Unit 1: Representing relationships mathematically 450 mins~ 5.63 days In this unit, students solidify their previous work with functional relationships as they begin to formalize the concept of mathematical function. This unit provides an opportunity for students to reinforce their understanding of the various representations of a functional relationship– words, concrete elements, numbers, graphs, and algebraic expressions. Students review the distinction between independent and dependent variables in a functional relationships and connect those to the domain and range of a function. The standard listed here will be revisited multiple time throughout the course, as students encounter new function families. Quantities ★ —N--Q A. Reason quantitatively and use units to solve problems 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. 2.Define appropriate quantities for the purpose of descriptive modeling. Seeing in Expressions- A-SSE A. Interpret the structure of expressions 1.Interpret expressions that represent quantity in terms of its context* a. Interpret parts of an expression, such as terms, factors, and coefficients. Creating equations* A-CED A. Create equations that describe numbers or relationships 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. 2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. Reasoning with Equations and Inequalities-A-REI D. Represent and solve equations and inequalities graphically. 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).

Interpreting Functions F-IF B. Interpret functions that arise in applications in terms of the context 5. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.* Building Functions –F-BF A. Build a function that models a relationship between two quantities 1.Write a function that describes a relationship between two quantities* a. Determine an explicit expression, a recursive processes, or steps for calculations from a context. Common Core State Standards for Mathematical Practice 2. Reason abstractly and quantitatively 4. Model with mathematics 6. Attend to precision Comments To make the strongest connection between students’ previous work and the work of this course, the focus for A-CED.A.1, A-CED.A.3 and F-BF.A.1a should be on linear functions and equations. Students will have solved linear equations using algebraic properties in their previous courses, but that should not be the focus of this unit. Instead, use students’ work with A-REI.D10, F-IF.B.5, and F-IF.C.9 to reinforce students’ understanding of the different kinds of information about a function that is revealed by its graph. This will build a solid foundation for students’ ability to estimate solutions and their reasonableness using graphs. In this unit, students can begin to build proficiency with MP.4 as they create mathematical models of contextual situations, while attending to limitations on those models. In order to create the models and interpret the results, students must attend to MP.2. As students create graphs of functional relationships, they must pay careful attention to quantities and scale, and so should be demonstrating MP.6.