-Sequences -Linear and Exponential Functions -Features of Functions -Equations and Inequalities -Systems of Equations and Inequalities -Quadratic Functions -Connecting Algebra and Geometry -Modeling Data -Quadratic FunctionsConnecting Algebra and GeometryModeling Data
UNIT 1 - SEQUENCES
- Defining quantities and interpreting expressions -Representing arithmetic sequences with equations, tables, graphs, and story context - Representing geometric sequences with equations, tables, graphs and story context - Arithmetic Sequences: Constant difference between consecutive terms, initial values - Geometric Sequences: Constant ration between consecutive terms, initial values -Arithmetic Sequences: Increasing and decreasing at a constant rate -Comparing rates of growth in arithmetic and geometric sequences -Recursive and explicit equations for arithmetic and geometric sequences -Using rate of change to find missing terms in a an arithmetic sequence -Using a constant ratio to find missing terms in a geometric sequence -Developing fluency with geometric and arithmetic sequences
UNIT 2- LINEAR & EXPONENTIAL FUNCTIONS -Use the structure of an expression to identify ways to re-write it. -Learners develop rules to re-express products, quotients, and powers of variable expressions in equivalent forms. - Look for and express regularity in repeated reasoning. -Learners will work from definitions of powers of exponents to notice patterns that can suggest rules for re-expressing variable expressions involving exponents in equivalent, simpler forms. -Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. - Write a function that describes a relationship between two quantities. -Distinguish between situations that can be modeled with linear functions and with exponential functions. - Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). - Determine an explicit expression, a recursive process, or steps from a calculation from a context. - Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. - Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. - Interpret the parameters in a linear or exponential function in terms of a context. - Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. -Interpret expressions that represent a quantity in terms of its context. a) Interpret parts of an expression, such as terms, factors, and coefficients. - Use the structure of an expression to identify ways to rewrite it. -Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. - Interpret the parameters in a linear or exponential function in terms of a context. -focus on linear and exponential functions. Include comparisons of two functions presented algebraically. For example, compare the growth of two linear functions, or two exponential functions such as y=3n and y=100·2n. -Use the structure of an expression to identify ways to rewrite it. -Will use mathematical models to make predictions about future values of exponential functions. In addition, will use technology to predict a domain value that produces a particular output value. New Vocabulary: Domain Discrete function Continuous function
For each task in each unit, there are links to the Student Task, the Ready Set Go! Homework, and the Homework Help Video. https://wcpss.instructure.com/courses/273681/pages/unit-2#
UNIT 3: Features of Function 3.1 Getting Ready for a Pool Party – A Develop Understanding Task Using a story context to graph and describe key features of functions READY, SET, GO Homework: Features of Functions 3.1 3.2 Floating Down the River – A Solidify Understanding Task Using tables and graphs to interpret key features of functions READY, SET, GO Homework: Features of Functions 3.2 3.3 Features of Functions – A Practice Understanding Task Working to achieve fluency with the identification of feature of functions from various representations READY, SET, GO Homework: Features of Functions 3.3 3.4 The Water Park – A Solidify Understanding Task Interpreting functions and their notation READY, SET, GO Homework: Features of Functions 3.4 3.5 Pooling it Together – A Solidify Understanding Task Combining functions and analyzing contexts using functions READY, SET, GO Homework: Features of Functions 3.5 3.6 Interpreting Functions – A Practice Understanding Task Using graphs to solve problems when given function notation READY, SET, GO Homework: Features of Functions 3.6 3.7 To Function or Not to Function – A Practice Understanding Task Identify whether or not a relation is a function given various representations READY, SET, GO Homework: Features of Functions 3.7 3.8 It’s a Match – A Performance Assessment Tasks Matching stories, graphs and equations to assess how well you can connect features across representations UNIT 4: EQUATIONS & INEQUALITIES 4. 1 Cafeteria Actions and Reactions :A Develop Understanding Task 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.
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
4. 3 Solving Equations Literally :A Practice Understanding Task – Look and make use of structure Students will make use of the structure of solving the one-variable equation from the left column to solve the related two-variable equation in the right column.
Look for and express regularity in repeated reasoning Because this is a practice task, students should be able to identify the appropriate inverse operations, and the appropriate sequence of operations, that can be applied to solve multi- step equations and literal equations. 4.4 Greater Than? A Develop Understanding Task 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. a. Construct a viable argument to justify a solution method. b. Solve equations and inequalities in one variable. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
4.5 May I Have More, Please? A Solidify Understanding Task
Reason abstractly and quantitatively Students are given a story context and asked to represent the situation symbolically with an inequality (to decontexualize). They use the inequality to find a solution to the problem, which in many cases may include more numbers that do not make sense for the problem situation. They are then asked to contextualize the solution to the inequality so that it matches the original story situation. Model with mathematics In the task, students are given several situations that may occur in a school cafeteria and asked to model those situations with inequalities. They interpret their solutions to ensure that they are appropriate for the problem situation.
4.6 Taking Sides :A Practice Understanding Task
Construct viable arguments and critique the reasoning of others. In this task students are asked to consider the arguments of other students and to decide if they are correct or incorrect. They will take a position and articulate a mathematical argument to justify their positions. Attend to precision. The task is designed for students to polish their understanding of inequalities by examining common misconceptions. As students construct their arguments, they will be using precise mathematical language and symbols. They will also be examining the way that others have used symbols and determine if they are used properly for a given context.