequality from a word problem Solve equations, inequalities, quadratics, and exponential equations create equations arising from functions containing square and cube roots with integer inputs and use them to solve problems Vocabulary create a quadratic equation from a word problem create an exponential equation from a word problem solve a linear equation or inequality from a word problem solve a quadratic equation from a word problem solve an exponential equation from a word problem Graphing equations and inequalities in two variables Finding the solution to the system of equations and inequalities A.CED.2 Write linear equations using two variables Rewrite an equation in terms of one variable (y = form) Identify parts of the coordinate plane (axes and quadrants) Graph systems of equations with correct labels and scales from a word problem Write quadratic equations using two variables Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only. Rewrite a quadratic equation in terms of one variable (y = form) Graph quadratic equations from a table of values with an appropriate scale and labels from a word problem Write exponential equation using two variables Rewrite exponential equations in terms of one variable (y= form) 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.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. A.CED.3 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.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. Constraints on equations and inequalities Solving literal equations Graph an exponential equation from a table of values with an appropriate scale from a work problem A.CED.3 explain whether solutions to a given problem are valid Explain what the solution to a problem represents Solve inequalities and identify the correct domain for the solution within the constraints of the word problem A.CED.4 rewrite equations in terms of a different variable Rewrite equations in terms of a different variable with squared variables SAMPLE TASKS Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only. SAMPLE TASKS continued: Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only. Common Core Learning Standards Understand solving equations as a process of reasoning and explain the reasoning. Students should focus on and master A.REI.1 for linear equations and be able to extend and apply their reasoning to other types of equations in future courses. Students will solve exponential equations with logarithms in Algebra II. Concepts Embedded Skills A.REI.1 Vocabulary 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. SAMPLE TASKS Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only. Common Core Learning Standards Solve equations and inequalities in one variable. Extend earlier work with solving linear equations to solving linear inequalities in one variable and to solving literal equations that are linear in the variable being solved for. Include simple exponential equations that rely only on application of the laws of exponents, such as 5x=125 or 2x=1/16. Concepts Embedded Skills A.REI.3 Vocabulary A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. SAMPLE TASKS Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only. Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only.