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Mifflin County School District – Mathematics Department Planned Course Planned Course: Algebra I Remediation Mifflin County School District 2014 Mifflin County School District – Mathematics Department Planned Course Glossary of Curriculum Summative Assessment: Seeks to make an overall judgment of progress made at the end of a defined period of instruction. Formative Assessment: Used by teachers and students during instruction to provide feedback to adjust ongoing teaching and learning to improve students’ achievement of intended instructional outcomes. Benchmark Assessment: Designed to provide feedback to both the teacher and the student about how the student is progressing towards demonstrating proficiency on grade level standards. Diagnostic Assessment: Ascertains, prior to instruction, each student’s strengths, weaknesses, knowledge, and skills. Big Ideas: Declarative statements that describe concepts that transcend grade levels. Big Ideas are essential to provide focus on specific content for all students. Concepts: Describe what students should know (key knowledge) as a result of this instruction specific to grade level. Competencies: Describe what students should be able to do (key skills) as a result of this instruction, specific to grade level. Essential Questions: Questions that are specifically linked to the Big Ideas. They should frame student inquiry, promote critical thinking, and assist in learning transfer. Assessment Anchor: The Assessment Anchors represent categories of subject matter that anchor the content of the Keystone Exams. Each Assessment Anchor is part of a module and has one or more Anchor Descriptors unified under it. Anchor Descriptor: The Anchor Descriptor level provides further details that delineate the scope of content covered by the Assessment Anchor. Each Anchor Descriptor is part of an Assessment Anchor and has one or more Eligible Content unified under it. Eligible Content: The Eligible Content is the most specific description of the content that is assessed on the Keystone Exams. This level is considered the assessment limit and helps educators identify the range of the content covered on the Keystone Exams. Enhanced Standard: Enhanced Standards correlate to the Eligible Content statement. Some Eligible Content statements include annotations that indicate certain clarifications about the scope of an eligible content. Mifflin County School District – Mathematics Department Planned Course Course Description: Algebra 1 Remediation is a data driven review of Keystone Exam Assessment Anchors and Eligible Content. The course will use data from the Keystone Exam to identify areas of strength and weakness for individuals as well as the class and then provide specific content area practice in order to further develop Algebraic skills. At the conclusion of the course, students will retake the Keystone Algebra 1 Exam. References: Algebra I Standards, PA Department of Education http://www.pdesas.org/Standard/Views#0|0|705|0 Common Core State Standards http://www.corestandards.org/the-standards/mathematics/high-school-algebra/introduction/ National Council of Teachers of Mathematics http://www.nctm.org/standards/content.aspx?id=3874 SAT – College Board http://sat.collegeboard.com/practice/sat-subject-test-preparation/mathematics-level-1 Mifflin County School District – Mathematics Department Planned Course Mathematical Practice Standards Mathematical Practice Standards describes the habits of mind required to reach a level of mathematical proficiency. Standards for Mathematical Practice Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and make sense of regularity in repeated reasoning. Mifflin County School District – Mathematics Department Planned Course Subject: Algebra I Remediation Unit Title: Operations with Real Numbers and Expressions Grade levels: 11 Rational/Summary of Unit There are some mathematical relationships that are always true. These relationships are used as the rules of arithmetic and algebra and are useful for writing equivalent forms of expressions and solving equations and inequalities. Common Core Standards Assessment Anchors and Eligible Content CC.2.1.8.E.1 Distinguish between rational and irrational numbers using their properties. A1.1.1.1 Represent and/or use numbers in equivalent forms (e.g., integers, fractions, decimals, percents, square roots, and exponents). A1.1.1.1.1 Compare and/or order any real numbers (rational and irrational may be mixed). A1.1.1.1.2 Simplify square roots (e.g., √24 = 2√6). CC.2.1.8.E.4 Estimate irrational numbers by comparing them to rational numbers. CC.2.1.HS.F.1 Apply and extend the properties of exponents to solve problems with rational exponents. CC.2.1.HS.F.2 Apply properties of rational and irrational numbers to solve real world or mathematical problems. CC.2.1.6.E.3 Develop and/or apply number theory concepts to find common factors and