Mathematics Department Scope and Sequence

Transcription

1 Mathematics Department for grades Kindergarten through High School

2 Common Core Learning Standards Mathematics Standards Progressions EngageNY Math Curriculum Modules Story of Units Story of Ratios Story of Functions Grade K High School Counting and Cardinality Number and Operations in Base Ten Number and Operations - Fractions Ratios and Proportional Relationships The Number System Number and Quantity Domains Operations and Algebraic Thinking Expressions and Equations Algebra Functions Functions Geometry Geometry Geometry Common Core Practices Measurement and Data Standards for Mathematical Practice Statistics and Probability Statistics and Probability

3 Grade K Overview MAEKG K.CC Counting and Cardinality Know number names and the count sequence. Count to tell the number of objects. Compare numbers. K.OA Operations and Algebraic Thinking Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. K.NBT Number and Operations in Base Ten Work with numbers to gain foundations for place value. K.MD Measurement and Data Describe and compare measurable attributes. Classify objects and count the number of objects in categories. K.G Geometry Identify and describe shapes. Analyze, compare, create, and compose shapes. Required Fluency: K.OA.5 Add and subtract within 5

4 Grade K Checklist F Fluency Standard * Major Emphases Standard 4

5 Grade 1 Overview MAE1G 1.OA Operations and Algebraic Thinking Represent and solve problems involving addition and subtraction. Understand and apply properties of operations and the relationship between addition and subtraction. Add and subtract within 20. Work with addition and subtraction equations. 1.NBT Number and Operations in Base Ten Extend the counting sequence. Understand place value. Use place value understanding and properties of operations to add and subtract. 1.MD Measurement and Data Measure lengths indirectly and by iterating length units. Tell and write time and money. Represent and interpret data. 1.G Geometry Reason with shapes and their attributes. Required Fluency: 1.OA.6 Add and subtract within 10 5

6 Grade 1 Checklist F Fluency Standard * Major Emphases Standard 6

7 Grade 2 Overview MAE2G 2.OA Operations and Algebraic Thinking Represent and solve problems involving addition and subtraction. Add and subtract within 20. Work with equal groups of objects to gain foundations for multiplication. 2.NBT Number and Operations in Base Ten Understand place value. Use place value understanding and properties of operations to add and subtract. 2.MD Measurement and Data Measure and estimate lengths in standard units. Relate addition and subtraction to length. Work with time and money. Represent and interpret data. 2.G Geometry Reason with shapes and their attributes. Required Fluency: 2.OA.2 Add and subtract within 20 2.NBT.5 Add and subtract within 100 7

8 Grade 2 Checklist F Fluency Standard * Major Emphases Standard 8

9 Grade 3 Overview MAE3G 3.OA Operations and Algebraic Thinking Represent and solve problems involving multiplication and division. Understand properties of multiplication and the relationship between multiplication and division. Multiply and divide within 100. Solve problems involving the four operations, and identify and explain patterns in arithmetic. 3.NBT Number and Operations in Base Ten Use place value understanding and properties of operations to perform multi-digit arithmetic. 3. NF Number and Operations Fractions Develop understanding of fractions as numbers. 3.MD Measurement and Data Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. Represent and interpret data. Geometric measurement: understand concepts of area and relate area to multiplication and to addition. Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. 3.G Geometry Reason with shapes and their attributes. Required Fluency: 3.OA.7 Multiply and divide within NBT.2 Add and subtract within

10 Grade 3 Checklist 10

11 Grade 4 Overview MAE4G 4.OA Operations and Algebraic Thinking Use the four operations with whole numbers to solve problems. Gain familiarity with factors and multiples. Generate and analyze patterns. 4.NBT Number and Operations in Base Ten Generalize place value understanding for multidigit whole numbers. Use place value understanding and properties of operations to perform multi-digit arithmetic. 4.NF Number and Operations Fractions Extend understanding of fraction equivalence and ordering. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. Understand decimal notation for fractions, and compare decimal fractions. 4.MD Measurement and Data Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Represent and interpret data. Geometric measurement: understand concepts of angle and measure angles. 4.G Geometry Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Required Fluency: 4.NBT.4 Add and subtract within 1,000,000 11

