rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Domain: Seeing Structure in Expressions Cluster: Interpret the structure of expressions Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.★ numbers. Expressions can be written in multiple ways using algebra. Essential Question(s) How can you represent quantities, patterns, and relationships? Why structure expressions in different ways? How are properties related to algebra? Objective(s): Students will classify, graph and compare real numbers. Students will explain the outcomes of operations of rational and irrational numbers. Students will interpret the structure of expressions Glencoe 0-2 Real Numbers 1-3 Properties of Numbers 1-4 The Distributive Property Use the following resources to ensure that the intended outcome and level of rigor of the standards are met. Task(s) Sorting Equations and Identities (MARS) Additional Resource(s) Ordering positive and negative fractions Video Classifying numbers Video Simplifying square roots of rational numbers Video Estimating square of rational numbers Video integers, irrational numbers, real numbers, inequality Writing in Math Tell whether √100 and √0.29 are rational or irrational. Explain. A friend has asked you to explain commutative properties to him. After you explain the commutative properties for addition and multiplication, he asks you about commutative properties for subtraction and division. Use examples to show that the operations of subtraction and division are not commutative. Domain: Create equations Cluster: Create equations that describe numbers or relationships Create equations and inequalities in one variable and use them to problems. Include equations arising from linear and quadratic functions, and simple rational Enduring Understanding(s): Different of relationships between quantities can be modeled with different types of functions. Graphs are visual representations of solution sets of equations and inequalities. Pearson 2-1 Solving One-Step Equations 2-2 Solving Two-Step Equations 2-3 Solving Multi-Step Equations 2-4 Solving Equations With Variables on Both Sides 2-5 Literal Equations & Formulas Vocabulary Equivalent equations, Addition Property of Equality, Subtraction Property of Equality, isolate, inverse operations, Multiplication Property of Equality, Division Property of Equality, identity, literal equation, formula
Solving multi-step equations by combining like terms Video Solving equations with variables on both Video Domain: Create equations Cluster: Create equations that describe numbers or relationships 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. Domain: Reasoning with Equations and Inequalities Cluster: Solve equations and inequalities in one variable Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Enduring Understanding(s): Different types of relationships between quantities can be modeled with different types of functions. Graphs are visual representations of solution sets of equations and inequalities. Essential Question(s) How are inequalities different from equations? How are inequalities useful in the real world? Objective(s): Students will graph, represent, model, compare and contrast linear functions-- linear inequalities, and linear equations. Students create equations (linear and exponential) and inequalities in one variable and use them to problems. Students create equations and inequalities in one variable to real-world situations. . Pearson 3-4 Solving Multi-Step Inequalities Glencoe 5-3 Solving Multi-Step Inequalities Use the following resources to ensure that the intended outcome and level of rigor of the standards are met. Task(s) Additional Resource(s): Writing in Math Explain when the solution set of an inequality will be the set or the set of all real numbers. Show an example of each. A-REI.B.3 Enduring Understanding(s):. Understand general linear equations and their graphs and extend this to work with absolute value equations, linear inequalities, and systems of linear equations. Pearson 3-6 Solving Compound Inequalities Glencoe 5-4 Solving Compound Inequalities Vocabulary Compound Inequalities Writing in Math Compare the graph of a compound inequality involving “and” with the graph of a compound inequality involving “or”. Give a real-world
Domain: Creating Equations Cluster Create equations that describe numbers or relationships A-CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Domain: Interpreting Functions Cluster: Interpret functions that arise in applications in terms of the context. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥1. Enduring Understanding(s) You can some sequences with a function rule that you can use to find any term of the sequence. Essential Question(s) What information can a slope (rate of change) and intercept (constant term) of a linear model provide regarding the context of a situation? Objective(s): Students will identify and extend patterns in sequences. Students will recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Pearson 4-7 Sequences & Functions Glencoe 3-5 Arithmetic Sequences as Linear Functions Use the following resources to ensure that the intended outcome and level of rigor of the standards are met. Task(s) TN Algebra I Task: The Speeding Ticket Problem Additional Resource(s): Finding the common difference of an arithmetic sequence Finding the value of the nth term an arithmetic sequence Video Vocabulary Sequence, term of a sequence, arithmetic sequence, common difference Writing in Math Use KNWS, SQRQCQ, or UPS√ Strategy to complete Chapter 4 Performance Task 1. √ Compare and Contrast – You can use a mapping diagram or the vertical line test to tell if a relation is a function. Which method do you prefer? Explain. PH Algebra I Book Page 280 Use KNWS, SQRQCQ, or UPS√ Strategy to complete Tasks 1 – 3. √