multiples. CC.2.2.8.B.1 Apply concepts of radicals and integer exponents to generate equivalent expressions. CC.2.2.7.B.3 Model and solve real-world and mathematical problems by using and connecting numerical, algebraic, and/or graphical representations. A1.1.1.2.1 Apply number theory concepts to show relationships between real numbers in problem solving setting. A1.1.1.2.1 Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials. A1.1.1.3 Use exponents, roots, and/or absolute values to solve problems. A1.1.1.3.1 Simplify/evaluate expressions involving properties/laws of exponents, roots and/or absolute value to solve problems (exponents should be integers from -10 to 10). A1.1.1.4 Use estimation strategies in problem-solving situations. A1.1.1.4.1 Use estimation to solve problems. Mifflin County School District – Mathematics Department Planned Course CC.2.2.HS.D.9 Use reasoning to solve equations and justify the solution method. CC.2.2.HS.D.1 Interpret the structure of expressions to represent a quantity in terms of its context. CC.2.2.HS.D.2 Write expressions in equivalent forms to solve problems. CC.2.2.HS.D.3 Extend the knowledge of arithmetic operations and apply to polynomials. A1.1.1.5 Simplify expressions involving polynomials. A1.1.1.5.1 Add, subtract and/or multiply polynomial expressions (express answers in simplest form – nothing larger than a binomial multiplied by a trinomial). A1.1.1.5.2 Factor algebraic expressions, including difference of squares and trinomials (trinomials limited to the form ax2+bx+c where a is equal to 1 after factoring out all monomial factors). A1.1.1.5.3 Simplify/reduce a rational algebraic expression. CC.2.2.HS.D.5 Use polynomial identities to solve problems. CC.2.2.HS.D.6 Extend the knowledge of rational functions to rewrite in equivalent forms. Big Ideas Numbers can be expressed and transformed to various equivalent forms. Factoring can be used to break down composite expressions into primes. Exponents model real world situations. Rules are applied to numbers to develop universal precision and accuracy. Essential Questions How can we show that algebraic properties and processes are extensions of arithmetic properties and processes? How can we use algebraic properties and processes to solve problems? How do we use rules and properties to simplify algebraic expressions, combine simple rational and/or polynomial expressions, and/or factor polynomial expressions? Mifflin County School District – Mathematics Department Planned Course Concepts Students will know… Numbers can be represented in equivalent forms. Radical numbers can be written in many forms. Every set of monomials has a greatest common factor and a least common multiple. Expressions can be simplified using properties and laws of exponents, roots, and/or absolute values. Estimation is a strategy for problem solving. Polynomial expressions can be simplified. Factoring is a process to represent algebraic expressions in equivalent forms. Algebraic expressions can be represented in equivalent forms. Competencies Students will be able to… Identify irrational numbers at the approximate location on a number line. Compare and/or order any real numbers (rational and irrational may be mixed). Estimate the value of an irrational number. Use prime factorization to rewrite a composite number (numerical). Find the square root of an integer to the nearest tenth using either a calculator or estimation. Use perfect square factors to write square roots in simplest radical form. Evaluate expressions using substitution for an unknown quantity and apply the order of operations (absolute value, positive & negative exponents, square roots, power rules). Simplify expressions involving… absolute value + and - exponents roots multiplying with exponents powers of powers powers of products (integer exponents from -10 to 10) Add and subtract polynomial expressions. Multiply a monomial by a polynomial using the distributive property. Multiply polynomial expressions (express answers in simplest form – nothing larger than a binomial multiplied by a trinomial). Use prime factorization to rewrite a composite number (algebraically). Find the Greatest Common Factor (GCF) for sets of monomials. Find the Least Common Multiple (LCM) for sets of monomials. Recognize and factor out a GCF, if applicable. Mifflin County School District – Mathematics Department Planned Course Absolute value Algebraic expression Base Binomial Composite number Difference of squares Distributive Property Evaluate Exponent Expression Factor (monomials & polynomials) Greatest common factor(GCF) Integers Completely factor algebraic expressions (difference of squares and trinomials: trinomials limited to the form ax2+bx+c where a is equal to 1 after factoring out all monomial factors). Simplify and reduce a rational algebraic expression. Use the factoring process to reduce algebraic expressions. Vocabulary Irrational number Prime factorization Least