12 Grade 4 Checklist 12

13 Grade 5 Overview MAE5G 5.OA Operations and Algebraic Thinking Write and interpret numerical expressions. Analyze patterns and relationships. 5.NBT Number and Operations in Base Ten Understand the place value system. Perform operations with multi-digit whole numbers and with decimals to hundredths. 5.NF Number and Operations Fractions Use equivalent fractions as a strategy to add and subtract fractions. Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 5.MD Measurement and Data Convert like measurement units within a given measurement system. Represent and interpret data. Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. 5.G Geometry Graph points on the coordinate plane to solve real-world and mathematical problems. Classify two-dimensional figures into categories based on their properties. Required Fluency: 5.NBT.5 Multi-digit multiplication 13

14 Grade 5 Checklist 14

15 Grade 6 Overview MAE6G 6.RP Ratios and Proportional Relationships Understand ratio concepts and use ratio reasoning to solve problems. 6.NS The Number System Apply and extend previous understandings of multiplication and division to divide fractions by fractions. Compute fluently with multi-digit numbers and find common factors and multiples. Apply and extend previous understandings of numbers to the system of rational numbers. 6.EE Expressions and Equations Apply and extend previous understandings of arithmetic to algebraic expressions. Reason about and solve one-variable equations and inequalities. Represent and analyze quantitative relationships between dependent and independent variables. 6.G Geometry Solve real-world and mathematical problems involving area, surface area, and volume. 6.SP Statistics and Probability Develop understanding of statistical variability. Summarize and describe distribution Required Fluency: 6.NS.2 Multi-digit division 6.NS.3 Multi-digit decimal operations 15

16 Grade 6 Checklist F Fluency Standard * Major Emphases Standard + NYSED May-June Standard 16

17 Grade 7 Overview MAE7G 7.RP Ratios and Proportional Relationships Analyze proportional relationships and use them to solve real-world and mathematical problems. 7.NS The Number System Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. 7.EE Expressions and Equations Use properties of operations to generate equivalent expressions. Solve real-life and mathematical problems using numerical and algebraic expressions and equations. 7.G Geometry Draw, construct and describe geometrical figures and describe the relationships between them. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. 7.SP Statistics and Probability Use random sampling to draw inferences about a population. Draw informal comparative inferences about two populations. Investigate chance processes and develop, use, and evaluate probability models. Required Fluency: 7.EE.4 Solve px + q = r and p(x + q) = r 17

18 Grade 7 Checklist F Fluency Standard * Major Emphases Standard + NYSED May-June Standard 18

19 Grade 8 Overview MAE8G 8.NS The Number System Know that there are numbers that are not rational, and approximate them by rational numbers. 8.EE Expressions and Equations Work with radicals and integer exponents. Understand the connections between proportional relationships, lines, and linear equations. Analyze and solve linear equations and pairs of simultaneous linear equations. 8.F Functions Define, evaluate, and compare functions. Use functions to model relationships between quantities. 8.G Geometry Understand congruence and similarity using physical models, transparencies, or geometry software. Understand and apply the Pythagorean Theorem. Solve real-world and mathematical problems involving volume of cylinders, cones and spheres. 8.SP Statistics and Probability Investigate patterns of association in bivariate data. Required Fluency: 8.EE.8b Solve simple 2 2 systems by inspection 19

20 Grade 8 Checklist F Fluency Standard * Major Emphases Standard + NYSED May-June Standard 20

21 Algebra I Year 1 of 2 Overview First part in a TWO-PART SEQUENCE AL01GXX1 Number and Quantity The Real Number System (N-RN) Quantities (N-Q) Algebra Seeing Structure in Expressions (A-SSE) Interpret the structure of expressions Arithmetic with Polynomials and Rational Expressions (A-APR) Perform arithmetic operations on polynomials Creating Equations (A-CED) Create equations that describe numbers or relationships Reasoning with Equations and Inequalities (A-REI) Understand solving equations as a process of reasoning and explain the reasoning Solve equations and inequalities in one variable Represent and solve equations and inequalities graphically Functions Interpreting Functions (F-IF) Understand the concept of a function and use function notation Interpret functions that arise in applications in terms of the context Building Functions (F-BF) Linear, Quadratic, and Exponential Models (F-LE) Statistics and Probability Interpreting categorical and quantitative data (S-ID) Interpret linear models Modeling Specific modeling domains, clusters, and standards, indicated by a star symbol Fluency Recommendations The PARCC Model Content Frameworks recommend the following fluencies for Algebra I students: A/G Algebra I students become fluent in solving characteristic problems involving the analytic geometry of lines, such as writing down the equation of a line given a point and a slope. Such fluency can support them in solving less routine mathematical problems involving linearity, as well as in modeling linear phenomena (including modeling using systems of linear inequalities in two variables). A-APR.A.1 Fluency in adding, subtracting, and multiplying polynomials supports students throughout their work in algebra, as well as in their symbolic work with functions. Manipulation can be more mindful when it is fluent. A-SSE.A.1b Fluency in transforming expressions and chunking (seeing parts of an expression as a single object) is essential in factoring, completing the square, and other mindful algebraic calculations. 21

