Essential Questions - PC\|MAC

Unit 3-Linear Equations and Inequalities Algebra I

5 Weeks

Essential Questions

How can Algebra Skills be used in solving real world problems? Can equations that appear to be different be equivalent? Can I analyze, model, and solve mathematical situations using algebraic symbols? What kinds of relationships can proportions represent? How do you represent relationships between quantities that are not equal? Can inequalities that appear to be different be equivalent? How can inequalities be used to represent relationships and solve problems?

Enduring Understandings

1. To obtain a solution to an equation, no matter how complex, always involves the process of undoing operations.

2. Proportionality involves a relationship in which the ratio of two quantities remains constant as the corresponding values of the quantities change.

3. Real world situations can be modeled and solved by using equations and inequalities.

Topics (Pearson):

Content

Students will know...

(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 and Formulas (3-7) Absolute Value Equations (3-1) Inequalities and Their Graphs (3-2) Solving Inequalities using Addition and Subtraction (3-3) Solving Inequalities using Multiplication and Division (3-4) Solving Multi-Step Inequalities (3-5) Compound Inequalities (3-7) Absolute Value Equations (2-6) Ratios, Rates and Conversions

The difference between an expression and an equation.

Algebraic properties. Inverse operations. How to solve linear equations,

inequalities, and absolute value equations. How to graph the solution of an inequality. Ratios and rates can be used to compare quantities and make conversions.

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Unit 3-Linear Equations and Inequalities Algebra I

5 Weeks

(2-7) Solving Proportions (2-8) Percents (2-9) Change expressed as a Percent

21st Learning Expectations

Students will be able to... Employ mathematical problem solving skills effectively. Make decisions and solve problems in independent and collaborative settings.

21st Century Learning Skills

Students will be able to... ML #1 ? Make sense of problems and persevere in solving them. ML #6 ? Attend to precision. ML # 7 ? Look for and make use of structure.

Connecticut State Standards

CCSS N-Q1 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 origin in graphs and data displays. N-Q2 Define appropriate quantities for the purpose of descriptive modeling. N-Q3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. A-SSE1 Interpret expressions that represent a quantity in terms of its context. A-CED 1 Create equations and inequalities in one variable and us them to solve problems. A-CED 4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. 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 represent by letters.

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Unit 3-Linear Equations and Inequalities Algebra I

5 Weeks

CT Standards 1.3 Determine equivalent representations of an algebraic equation or inequality to simplify and solve a problem. 1.3 Model and solve problems with linear, quadratic, and absolute value equations and linear inequalities. 2.2 Solve problems involving absolute value. Model and solve problems with linear equations. Select and use appropriate methods for computing to solve problems in a variety of contexts. Use dimensional analysis to determine equivalent rates. Solve problems using direct and inverse variation.

Objectives

Students will be able to... Translate real life problems into linear equations or inequalities and solve. Solve one-step equations, including fractional equations by applying inverse operations. Solve multi-step equations with variables on both sides involving parentheses, brackets, fractions, and including those that may have no solution or be an identity. Solve multi-step equations by applying the distributive property, combining like terms, and applying inverse operations. Apply I=prt to solve interest rate problems involving percent. Apply proportional reasoning to solve problems comparing quantities. Use inverse operations to solve multi-step and compound inequalities. Use inverse operations to solve multi-step absolute value equations. Apply inequalities to solve real-world problems involving a range in values. Graph the solution set of both an inequality and absolute value equation. Use set notation to represent the solution set of an inequality.

Assessments

Quiz - EU1a Solving Linear Equations Quiz - EU1b Solving Inequality and Absolute Value Equations Quiz ? EU2 Proportions and Percents Quiz - EU3 Real World Problems Unit Test ? Linear Equations and Inequalities

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Unit 3-Linear Equations and Inequalities Algebra I

5 Weeks

Algebra I- Pearson Textbook

Resources

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