common multiple Prime number (LCM) Product of powers Like terms Radical expression Monomial Rational expression Natural number Rational number Negative exponent Real number Number line Simplest form Order of operations Simplify Perfect square number Square root Polynomial Term Positive exponent Trinomial Powers Whole number Power of a power Evidence of Learning Formative Assessments Summative Assessments Daily Participation 5 min warm ups Quizzes Performance Assessment Anchor Assessments Resources KEYSTONE Finish Line Supplemental Materials on “R:” drive Kuta Software (search by topic and customize) Hippo Math Khan Academy Other print and digital resources at teacher’s discretion. Mifflin County School District – Mathematics Department Planned Course Subject: Algebra I Remediation Unit Title: Linear Equations Grade levels: 11 Rational/Summary of Unit Represent a linear equation and systems of equations in multiple ways, including tables, algebraic rules, graphs, and contextual situations and make connections among these representations. Choose the appropriate representation to model, solve and interpret problems relating to real world situations and justify the solution. Linear inequalities can be used to model real-world situations and can represent various mathematical relationships. Common Core Standards CC.2.2.8.B.3 Analyze and solve linear equations and pairs of simultaneous linear equations. CC.2.1.HS.F.3 Apply quantitative reasoning to choose and interpret units and scales in formulas, graphs and data displays. CC.2.1.HS.F.4 Use units as a way to understand problems and to guide the solution of multi-step problems. CC.2.1.HS.F.5 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. CC.2.2.HS.D.7 Create and graph equations or inequalities to describe numbers or relationships. CC.2.2.HS.D.8 Apply inverse operations to solve equations or formulas for a given variable. Assessment Anchors and Eligible Content A1.1.2.1 Write, solve, and/or graph linear equations using various methods. A1.1.2.1.1 Write, solve and/or apply a linear equation (including problem situations). A1.1.2.1.2 Use and/or identify an algebraic property to justify any step in an equation solving process (linear equations only). A1.1.2.1.3 Interpret solutions to problems in the context of the problem situation (linear equations only). A1.1.2.2 Write, solve, and/or graph systems of linear equations using various methods. A1.1.2.2.1 Write and/or solve a system of linear equations (including problem situations) using graphing, substitution and/or elimination (limit systems to 2 linear equations). A1.1.2.2.2 Interpret solutions to problems in the context of the problem situation (systems of 2 linear equations only). Mifflin County School District – Mathematics Department Planned Course CC.2.2.HS.D.9 Use reasoning to solve equations and justify the solution method. CC.2.2.HS.D.10 Represent, solve and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically. CC.2.2.HS.C.3 Write functions or sequences that model relationships between two quantities. Big Ideas Mathematical operations have inverse operations that “undo” what other operations perform. Rules can be applied to equations to determine the input for a given output. Systems of linear equations can be used to model real world problems. Essential Questions How can we use algebraic properties and processes to solve problems and justify the solution process? How do you decide which linear representation to choose when modeling a real world situation, and how would you explain and justify your solution to the problem? How do you write, solve, graph, and interpret linear equations to model relationships between quantities? How do you write, solve, and interpret systems of two linear equations using various techniques, and how do you apply them to real world situations? Concepts Students will know… Algebraic properties can be used to solve one variable equations in multiple steps. Competencies Students will be able to… Identify properties of equality. Emphasize Inverse, Identity, Commutative, Associative (for solving) & Substitution (for checking) Mifflin County School District – Mathematics Department Planned Course Algebraic properties can be used to manipulate equations to a particular form (slope intercept, point-slope, standard). Linear equations model real world problems. Algebraic properties illustrated in mathematical relationships are always true. Linear equations can be used to model real world problems. A system of linear equations can be used to model real world problems that can be solved in multiple ways. Solutions of linear equations can be used to predict real world situations. Recognize a linear relationship given data. Translate between algebraic and verbal statements. Write linear equations. Use properties of equality to solve linear equations… Multi – step Variables on both side Proportional form Use the substitution property to check