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Common Core Learning Standards for Mathematics High School Algebra 1 Relationships Between Quantities and Reasoning with Equations Common Core Learning Concepts Embedded Skills Vocabulary Standards Reason quantitatively and use units to solve Units of N.Q.1 create and translate units consistently with data Accuracy problems. measurement and graphs Measurement Working with quantities and the in data Quantities relationships between them provides Create a reasonable and appropriate scale for graphs Limitations and data displays (charts) Units grounding for work with expressions, Units of Formulas equations, and functions. measure in Scale solving Origin problems Data displays Graphs Solution Modeling Conversions Table Chart Appropriate N.Q.1 Use units as a way to understand problems N.Q.2 create appropriate units for multi-step problems scales and and to guide the solution of multi-step problems; choose and interpret units consistently in units for Create appropriate units to write an equation for a real formulas; choose and interpret the scale and the descriptive world situation origin in graphs and data displays. modeling Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only. N.Q.2 Define appropriate quantities for the N.Q.3 identify variable quantities, choose a level of purpose of descriptive modeling. Limiting data accuracy based on the problem situation N.Q.3 Choose a level of accuracy appropriate to for limitations on measurement when reporting measurement quantities. SAMPLE TASKS I.) a.) You are purchasing jeans and T-shirts. Jeans cost $35 and T-shirts cost $15. You only have $115 to spend and plan on purchasing a total of 5 items. Graph the system and on the grid below. b.) What variable represents the number of jeans purchased? c.) What variable represents the number of T-shirts purchased? d.) How many pairs of jeans and how many T-shirts can you buy? e.) Explain why a point in the fourth quadrant does not satisfy the system. II.) 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 Concepts Embedded Skills Vocabulary Standards Interpret the structure of expressions. Identify terms A.SSE.1 Identify parts of an expression, including its Terms Limit to linear expressions and to exponential and terms, factors and coefficients. Expression expressions with integer exponents. coefficients in Monomial an algebraic Identify the factors within a term Binomial Trinomial expression A.SSE.1 Interpret expressions that represent a Identify the difference between monomials, binomials, Polynomial quantity in terms of its trinomials, and polynomials Factor Identify parts Coefficient context.★ a. Interpret parts of an expression, such as terms, of multi-term Translate a complex expression by dissecting it into its factors, and coefficients. expressions individual parts b. Interpret complicated expressions by viewing and formulas one or more of their parts as a single entity. For by breaking example, interpret as the product of P them up into and a factor not depending on P. their parts SAMPLE TASKS I.) Match the following with their classification _____ 1.) A.) Monomial _____2.) B.) Binomial _____ 3.) C.) Trinomial _____ 4.) D.) Polynomial Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only. II.) a.) Simplify the following: b.) When in standard form what is the leading coefficient? III.) In the expression a.) List the term(s) b.) List the coefficient(s) c.) List the constant(s) Common Core Learning Standards Concepts Embedded Skills Vocabulary Create equations that describe numbers or Creating A.CED.1 create and solve a linear equation or linear relationships. equations, inequality from a word problem exponential Limit A.CED.1 and A.CED.2 to linear and inequalities, and exponential equations, and, in the case of exponential equation Create and solve an exponential equation from a inequality exponential equations, limit to situations requiring equations word problem evaluation of exponential functions at integer systems of inputs. Solve equations, equations Limit A.CED.3 to linear equations and inequalities. inequalities, Limit A.CED.4 to formulas which are linear in the and exponential systems of variable of interest. equations inequalities solution set of Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only. equations and inequalities Graphing A.CED.2 Write linear equations using two variables Variable equations and (y= form) inequalities in Coordinate plane two variables Identify parts of the coordinate plane (axes and quadrants) Axes Graph linear with correct labels and scales from a Quadrants word problem Labels Write exponential equation using two variables (y= form) Scales Graph an exponential equation from a table of Standard form values with an appropriate scale from a word problem Appropriate Table of values Growth and decay Finding the solution to the A.CED.1 Create equations and inequalities in one A.CED.3 Graph systems of equations and or Domain variable and use them to solve problems. Include system of inequalities with correct labels and scales from a equations arising from linear and quadratic functions, equations and word problem Constraints and simple rational and exponential