Scope and Sequence Overview Lesson Topic Suggesting Pacing and 1 16.1 – Introducing Systems of Equations 1 day 2 16.2 – Solving Systems of Linear Equations Using Number Sense 1 day 3 16.3 – Modeling with Systems of Linear Equations 1 day 4 16.4 – Solving Systems of Equations with Tables 1 day 5 16.5 – Solving Other Systems of Equations with Tables 1 day 6 16.6 – Using Graphs to Solve Systems of Equations 1 day 7 16.7 - Using Graphs to Solve Systems of Equations Continued 1 day 8 16.8 – Systems of Inequalities 1 day 9 16.9 – Modeling with Systems of Inequalities 1 day 10 17.1 – Checking for Understanding 1 day 11 17.2 – Problem Solving and Mindset 1 day 12 17.3 – Fluency with Multi-step Equations 1 day 13 18.1 – The Substitution Method 1 day 14 18.2 – More on the Substitution Method 1 day 15 18.3 – Applying the Substitution Method 1 day 16 18.4 – The Linear Combination Method 1 day 17 18.5 – The Linear Combination Method Continued 1 day 18 18.6 – Connecting the Algebra and Geometry of Systems of Equations 1 day 19 18.7 – Choosing a Linear System Solution Method 1 day 20 18.8 – End of Unit Assessment 1 day
Focused Mathematical Practices MP 1: Make sense of problems and persevere in solving them MP 5: Use appropriate tools strategically MP 6: Attend to precision MP 7: Look for and make use of structure Vocabulary: input, output, delta-table function, three-column table Common Misconceptions: Not putting both equations into the equation editor on the graphing calculator Looking at the wrong columns of the table function when trying to find a match (misunderstanding a 3 column table) Switching up x and y values on a given table CCSS Concepts What students will know Skills What students will be able to do Material/ Resource Suggested Pacing Assessment Point Review An x/y table is one way to represent a linear function A table has input (x) values and output (y) values New A solution to a system of equations can be in a table by finding matching values of y for the same x-value A graphing calculator can be used to create and use tables to solve linear equations Review Entering a linear equation into the graphing calculator and analyzing the table function Analyzing a linear equation from a table New Solving a system of linear equations using two tables Locating a function’s table on a graphing calculator Solving a system of linear equations using table on the graphing calculator Agile Minds 16.4, Student activity book, 1 day Staying Sharp 16.4 Lesson 5: 16.5 - Solving other Systems of Equations with Tables Objective Using tables along with a “generate and test” method SWBAT work in ________________________ to solve linear systems of equations with at least 80% efficiency on the staying sharp wrap up activity. Focused Mathematical Practices
Vocabulary: intersection, slope, y-intercept, coordinate plane, equation editor Common Misconceptions: Graphing difficulties Not graphing both on the same coordinate plane Not entering both equations into the equation editor in the graphing calculator Misunderstanding what the solution of a system of equations is when graphed CCSS Concepts What students will know Skills What students will be able to do Material/ Resource Pacing Assessment Check Point Review Slope-intercept form of an equation gives you the slope and of a linear function A linear equation is a straight line when graphed on a coordinate plane New The solution of a system of equations will be the of intersection between the two lines when graphed on a single coordinate plane Review Analyze solving a system of equations with tables Graph linear equations Entering a linear function into a graphing calculator and analyzing the New Graph both equations of a system of equations on one coordinate plane Use graphing calculators to graph systems of equations Use the intersection function on a graphing calculator to identify the solution to a system of equations Agile Minds 16.7, Student activity book, calculator intersection directions 1 day Staying Sharp 16.7 Lesson 8: 16.8 - Systems of Inequalities Objective coordinate planes SWBAT work in ________________________ to analyze and explore solutions to systems of inequalities with at least 80% efficiency on the staying sharp wrap up activity. Focused Mathematical Practices MP 1: Make of problems and persevere in solving them MP 6: Attend to precision MP 7: Look for and make use of structure Vocabulary: solution sets, coordinate plane, system of inequalities
Common Misconceptions: Identifying the same solution for inequalities as you would for an equation Difficulties visually seeing on the graph the solution set of a system of inequalities Mixing up inequality symbols (i.e. < means greater than and > means less than) CCSS Concepts What students will know Skills What students will be able to do Material/ Resource Suggested Pacing Assessment Check Point Review Inequalities have solution sets rather than just one single solution New A solution to a system of inequalities is the solution set that satisfies both inequalities Systems of inequalities can also be graphed on the same coordinate plane to identify the solution set Review Graphing linear inequalities Graphing compound inequalities New Graph systems of inequalities involving three inequalities Solving for the unknown variable after the equation has been rearranged Agile Minds 16.8, student activity book, Computer lab 1 day Staying Sharp 16.8 Lesson 9: 16.9 - Modeling with Systems of Inequalities Objective Using knowledge of linear inequalities SWBAT work in ________________________ to solve systems of inequalities for at least 80% efficiency on the staying sharp wrap up activity. Focused Mathematical Practices MP 1: Make of problems and persevere in solving them MP 4: Model with mathematics MP 5: Use appropriate tools strategically MP 7: Look for and make use of structure Vocabulary: linear inequalities