solutions. Model real world situations by writing and solving equations. Apply linear equations in problem solving situations. Solve literal equations (formulas) for a specified variable. Model real world situations writing and solving equations. Solve a system of equations in two variables by graphing (manually and with technology). Solve a system of equations in two variables by the substitution method. Solve a system of equations using linear combination/elimination method. Identify the number of solutions to a system of equations. Identify when a system has one solution, no solution, or infinite solutions. Write systems of equations from tables, graphs and data. Apply a system of linear equations to solve word problems. Identify which systems of equations will model the situation. Evaluate reasonability of a solution and what that tells you about your solution. Identify what the parts of the ordered pair represent. Mifflin County School District – Mathematics Department Planned Course Additive inverse Associative Property Coefficient Commutative Property Compound inequality Constant Dependent variable Distributive Property Vocabulary Equation Identity (addition & multiplication) Independent variable Inequality Inverse operations Inverse Property Linear equation Proportion Multiplicative inverse Reciprocal Solution Systems of Linear Equations Variable Evidence of Learning Formative Assessments Summative Assessments Daily Participation 5 min warm ups Quizzes Performance Assessment Anchor Assessments Resources KEYSTONE Finish Line Supplemental Materials on “R:” drive Kuta Software (search by topic and customize) Hippo Math Khan Academy Other print and digital resources at teacher’s discretion. Mifflin County School District – Mathematics Department Planned Course Subject: Algebra I Unit Title: Linear Inequalities Grade levels: 11 Rational/Summary of Unit Rules of arithmetic and algebra are useful for writing equivalent forms of expressions, solving inequalities, and systems of linear inequalities. Common Core Standards Assessment Anchors and Eligible Content CC.2.2.HS.D.7 Create and graph equations or inequalities to describe numbers or relationships. CC.2.2.HS.D.8 Apply inverse operations to solve equations or formulas for a given variable. CC.2.2.HS.D.10 Represent, solve and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically. CC.2.1.HS.F.5 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. . A1.1.3.1 Write, solve, and/or graph linear inequalities using various methods. A1.1.3.1.1 Write or solve compound inequalities and/or graph their solution sets on a number line (may include absolute value inequalities). A1.1.3.1.2 Identify or graph the solution set to a linear inequality on a number line. A1.1.3.1.3 Interpret solutions to problems in the context of the problem situation (limit to linear inequalities). A1.1.3.2 Write, solve, and/or graph systems of linear inequalities using various methods. A1.1.3.2.1 Write and/or solve a system of linear inequalities using graphing (limit systems to 2 linear inequalities). A1.1.3.2.2 Interpret solutions to problems in the context of the problem situation (systems of 2 linear inequalities only). Big Ideas The intersection of two linear functions can be found through various techniques. Systems of inequalities can be used to model real world situations. Essential Questions How do you write, solve, graph, and/or interpret linear inequalities to model relationships between quantities? Mifflin County School District – Mathematics Department Planned Course How do you decide which linear inequality representation to choose when modeling a real world situation, and how would you explain your solution to the problem How do you write, solve, and/or interpret systems of two linear inequalities using various techniques? Concepts Students will know… Competencies Students will be able to… Algebraic properties can be used to solve one variable equations in multiple steps. Algebraic properties illustrated in mathematical relationships are always true. Compound inequalities have multiple solutions, and the graph is a visual representation of these solutions. Inequalities have multiple solutions, and the graph is a visual representation of these solutions. Linear inequalities represent realworld situations with feasible solutions. Systems of linear inequalities have multiple solutions, and the graph is a visual representation of these solutions. Systems of linear inequalities represent real-world situations with feasible solutions. Absolute value inequality Linear combination/elimination method Write, graph, and solve compound inequalities. Solve and graph absolute-value inequalities in one variable. Read and interpret algebraic inequalities. Write an inequality from a graph on a number line. Create a graph from the solution to a linear inequality. Use the solution to a linear inequality to solve a real world problem. Write a system of linear inequalities