Algebra 1 Unit 0: Linear Equations and Proportions

Enduring understanding (Big Idea): Students will understand that quantities are used to form expressions, equations and inequalities that represent real-world situations.

Essential Questions: 1. How might equations and inequalities be used to model real-world situations? 2. How can you solve equations/inequalities? 3. What kinds of relationships can proportions represent?

BY THE END OF THIS UNIT: Students will know… Students will be able to…  Create and solve multi-step equations  Properties  Write, graph and identify solutions of inequalities  Conversion factors  Rearrange formulas that are linear (in the variable of  Inverse operations interest)  Solve literal equations   Find ratios and rates  Convert units and rates Vocabulary: variable, dependent variable, independent variable, domain, range, scale, constant, formula, literal equation, coefficient,  Solve and apply proportions properties of operations and properties of equality  Evaluate algebraic expressions

Unit Resources Mathematical Practices in Focus: MARS Lesson: Interpreting Algebraic Expressions MARS Lesson: Modeling Situations with Linear Equations 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively  Performance Task: 6. Attend to precision Sale T-Shirt sale Common Core Standards Addressed: A.CED.2, A.CED.4, A.REI.1, Yogurt A.REI.3 Cross Total Ponzi Pyramid Schemes

Standards on successive pages were unpacked by Utah State Office of Education, CMS-district specific modifications and resources for this unit were created by CMS teacher leaders. Standards are listed in alphabetical /numerical order not suggested teaching order. PLC’s must order the standards to form a reasonable unit for instructional purposes. Algebra 1 Unit 0: Linear Equations and Proportions

CORE CONTENT Cluster Title: Create equations that describe numbers or relationships Standard A.CED.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axe with labels and scales. Concepts and Skills to Master  Write and graph an equation to represent a linear relationship  Write and graph an equation to represent an exponential relationship  Model a data set using an equation  Choose the best form of an equation to model linear and exponential functions SUPPORTS FOR TEACHERS Critical Background Knowledge  Graph points  Choose appropriate scales and label a graph  Understand slope as a rate of change of one quantity in relation to another quantity Academic Vocabulary Variable, dependent variable, independent variable, domain, range, scale

Suggested Instructional Strategies Resources  Use story contexts to create linear and exponential  Textbook Correlation: 1-9, 4-5, 5-2, 5-3, 5-4, 5-5, 7-6, 7- graphs. 7, 9-1, 9-2, 10-5, 11-6, 11-7, CB 11-7  Use technology to explore a variety of linear and  MARS Apprentice Tasks: exponential graphs. Functions  Use data sets to generate linear and exponential Multiplying Cells graphs and equations Printing Tickets  MARS Expert Tasks: Fearless Frames Skeleton Tower Best Buy Tickets

Sample Formative Assessment Tasks Skill-based task Problem Task

Write and graph an equation that models the cost of Jeanette can invest $2000 at 3% interest compounded annually or buying and running an air conditioner with a purchase she can invest $1500 at 3.2% interest compounded annually. price of $250 which costs $0.38/hr to run. Which is the better investment and why?

CORE CONTENT Cluster Title: Create equations that describe numbers or relationships Standard A.CED.4: Rearrange formulas to highlight a quantity of interest Concepts and Skills to Master  Extend the concepts used in solving numerical equations to rearranging multi-variable formulas or literal equations to solve for a specific variable. SUPPORTS FOR TEACHERS Critical Background Knowledge  Recognize variables as representing quantities in context  Solve multi-step equations Academic Vocabulary Constant, variable, formula, literal equation

Suggested Instructional Strategies Resources  Use formulas for a variety of disciplines such as  Textbook Correlation: 2-5 physics, chemistry, or sports to explore the advantages of different formats of the same formula.

I = Prt Solve for r. Paul just arrived in England and heard the temperature in degrees 5 Celsius. He remembers that C  (F  32) . How will Paul find the 9 temperature in Fahrenheit?

CORE CONTENT Cluster Title: Understand solving equations as a process of reasoning and explain the reasoning Standard 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. Concepts and Skills to Master  Understand, apply, and explain the results of using inverse operations  Justify the steps in solving equations by applying and explaining the properties of equality, inverse and identity. Justifications may include the associative, commutative, and division properties, combining like terms, multiplication by 1, etc.  Use the names of the properties and common sense explanations to explain the steps in solving an equation

SUPPORTS FOR TEACHERS Critical Background Knowledge  Use order of operations  Simplify expressions using properties of algebra Academic Vocabulary Constant, coefficient, properties of operations and properties of equality, like terms, variable, evaluate, justify, viable Suggested Instructional Strategies Resources  Have students share different ways of solving  Textbook Correlation: 2-2, 2-3, 2-4, 2-5, 9-4, 9-5 equations that lead to the same answer.  Find and analyze mistakes in student work samples  Partner problems: one student solves, the other writes reasons why steps work.  Introduce a two-column proof as a way of organizing justifications

Justify the equation solution by writing the property or When Sally picks any number between 1 and 20, doubles it, adds reason why each step works. 6, divides by 2 and subtracts 3, she always gets the number she 3x + 7 = 12 started with. Why? Evaluate and use algebraic evidence to support 3x + 7 – 7 = 12 – 7 your conclusion. 3x + 0 = 5 3x = 5 (3x)(1/3) = (5)(1/3) 1x = 5/3 Standards on successive pages were unpacked by Utah State Office of Education, CMS-district specific modifications and resources for this unit were created by CMS teacher leaders. Standards are listed in alphabetical /numerical order not suggested teaching order. PLC’s must order the standards to form a reasonable unit for instructional purposes. Algebra 1 Unit 0: Linear Equations and Proportions

x = 5/3

CORE CONTENT Cluster Title: Solve equations and inequalities in one variable Standard A.REI.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Concepts and Skills to Master  Write equations in equivalent forms to solve problems.  Analyze and solve literal equations for a specified variable.  Understand and apply the properties of inequalities.  Verify that a given number or variable is a solution to the equation or inequality.  Interpret the solution of an inequality in real terms. SUPPORTS FOR TEACHERS Standards on successive pages were unpacked by Utah State Office of Education, CMS-district specific modifications and resources for this unit were created by CMS teacher leaders. Standards are listed in alphabetical /numerical order not suggested teaching order. PLC’s must order the standards to form a reasonable unit for instructional purposes. Algebra 1 Unit 0: Linear Equations and Proportions

Critical Background Knowledge  Solving linear equations Academic Vocabulary Properties of inequality as interpreted in table 5 of the CCSS glossary page 90 Suggested Instructional Strategies Resources  Solve specified variables, using common formulas used in  Textbook Correlation: 2-1, 2-2, 2-3, 2-4, 2-5, 2-7, 2-8, 3- science, economics, or other disciplines 2, 3-3, 3-4, 3-5, 3-6  Examine and prove why dividing or multiplying by a negative reverses the inequality sign.  Use applications from a variety of disciplines to motivate solving linear equations and inequalities Sample Formative Assessment Tasks Skill-based task Problem Task

Solve 2(x + 4) – 3 ≥ 4x – 2 The perimeter of a rectangle is given by P = 2W + 2L. Solve for W and restate in words the meaning of this new formula in terms of the meaning of the other variables.

Standards on successive pages were unpacked by Utah State Office of Education, CMS-district specific modifications and resources for this unit were created by CMS teacher leaders. Standards are listed in alphabetical /numerical order not suggested teaching order. PLC’s must order the standards to form a reasonable unit for instructional purposes.