Common Misconceptions: Incorrectly identifying solution sets Misunderstanding the context of the problem and exactly what solution the problem is asking for Incorrectly identifying the unknown quantities with variables CCSS Concepts What students will know Skills What students will be able to do Material/ Resource Pacing Assessment Check Point Review A system of equations is needed when there is more than one variable in a given problem A system of inequalities can be written when you have an inequality with more than one variable New A problem scenario can be represented by a system of inequality just like it can be represented by a system of inequalities Review Graphing systems of inequalities Modeling problem scenarios with systems of equations New Apply a system of inequalities to a problem situation Model a problem by writing a system of inequalities Agile Minds 16.9, Student activity book, Assessment reports 1 day Staying Sharp 16.9 Lesson 10: 17.1 – Checking For Understanding Objective Using algebraic properties SWBAT work in ________________________ to arrange steps to solving multi-step equations with justifications for at least 80% efficiency on the staying sharp wrap up activity. Focused Mathematical Practices MP 1: Make sense of problems and persevere in solving them MP 6: Attend to precision MP 7: Look for and make use of structure Vocabulary: solution step, justification, algebraic properties Common Misconceptions: Incorrectly using the algebraic properties Forgetting inverse operations
Difficulties understanding what each property actually connects to which makes it difficult for students to name the property they are using even if they know the skill CCSS Concepts What students will know Skills What students will be able to do Material/ Resource Pacing Assessment Check Point Review A solution to a system has a solution set while a solution to an equation, most often, is only one number An algebraic property is used in every step while solving mult-step equations New Each algebraic property is used as a justification for each step made solving equations Review Explain the difference between a solution to a system and a solution to an equation multi-step equations New Build efficiency solving multi-step equations Justify each step of a multi-step equation using algebraic properties Agile Minds 17.1, Student activity book, mid unit assessment, equation solution cards 1 day Staying Sharp 17.1 Lesson 11: 17.2 – Problem Solving and Mindset Objective Using growth mindset strategies SWBAT work in ________________________ to work out an algebraic problem with a positive mindset and reasoning with at least 80% efficiency on the staying sharp wrap up activity. Focused Mathematical Practices MP 1: Make sense of problems and persevere in solving them MP 3: Construct viable arguments and critique the reasoning of others MP 7: Look for and make use of structure Vocabulary: mindset, positive mindset, growth mindset , phases or problem solving Common Misconceptions: Students who feel uncomfortable open about weaknesses Difficulties with the reflective nature of this lesson
CCSS Concepts What students will know Skills What students will be able to do Material/ Resource Pacing Assessment Check Point Review A solution to a system has a solution set while a solution to an equation, most often, is only one number An algebraic property is used in every step while solving mult-step equations New There are multiple ways to solve multi-step equations that when done correctly will result in the same answer Each algebraic property is used as a justification for each step made while solving equations Review Explain the difference between a solution to a system and a solution to an equation multi-step equations in two different ways New Compare different methods to solving equations Build efficiency solving multi-step equations Justify each step of a multi-step equation using algebraic properties Agile Minds 17.3, Student activity book, White boards 1 day Staying Sharp 17.3 Lesson 13: 18.1 – The Substitution Method Objective substitution method SWBAT work in ________________________ to solve systems of equations algebraically with at least 80% efficiency on the staying sharp wrap up activity. Focused Mathematical Practices MP 1: Make sense of problems and persevere in solving them MP 6: Attend to precision MP 7: Look for and make use of structure Vocabulary: Substitution method Common Misconceptions: Difficulties substituting expressions into an equation (most often not properly using distributive property) Solving for one variable but forgetting to use it to for the second variable CCSS Concepts What students will know Skills What students will be able to do Material/ Resource Suggested Pacing Assessment Check Point
Review You can use a variety of methods to solve equations by New Systems of equations also have a variety of methods to choose from in order to solve Substitution method solves for one variable and substitutes that expression into the equation so that you are left with an equation that only has one variable Review Solving systems of equations informal methods New Explore substitution method and identify else in algebra the idea of substitution is used Identify the skills needed to use substitution method Use substitution method to solve systems of equations Agile Minds 18.1, Student activity book, 1 day Staying Sharp 18.1 Lesson 14: 18.2 – More on the Substitution Method Objective substitution method SWBAT work in ________________________ to solve systems of equations algebraically with at least 80% efficiency on the staying sharp wrap up activity. Focused Mathematical Practices MP 1: Make sense of problems and persevere in solving them MP4: Model with mathematics MP 6: Attend to precision MP 7: Look for and make use of structure Vocabulary: substitution method Common Misconceptions: Difficulties substituting expressions into an equation (most often not properly using distributive property) Solving for one variable but forgetting to use it to solve for the second variable Difficulties graphing