for a given situation. Solve a system of linear inequalities using graphing (manually and with technology). Justify the solution to a system of linear inequalities by showing any point in the overlapping shaded region satisfies both inequalities. Use the solution of a system of linear inequalities to solve a real world problem. Vocabulary Linear inequality Solution set Substitution Systems of linear inequalities Mifflin County School District – Mathematics Department Planned Course Evidence of Learning Formative Assessments Summative Assessments Daily Participation 5 min warm ups Quizzes Performance Assessment Anchor Assessments Resources KEYSTONE Finish Line Supplemental Materials on “R:” drive Kuta Software (search by topic and customize) Hippo Math Khan Academy Other print and digital resources at teacher’s discretion. Mifflin County School District – Mathematics Department Planned Course Subject: Algebra I Remediation Unit Title: Functions Grade levels: 11 Rational/Summary of Unit Functions can be used to analyze patterns and relations using multiple representations, including words, graphs, tables and equations. Functions can be transformed and composed to model real world situations. Common Core Standards CC.2.2.HS.C.2 Graph and analyze functions and use their properties to make connections between the different representations. CC.2.2.HS.C.1 Use the concept and notation of functions to interpret and apply them in terms of their context. CC.2.2.HS.C.3 Write functions or sequences that model relationships between two quantities. CC.2.4.HS.B.2 Summarize, represent, and interpret data on two categorical and quantitative variables. CC.2.2.8.B.2 Understand the connections between proportional relationships, lines, and linear equations. CC.2.1.HS.F.3 Apply quantitative reasoning to choose and interpret units and scales in formulas, graphs and data displays. Assessment Anchors and Eligible Content A1.2.1.1 Analyze and/or use patterns or relations. A1.2.1.1.1 Analyze a set of data for the existence of a pattern and represent the pattern algebraically and/or graphically. A1.2.1.1.2 Determine if a relation is a function given a set of points or a graph. A1.2.1.1.3 Identify the domain or range of a relation (may be presented as ordered pairs, a graph, or a table). A1.2.1.2 Interpret and/or use linear functions and their equations, graphs, or tables. A1.2.1.2.1 Create, interpret and/or use the equation, graph or table of a linear function. A1.2.1.2.2 Translate from one representation of a linear function to another (graph, table and equation). Mifflin County School District – Mathematics Department Planned Course CC.2.1.HS.F.4 Use units as a way to understand problems and to guide the solution of multi-step problems. CC.2.2.HS.C.4 Interpret the effects transformations have on functions and find the inverses of functions. CC.2.2.HS.C.6 Interpret functions in terms of the situation they model. Big Ideas The regularity and predictability of patterns can be used as a vehicle to stimulate thinking about variables and functions. Patterns can be represented by functions, graphically, numerically, and algebraically. Functions can be used to describe the relationship between two quantities. Essential Questions How do you decide which functional representation to choose when modeling a real world situation, and how would you explain your solution to the problem? How do you use functions to analyze relationships and make predictions? How do you determine if a relation is a function? Concepts Students will know… Various representations of data allow us to interpret and make predictions. A set of points or a graph can represent a relation and/or a function. Competencies Students will be able to… Analyze a set of data for the existence of a pattern. Represent the pattern of a set of data algebraically and graphically (manually and with technology). Given a set of data, write an equation. Mifflin County School District – Mathematics Department Planned Course The domain and range of a relation can be related to its graph and, where applicable, to real world situations. Graphs, tables and equations represent real life situations. Functions can be represented in different forms. Arithmetic sequence Coordinate plane Domain Function Function notation Geometric sequence Represent a set of data in different formats. Analyze and/or interpret x,y tables. Identify patterns. Determine if a relation is a function given a graph or given a set of points (ordered pairs). Plot the points on the coordinate plane and perform the vertical line test. Determine whether each member of the domain is paired with one and only one member of the range. Use mapping techniques to test for a function. Determine the domain by identifying the x-coordinates in a relation. Determine the range by identifying the ycoordinates in a relation. Use the equation to find the range, given the domain. Identify the values along the vertical