functions. inequalities A.CED.2 Create equations in two or more variables to explain whether solutions to a given problem are Solution set represent relationships between quantities; graph Constraints on valid equations on coordinate axes with labels and scales. equations and A.CED.3 Represent constraints by equations or inequalities Explain what the solution to a problem represents inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non- Solve inequalities and identify the correct domain Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only. viable options in a modeling context. For example, for the solution within the constraints of the word represent inequalities describing nutritional and cost problem 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. A.CED.4 rewrite equations in terms of a different Literal equations Solving literal variable equations Rewrite equations in terms of a different variable with squared variables SAMPLE TASKS I.) a.) Sue’s total cell phone bill was $56.60. If her plan includes $50 for 1000 minutes a month plus $0.30 for every minute over 1000, how many extra minutes did Sue use this month? Write and solve a linear equation to prove your answer. Only an algebraic solution will be accepted. b.) Explain why 18 minutes is not a solution to the equation. II.) The volume of a rectangular solid is K cm3, the height is represented by M cm, and the length is represented by N cm. Solve for the width in terms of K, M, and N. Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only. III a.) A new museum had 7500 visitors this year. The museum expects the number of visitors to grow by 5% each year. The function models the predicted number of visitors each year after x years. Graph the function for the domain . b.) Predict the number of visitors in year 7. c.) How many years would it take for the museum to reach 20,000 visitors? Explain how you arrived at your answer. Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only. III.) Write a system of linear inequalities with the given characteristics. a.) All solutions are in Quadrant III. b.) Graph to prove your work Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only. IV.) Graph the system of linear inequalities: a.) Describe the shape of the solution region b.) Find the vertices of the solution region c.) Find the area of the solution region 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 Concepts Embedded Skills Vocabulary Standards Understand solving equations as a process of A.REI.1 Properties reasoning and explain the reasoning. Explain steps Assuming an equation has a solution, create a convincing Method Students should focus on and master A.REI.1 to solving an argument that justifies each step in the solution process. Reasonable for linear equations and be able to extend equation Justifications may include the associative, commutative, Solution and division properties, combining like terms, Justify and apply their reasoning to other types of multiplication by 1 equations in future courses. Students will solve exponential equations with logarithms in Algebra II. Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only. A.REI.1 Explain each step in solving a simple Explain the steps in solving an equation from another equation as following from the equality of students work numbers asserted at the previous step, starting from the assumption that the original equation has Describe the reasonableness of a solution a solution. Construct a viable argument to justify a solution method. Describe the method used to solve an equation SAMPLE TASKS I.) Use properties of equality and other properties to justify the solution below Equation Property Reasons ____________________ ____________________ -12 -12 4x = 32 ____________________ 4 4 x = 8 ____________________ II.) Two students solved the same inequality for x. Explain which student solved the inequality correctly and describe where the error occurred. Student A Student B 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 Concepts Embedded Skills Vocabulary Standards Solve equations and inequalities in one Solve linear A.REI.3 Construct variable. Extend earlier work with solving equations Construct a solution to a linear equation in one variable Coefficients linear equations to solving linear inequalities Variables in one variable and to solving literal Solve simple Solve simple exponential equations that use the laws of Exponential exponents Literal equations that are linear in the variable being exponential Solution set solved for. Include simple exponential equations Construct a solution to an equation with variable equations that rely only on application of the coefficients laws of exponents, such as or Solve literal . equations A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients Solve linear represented by letters. inequalities SAMPLE TASKS I.) Solve for x: II.) Solve for x: III.) Solve for p in the equation IV.) Solve for x: and explain why your solution is unique. V.) Solve for x: and explain why your solution is unique. Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only. VI.) Is the point (5, -2) a solution to , justify your answer. Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only.