: Algebra IA Mifflin County School District Date of Board Approval: April 25, 2013
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.
Course Description: Mifflin County School District Mathematics Department Algebra 1A is the first half of the bridge from the concrete to the abstract study of mathematics. This class will study the language, concepts, and techniques of algebra that will prepare students to approach and solve problems within the constraints of the algebraic properties. The students will learn the conceptual and procedural basics of algebra using various representations both manually and with technology. This course will help prepare students for the high level of mathematical thinking and problem solving needed in the workplace and in everyday life. The skills taught in this course provide a foundation for upper level math and sciences. 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
Algebra IA Power Standards Power Standards represent the safety net of standards that all teachers must teach and all students must learn prior to leaving their current grade/class. They are not an elimination of any content but a prioritization of standards that, if mastered, will give a student the ability to understand other curriculum objectives. Power standards give our school district a common FOCUS. MODULE 1 Operations and Linear Equations & Inequalities ASSESSMENT ANCHOR A1.1.1 Operations with Real Numbers and Expressions A1.1.1.2.1 Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials. A1.1.1.3.1 Simplify/evaluate expressions involving properties/laws of exponents, roots, and/or absolute values to solve problems. Note: Exponents should be integers from 10 to 10. A1.1.1.5.2 Factor algebraic expressions, including difference of squares and trinomials. Note: Trinomials are limited to the form ax 2 +bx+c where a is equal to 1 after factoring out all monomial factors. ASSESSMENT ANCHOR A1.1.2 Linear Equations A1.1.2.1.1 Write, solve, and/or apply a linear equation (including problem situations).
Algebra IA Power Standards MODULE 2 Data Organization ASSESSMENT ANCHOR A1.2.3 Data Analysis A1.2.3.2.2 Analyze data, make predictions, and/or answer questions based on displayed data (box and whisker plots, stem and leaf plots, scatter plots, measures of central tendency, or other representations). 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.
Mathematical Practice Standards Mifflin County School District Mathematics Department 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.
Subject: Algebra IA Unit Title: Operations with Real Numbers and Expressions Grade levels: 9-12 Approximate Time Frame: 90 Days (50 minute Periods) Rationale/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 CC.2.1.8.E.1 Distinguish between rational and irrational numbers using their properties. 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. Assessment Anchors and Eligible Content 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). 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.
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 ax 2 +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?
Concepts Students will know Competencies Students will be able to 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. 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.
Absolute value Algebraic expression Base Binomial Composite number Difference of squares Distributive Property Evaluate Exponent Expression Factor (monomials & polynomials) Greatest common factor(gcf) Integers Vocabulary Irrational number Least common multiple (LCM) Like terms Monomial Natural number Negative exponent Number line Order of operations Perfect square number Polynomial Positive exponent Powers Power of a power Completely factor algebraic expressions (difference of squares and trinomials: trinomials limited to the form ax 2 +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. Prime factorization Prime number Product of powers Radical expression Rational expression Rational number Real number Simplest form Simplify Square root Term Trinomial Whole number Formative Assessments Homework 5 min warm ups Evidence of Learning Summative Assessments Quizzes Unit Test Performance Assessment Common Assessments Resources Cord Algebra 1 (Chapter 1 all, Section 2.1, Chapter 10 all, Sections 12.3 & 6) Merrill Algebra (Section 2.4; Sections 6.2, 6.3, 6.5 6.9; Section 7.1 7.8; Section 12.2, 12.5, 12.6) Supplemental Materials on R: drive Kuta Software (search by topic and customize) Cord Bridges (Sections 1.1 1.8; Sections 3.1 3.7; Sections 5.1 5.6; Sections 6.1 & 6.2; Sections 7.1 7.3; Sections 10.1 10.4) Holt McDougal Larson Algebra 1 (Sections 1.1 1.3; Chapter 2 all; Section 8.1 8.4; Section 9.1 9.5, 9.8; Section 11.2) Other print and digital resources at teacher s discretion.
Subject: Algebra IA Unit Title: Linear Equations Grade levels: 9-12 Mifflin County School District Mathematics Department Approximate Time Frame: 45 Days (50 minute periods) Rationale/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). A1.1.3.1 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). 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. 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, graph, and/or interpret linear inequalities to model relationships between quantities? 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?
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 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. 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. Identify properties of equality. Emphasize Inverse, Identity, Commutative, Associative (for solving) & Substitution (for checking) 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. 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.
Absolute value inequality Additive inverse Associative Property Coefficient Commutative Property Compound inequality Constant Dependent variable Vocabulary Distributive Property Equation Identity (addition & multiplication) Independent variable Inequality Inverse operations Inverse Property Linear equation Linear inequality Proportion Multiplicative inverse Reciprocal Solution Variable Formative Assessments Homework 5 min warm ups Evidence of Learning Summative Assessments Quizzes Unit Test Performance Assessment Common Assessments Resources Cord Algebra 1 (Chapter 3 all, Sections 9.1 9.5) Merrill Algebra (Sections 3.1 3.3, 3.5 3.7; Sections 5.1 5.3, 5.5, 5.6) Supplemental Materials on R: drive Kuta Software (search by topic and customize) Cord Bridges (Sections 4.1 4.6; Sections 5.4 5.8; Section 6.3; Sections 7.4 7.6) Holt McDougal Larson Algebra 1 (Chapter 3 all, Chapter 6 all) Other print and digital resources at teacher s discretion
Subject: Algebra IA Unit Title: Data Analysis & Probability Grade levels: 9-12 Approximate Time Frame: 45 Days (50 minute periods) Rationale/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 problem-solving 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).
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 Competencies Students will be able to 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. 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.
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). Bar graph Box and whisker plot Circle graph Complement Compound (or combined event) Conjunction Dependent events Disjunction Experimental probability Extremes 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 Formative Assessments Homework 5 min warm ups Evidence of Learning Summative Assessments Quizzes Unit Test Performance Assessment Common Assessments
Resources Cord Algebra 1 (Chapter 6 all, Chapter 7 all) Merrill Algebra (Sections 14.1 14.8, 14.10) Supplemental Materials on R: drive Kuta Software (search by topic and customize) Cord Bridges (Sections 2.1 2.7; Sections 6.4 6.8) Holt McDougal Larson Algebra 1 (Section 5.6, Chapter 13 all) Other print and digital resources at teacher s discretion Pacing Suggestions UNIT Operations w/ Real Numbers and Expressions Linear Equations Data Analysis and Probability Eligible Content A1.1.1.1.1 A1.1.1.1.2 A1.1.1.2.1 A1.1.1.4.1 A1.1.1.5.1 A1.1.1.5.2 A1.1.1.5.3 A1.1.2.1.1 A1.1.2.1.2 A1.1.2.1.3 A1.1.3.1.1 A1.1.3.1.2 A1.1.3.1.3 A1.2.3.1.1 A1.2.3.2.1 A1.2.3.2.2 A1.2.3.2.3 A1.2.3.3.1 A1.2.2.2.1 Sept. Oct. Nov. Dec. Jan. Feb. Mar. April May