axis as the range and the horizontal axis as the domain, given the graph. Identify the domain, range and the inverse of a relation. Interpret linear functions to solve problems using linear equations, tables, or graphs. Write the function rule, given a table. Make a table, given the equation. Plot the points of a line, given a table. Vocabulary Linear function Mapping Ordered pair Pattern (or sequence) Quadrants Range Relation Table Slope/rate of change Vertical line test Mifflin County School District – Mathematics Department Planned Course Evidence of Learning Formative Assessments Summative Assessments Daily Participation 5 min warm ups Quizzes Performance Assessment Anchor Assessments Resources KEYSTONE Finish Line Supplemental Materials on “R:” drive Kuta Software (search by topic and customize) Hippo Math Khan Academy Other print and digital resources at teacher’s discretion. Mifflin County School District – Mathematics Department Planned Course Subject: Algebra I Remediation Unit Title: Coordinate Geometry Grade levels: 11 Rational/Summary of Unit Coordinate geometry can be used to interpret the rate of change (slope) and initial value (yintercept) of a linear function in terms of the situation it models. Coordinate geometry can be used to create a linear model using various methods to describe the given relationship. Common Core Standards Assessment Anchors and Eligible Content CC.2.2.8.C.1 Define, evaluate, and compare functions. CC.2.2.8.C.2 Use concepts of functions to model relationships between quantities. CC.2.2.HS.C.1 Use the concept and notation of functions to interpret and apply them in terms of their context. CC.2.2.HS.C.3 Write functions or sequences that model relationships between two quantities. A1.2.2.1 Describe, compute, and/or use the rate of change (slope) of a line. A1.2.2.1.1 Identify, describe and/or use constant rates of change. A1.2.2.1.2 Apply the concept of linear rate of change (slope) to solve problems. A1.2.2.1.3 Write or identify a linear equation when given the graph of the line 2 points on the line, or the slope and a point on a line (linear equation may be in point-slope, standard and/or slope-intercept form). A1.2.2.1.4 Determine the slope and/or y-intercept represented by a linear equation or graph. CC.2.2.HS.C.5 Construct and compare linear, quadratic and/or exponential models to solve problems. Big Ideas Relationships between two quantities can be described using equations, graphs, tables, and verbal representations. Rate of change (slope) models how one quantity affects another. Mifflin County School District – Mathematics Department Planned Course Essential Questions How do you identify, describe and apply the rate of change (slope)? How do you write, solve, graph and interpret linear equations to model relationships between quantities? Concepts Students will know… Rate of change can be determined from various forms of data. Slope can be correlated to real life data. Slope shows how two variables are related. Linear equations can be written to represent relationships between quantities. Linear equations or graphs can be used to determine slope or yintercept. Competencies Students will be able to… Explain the rate of change given a graph, equation or two points. Calculate rate of change (slope) from a set of data. Find the slope given two points or from a graph. Determine whether slopes are undefined, zero, positive or negative. Find another point on the graph, given a point and slope. Graph a line given data. Graph the line given the standard form. Graph the line given the intercepts. Identify the slope and y-intercept from a graph, data points or equation. Write the equation/inequality of a line in slope-intercept form given… Slope and y -intercept Slope and a point Two points Graph Table of data Graph linear functions/equations/ inequalities on a coordinate plane (manually and with technology). Interchange point-slope, slope-intercept, and standard form of a linear equation/inequality. Identify the equations of horizontal, vertical and oblique lines. Determine the relationship of lines using their slopes (parallel or perpendicular). Mifflin County School District – Mathematics Department Planned Course Graph of linear equation Horizontal lines Oblique lines Ordered pair Origin Parallel lines Vocabulary Perpendicular lines Point slope form Quadrant Rate of change Slope Slope intercept form Standard form Vertical lines X-axis X-intercept Y-axis Y-intercept Evidence of Learning Formative Assessments Summative Assessments Daily Participation 5 min warm ups Quizzes Performance Assessment Anchor Assessments Resources KEYSTONE Finish Line Supplemental Materials on “R:” drive Kuta Software (search by topic and customize) Hippo Math Khan Academy Other print and digital resources at teacher’s discretion. Mifflin County School District – Mathematics Department Planned Course Subject: Algebra I Remediation Unit Title: Data Analysis & Probability