Algebra: Concepts and connetions Course Overview

FIRST SEMESTER

UNIT 1:MODELING LINEAR FUNCTIONS Expected Dates: Beginning of School Year to End of August Students will construct and interpret arithmetic sequences as functions, algebraically and graphically, to model and explain real-life phenomena. They will use formal notation to represent linear functions and the key characteristics of graphs of linear functions, and informally compare linear and non-linear functions using parent graphs. UNIT 2: ANALYZING LINEAR INEQUALITIES Expected Dates: Late August to Late September In this unit, students will extend their understanding of linear inequalities by solving linear inequalities in two variables. Students will also extend their understanding of systems of equations by learning to solve systems of linear inequalities through graphing to model real life phenomena. This unit

UNIT 3: MODELING & ANALYZING EXPONENTIAL EXPRESSIONS AND EQUATIONS Expected Dates: Late September to Late October Students will interpret exponential expressions, one variable exponential equations in context, and understand parameters of two variable exponential equations. Students will be expected to engage with the Mathematical Modeling Framework to make sense of the nonlinear, exponential relationships in the context of real-life phenomena. Students should investigate the characteristics of exponential expressions and equations building on prior knowledge of linear and quadratic expressions and equations.

UNIT 4: ANALYZING EXPONENTIAL FUNCTIONS Expected Dates: Late October to December The learning plans, tasks, and activities included in this unit provide students with the opportunity to explore exponential functions. Students will construct and analyze the graph of an exponential function to explain a contextual situation for which the graph serves as a model. Students will also compare exponential functions with linear and quadratic functions.

SECOND SEMESTER

UNIT 5: INVESTIGATING RATIONAL AND IRRATIONAL NMBERS Expected Dates: January to Mid-January Students will investigate rational and irrational numbers and rewrite expressions involving square roots and cube roots. They should be able to use the operations of addition, subtraction, and multiplication, with radicals within expressions limited to square roots and cube roots. Additionally, they will be able to use and explain the properties of rational and irrational numbers. Through their work with rational and irrational numbers, students will come to understand that the operations of numbers from particular number sets do not yield the solution being from the same number set.

UNIT 6: MODELING AND ANALYZING QUADRATIC FUNCTIONS Expected Dates: Mid-January to Mid-March Students will analyze quadratic functions. Students will (1) investigate key features of graphs; (2) solve quadratic equations by taking square roots, factoring, completing the square, and using the quadratic formula; (3) compare and contrast graphs in standard, vertex, and intercept forms. Students will only work with real number solutions.

UNIT 7: INVESTIGATING DATA Expected Dates: March Students will collect, analyze, and interpret univariate quantitative data to answer statistical investigative questions that compare groups to solve real-life problems. Students will represent bivariate data on a scatter plot and fit a function to the data to answer statistical questions and solve real-life problems. Students will answer statistical questions and solve real-world problems by analyzing and interpreting univariate and bivariate data.

UNIT 8: ALGEBRAIC CONNECTIONS TO GEOMETRIC CONCEPTS Expected Dates: April Students will solve problems involving distance, midpoint, slope, area, and perimeter to model and explain real-life phenomena. Students have prior experiences with the concepts of approximating radicals, calculating slopes, and graphing lines. Students will now use Algebra to model Geometric ideas by solving problems involving distance, midpoint, slope, area, and perimeter. Characteristics of these terms will be used to classify quadrilaterals in the coordinate plane. Students will use properties of lines cut by a transversal along with the distance formula to explore characteristics of quadrilaterals. Students will use coordinates to prove simple geometric theorems using the properties of distance, slope, and midpoints. Students will use distance formula and problem solve to calculate area and perimeter of special parallelograms and triangles.