22 Algebra I Year 1 of 2 Checklist F Fluency Recommendations * Major Emphases Standard Modeling Standards 22

23 Algebra I Year 2 of 2 Overview Second part in a TWO-PART SEQUENCE AL01RXX2 Number and Quantity The Real Number System (N-RN) Quantities (N-Q) Algebra Seeing Structure in Expressions (A-SSE) Interpret the structure of expressions Arithmetic with Polynomials and Rational Expressions (A-APR) Perform arithmetic operations on polynomials Creating Equations (A-CED) Create equations that describe numbers or relationships Reasoning with Equations and Inequalities (A-REI) Understand solving equations as a process of reasoning and explain the reasoning Solve equations and inequalities in one variable Represent and solve equations and inequalities graphically Functions Interpreting Functions (F-IF) Understand the concept of a function and use function notation Interpret functions that arise in applications in terms of the context Building Functions (F-BF) Linear, Quadratic, and Exponential Models (F-LE) Statistics and Probability Interpreting categorical and quantitative data (S-ID) Interpret linear models Modeling Specific modeling domains, clusters, and standards, indicated by a star symbol Fluency Recommendations The PARCC Model Content Frameworks recommend the following fluencies for Algebra I students: A/G Algebra I students become fluent in solving characteristic problems involving the analytic geometry of lines, such as writing down the equation of a line given a point and a slope. Such fluency can support them in solving less routine mathematical problems involving linearity, as well as in modeling linear phenomena (including modeling using systems of linear inequalities in two variables). A-APR.A.1 Fluency in adding, subtracting, and multiplying polynomials supports students throughout their work in algebra, as well as in their symbolic work with functions. Manipulation can be more mindful when it is fluent. A-SSE.A.1b Fluency in transforming expressions and chunking (seeing parts of an expression as a single object) is essential in factoring, completing the square, and other mindful algebraic calculations. 23

24 Algebra I Year 2 of 2 Checklist F Fluency Recommendations * Major Emphases Standard Modeling Standards 24

25 Algebra I Overview AL01R Number and Quantity The Real Number System (N-RN) Quantities (N-Q) Algebra Seeing Structure in Expressions (A-SSE) Interpret the structure of expressions Arithmetic with Polynomials and Rational Expressions (A-APR) Perform arithmetic operations on polynomials Creating Equations (A-CED) Create equations that describe numbers or relationships Reasoning with Equations and Inequalities (A-REI) Understand solving equations as a process of reasoning and explain the reasoning Solve equations and inequalities in one variable Represent and solve equations and inequalities graphically Functions Interpreting Functions (F-IF) Understand the concept of a function and use function notation Interpret functions that arise in applications in terms of the context Building Functions (F-BF) Linear, Quadratic, and Exponential Models (F-LE) Statistics and Probability Interpreting categorical and quantitative data (S-ID) Interpret linear models Modeling Specific modeling domains, clusters, and standards, indicated by a star symbol Fluency Recommendations The PARCC Model Content Frameworks recommend the following fluencies for Algebra I students: A/G Algebra I students become fluent in solving characteristic problems involving the analytic geometry of lines, such as writing down the equation of a line given a point and a slope. Such fluency can support them in solving less routine mathematical problems involving linearity, as well as in modeling linear phenomena (including modeling using systems of linear inequalities in two variables). A-APR.A.1 Fluency in adding, subtracting, and multiplying polynomials supports students throughout their work in algebra, as well as in their symbolic work with functions. Manipulation can be more mindful when it is fluent. A-SSE.A.1b Fluency in transforming expressions and chunking (seeing parts of an expression as a single object) is essential in factoring, completing the square, and other mindful algebraic calculations. 25

26 Algebra I Checklist F Fluency Recommendations * Major Emphases Standard Modeling Standards 26

27 Survey of Geometry Overview AG01G Survey of Geometry combines the study of algebra topics with introductory geometry topics. The first semester includes principle Algebra topics that will prepare students to retake the Algebra I examination, and the second semester includes elemental geometry topics that will prepare students for Geometry next year. Geometry (7.G) Draw, construct and describe geometrical figures and describe the relationships between them. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. Geometry (8.G) Understand congruence and similarity using physical models, transparencies, or geometry software. Understand and apply the Pythagorean Theorem. Solve real-world and mathematical problems involving volume of cylinders, cones and spheres. 27