Grade levels: 11 Rational/Summary of Unit Bivariate data can be modeled with mathematical functions that approximate the data well and help us make predictions based on the data. Apply probability to real world situations. Common Core Standards CC.2.4.HS.B.1 Summarize, represent, and interpret data on a single count or measurement variable. CC.2.4.HS.B.3 Analyze linear models to make interpretations based on the data. CC.2.4.HS.B.5 Make inferences and justify conclusions based on sample surveys, experiments, and observational studies. CC.2.4.HS.B.4 Recognize and evaluate random processes underlying statistical experiments. CC.2.4.HS.B.7 Apply the rules of probability to compute probabilities of compound events in a uniform probability model. CC.2.4.HS.B.2 Summarize, represent, and interpret data on two categorical and quantitative variables. CC.2.2.HS.C.6 Interpret functions in terms of the situation they model. Assessment Anchors and Eligible Content A1.2.3.1 Use measures of dispersion to describe a set of data. A1.2.3.1.1 Calculate and/or interpret the range, quartiles and interquartile range of data. A1.2.3.2 Use data displays in problemsolving settings and/or to make predictions. A1.2.3.2.1 Estimate or calculate to make predictions based on a circle, line, bar graph, measures of central tendency, or other representations. A1.2.3.2.2 Analyze data, make predictions, and/or answer questions based on displayed data (box-andwhisker plots, stem-and-leaf plots, scatter plots, measures of central tendency, or other representations). A1.2.3.2.3 Make predictions using the equations or graphs of best-fit lines of scatter plots. A1.2.3.3 Apply probability to practical situations. A1.2.3.3.1 Find probabilities for compound events (e.g., find probability of red and blue, find probability of red or blue) and represent as a fraction, decimal or percent). Mifflin County School District – Mathematics Department Planned Course A1.2.2.2 Analyze and/or interpret data on a scatter plot. A1.2.2.2.1 Draw, find and/or write an equation for a line of best fit for a scatter plot. Big Ideas Data are gathered, displayed, summarized, examined, and interpreted to discover patterns and deviations from patterns. Statistics provide tools for describing variability in data and for making informed decisions or predictions. Essential Questions How can we use univariate and bivariate data to analyze relationships and make predictions? How do you decide which functional representation to choose when modeling a real world situation, and how would you explain your solution to the problem? How do you identify, apply, and analyze uses of probabilities in real world situations? Concepts Students will know… A box and whisker plot can be used to describe data. Outliers can skew data. Mean, median and mode are all measures of central tendency but average is most commonly used in reference to the mean. Various data displays can be created and used to make predictions. The line of best fit can be used to determine a general relationship or to predict trends. Probability can be used to determine the likelihood of a particular outcome. Competencies Students will be able to… Make predictions based on the scatter plot and/or line of best fit. Draw a scatter plot from existing data. Draw the line of best fit from data. Create an equation for the line of best fit (manually and with technology). Make predictions based on the graph(s). Determine the reasonableness of a prediction. Create, analyze and interpret circle, line and/or bar graphs. Calculate upper and lower quartile numbers. Mifflin County School District – Mathematics Department Planned Course Bar graph Box and whisker plot Circle graph Complement Compound (or combined event) Conjunction Dependent events Disjunction Experimental probability Extremes Create, analyze and interpret a box and whisker plot. Compare data sets. Determine if any of the data values are outliers. Create stem and leaf plots (including back to back). Determine which type of graph best represents the data set. Find probabilities for compound events. Find the probability of independent and dependent events (conjunction). Find the probability of mutually exclusive or not mutually exclusive events (disjunction). Vocabulary Favorable and unfavorable outcomes Frequency Independent events Interquartile range Line graph Mean Median Measures of central tendency Mode Mutually exclusive Outliers Probability (compound and simple) Quartiles Range Sample space Stem and leaf plot Theoretical probability Evidence of Learning Formative Assessments Summative Assessments Daily Participation 5 min warm ups Quizzes Performance Assessment Anchor Assessments Resources KEYSTONE Finish Line Supplemental Materials on “R:” drive Kuta Software (search by topic and customize) Hippo Math Khan Academy Other print and digital resources at teacher’s discretion. Mifflin County School District – Mathematics Department Planned Course