if the function h(n) gives the number of it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.* New 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. A.REI.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Review Inverse operations can be used to isolate a variable in a linear equation. The distributive property, combining like terms, and other mathematical properties can be used to manipulate equations to make them easier to solve. Each step to solving a linear equation can be justified with a mathematical property or reason. New Solutions to linear functions are determined both graphically and algebraically. Intersection points are used to determine solutions to linear functions. Review Find and justify a solution to a linear equation in 1 variable Justify each step in the process of solving a linear equation in 1 variable with a mathematical reason or property New A.REI.10: 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). Review New A graph of a function represents all its solutions. Each coordinate point located on the graph will make the function true. Review New Use a graph to find the solution to a linear equation in 1 variable N.Q.1: Use units as a way to understand problems and to guide the solution of Review Appropriate should be used when solving and reporting solutions Review Use units when reporting answers to problems in a context
New 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. 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. Review The function notation f(x) indicates that “f is a function of (depends on) x”, and that x is the variable. For a function that models a problem situation, equations can be created to solve unknown input or output values. Solutions can be written in function notation and interpreted in the context of the problem. New Review Given a description, create an equation in one variable that can be used to solve a problem in a context Use function notation evaluate functions Interpret statements that use function notation in of a context New A.REI.10: Understand that the 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). Review A of a function represents all its solutions. Each coordinate point located on the graph will make the function true. New Review Use a to find the solution to a linear equation in 1 variable New N.Q.1: Use units as a way to understand problems and to guide the solution of problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. Review Appropriate units should be used when solving and reporting solutions to problems situations. This provides context and insight to the situation it describes. New Review Use units when reporting answers to problems in a context New Lesson 8: Analyzing a linear function (Day 2) Objectives investigating a problem situation, students will be able to analyze and interpret features a linear function by earning ___/___ points on an open-ended task
choose and interpret the scale and the origin in graphs and data displays. the situation it describes. New Lesson 9: Solving linear inequalities Objectives By applying the concept of solving equations, students will be able to create and solve a linear inequality in one variable with at least ___ out of ___ answered correctly on an exit ticket. Focused Mathematical Practices MP 4: Model with mathematics (when creating linear inequalities in 1 variable to model a problem situation) MP 7: Look for and make use of structure (when making connections between linear equations and linear inequalities) Vocabulary Inequality, solution to an inequality Common Misconceptions Lesson Clarifications The main purpose of this lesson is to create linear inequalities (in 1 variable) in a context and use them to solve problems. The Student Text provides a lot of opportunities to review concepts and skills taught in previous lessons, allowing students to reinforce their understanding and make connections between different topics in Algebra. However, this lesson may be modified in order contain more practice on solving linear inequalities and fewer “analyze” problems. Students will not be assessed on graphing inequalities (in 1 variable) on a number line. CCSS Concepts What students will know Skills What students will be able to do Material/ Resource Suggested Pacing Assessment Check Point A.REI.3: linear equations and inequalities in one variable, including equations with coefficients represented by letters. Review Properties of solving linear equations in 1 variable can be applied to solve linear inequalities in 1 variable. The solution to a linear inequality is often a range of values. Solutions to linear inequalities are best represented graphically. New Solutions to linear inequalities are determined both Review Solve a linear inequality (in 1 variable) New CL ST 2.4 1 day CL SP 2.3 (#’s 14, 16)
Common Misconceptions Supplemental Material Tasks CCSS SMP Dropbox location and filename Link (original task and answer key) A.SSE.1 MP 4 MP 7 Orange 9-12 Math > Algebra 1 > Unit 1 > Supplemental Material > Mixing Candies task A.CED.1 N.Q.1 Orange 9-12 Math > Algebra 1 > Unit 1 > Supplemental Material > Planes and Wheat task A.CED.1 A.CED.2 N.Q.1 MP 4 Orange 9-12 Math > Algebra 1 > Unit 1 > Supplemental Material > Paying the Rent task A.REI.1 A.REI.3 MP 3 Orange 9-12 Math > Algebra 1 > Unit 1 > Supplemental Material > Reasoning with Linear Inequalities task A.REI.10 F.LE.1a A.SSE.1 MP 4 MP 7 Orange 9-12 Math > Algebra 1 > Unit 1 > Supplemental Material > Taxi task F.IF.1 N.Q.1 N.Q.2 MP 2 MP 3 Orange 9-12 Math > Algebra 1 > Unit 1 > Supplemental Material > The Parking Lot task F.IF.2 MP 2 Orange 9-12 Math > Algebra 1 > Unit 1 > Supplemental Material > Cell Phones task F.IF.5 Orange 9-12 Math > Algebra 1 > Unit 1 > Supplemental Material > Oakland Coliseum task Collaborative Activities CCSS SMP Dropbox location and filename Link A.REI.1 A.REI.3 MP 2 MP 3 MP 8 Orange 9-12 Math > Algebra 1 > Unit 1 > Supplemental Material > Building and Solving Equations activity (starts on page 8) (teacher’s guide) resources) A.REI.1 A.REI.3 MP 3 MP 7 Orange 9-12 Math > Algebra 1 > Unit 1 > Supplemental Material > Sorting Equations and Identities activity (starts on page 6) (teacher’s guide) (other resources)
Abstract f(x) = 7x where x represents the number of pizzas and f(x) represents the total cost (in dollars) Unit Authentic Assessment Performance Task CCSS SMP Dropbox location and filename Link N.Q.1 A.CED.1 A.CED.2 F.LE.1 A.REI.3 MP 1 MP 2 MP 4 MP 5 MP 6 Orange 9-12 Math > Algebra 1 > Unit 1 > Authentic Assessments > Ivy Smith Grows Up performance task PARCC Sample Assessment Items Myla’s Swimming Pool – Task Type 1 CCSS SMP Dropbox location and filename Evidence statement (from Algebra 1 EOY) F.LE A.CED.1 A.SSE.3 F.IF.B F.IF.7 MP 2 MP 4 MP 8 Orange 9-12 Math > Algebra 1 > Unit 1 > PARCC Sample Assessment Items > Myla’s Swimming Pool PARCC task type 1 HS-Int.3-2: Solve multi-step contextual word problems with degree of difficulty appropriate to the course, requiring application of course-level knowledge and skills articulated in F-LE, A-CED.1, A-SSE.3, F-IF.B, F-IF.7, limited to linear and quadratic functions.