28 Survey of Geometry Checklist * Major Emphases Standard + NYSED May-June Standard 28

29 Geometry Overview GE01R Geometry Congruence (G-CO) Understand congruence in terms of rigid motions Prove geometric theorems Similarity, Right Triangles, and Trigonometry (G-SRT) Understand similarity in terms of similarity transformations Prove theorems using similarity Define trigonometric ratios and solve problems involving right triangles Circles (G-C) Expressing Geometric Properties with Equations (G-GPE) Use coordinates to prove simple geometric theorems algebraically Geometric Measurement and Dimensions (G-GMD) Modeling with Geometry (G-GMD) Apply geometric concepts in modeling situations Modeling Specific modeling domains, clusters, and standards, indicated by a star symbol Recommended Fluencies for Geometry Triangle congruence and similarity criteria. Using coordinates to establish geometric results. Calculating length and angle measures. Using geometric representations as a modeling tool. Using construction tools, physical and computational to draft models of geometric phenomenon. 29

30 Geometry Checklist * Major Emphases Cluster ff Additional Fluency Suggestion Modeling Standards 30

31 Algebra II Overview AT02R Number and Quantity The Real Number System (N-RN) Extend the properties of exponents to rational exponents Quantities (N-Q) The Complex Number System (N-CN) Algebra Seeing Structure in Expressions (A-SSE) Interpret the structure of expressions Write expressions in equivalent forms to solve problems Arithmetic with Polynomials and Rational Expressions (A-APR) Understand the relationship between zeros and factors of polynomials Creating Equations (A-CED) Reasoning with Equations and Inequalities (A-REI) Understand solving equations as a process of reasoning and explain the reasoning Represent and solve equations and inequalities graphically Expressing Geometric Properties with Equations (G-GPE) * Functions Interpreting Functions (F-IF) Interpret functions that arise in applications in terms of the context Building Functions (F-BF) Build a function that models a relationship between two quantities Linear, Quadratic, and Exponential Models (F-LE) Trigonometric Functions (F-TF) Statistics and Probability Interpreting categorical and quantitative data (S-ID) Making Inferences and Justifying Conclusions (S-IC) Make inferences and justify conclusions from sample surveys, experiments and observational studies Conditional Probability and the Rules of Probability (S-CP) Recommended Fluencies for Algebra II Divide polynomials with remainder by inspection in simple cases. See structure in expressions and use this structure to rewrite expressions (e.g., factoring, grouping). Translate between recursive definitions and closed forms for problems involving sequences and series. 31

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33 Algebra II Checklist Continued * Major Emphases Cluster ff Additional Fluency Suggestion Modeling Standards 33

34 PreCalculus & Advanced Topics Overview PC03G Number and Quantity The Complex Number System (N-CN) Perform arithmetic operations with complex numbers. Represent complex numbers and their operations on the complex plane. Use complex numbers in polynomial identities and equations. Vector Quantities and Matrices (N-VM) Represent and model with vector quantities. Perform operations on vectors. Perform operations on matrices and use matrices in applications. Algebra Arithmetic with Polynomials and Rational Expressions (A-APR) Use polynomial identities to solve problems. Rewrite rational expressions. Reasoning with Equations and Inequalities (A-REI) Solve systems of equations. Functions Interpreting Functions (F-IF) Analyze functions using different representations. Building Functions (F-BF) Build a function that models a relationship between two quantities. Build new functions from existing functions. Trigonometric Functions (F-TF) Extend the domain of trigonometric functions using the unit circle. Model periodic phenomena with trigonometric functions. Prove and apply trigonometric identities. Geometry Congruence (G-CO) Experiment with transformations in the plane. Understand and apply theorems about circles. Expressing Geometric Properties with Equations (G-GPE) Translate between the geometric description and the equation for a conic section. Geometric Measurement and Dimension (G-GMD) Explain volume formulas and use them to solve problems. Similarity, Right Triangles, and Trigonometry (G-SRT) Apply trigonometry to general triangles. Statistics and Probability Conditional Probability and the Rules of Probability (S-CP) Use the rules of probability to compute probabilities of compound events in a uniform probability model. Using Probability to Make Decisions (S-MD) Calculate expected values and use them to solve problems. Use probability to evaluate outcomes of decisions. 34

35 PreCalculus & Advanced Topics Checklist Checklist continued on next page 35

36 PreCalculus & Advanced Topics Checklist Continued 36