curriculum Goal Area Descriptions 6 12
Measures of Academic Progress (MAP) Common Core Aligned Version 4 Page 5 of 17 Common Core Goal Structure Version 4 Created by NWEA in 2013 Using CCSSO 2010 Common Core Standards for Mathematics K-12 Mathematics 6+ Goal Structure Mathematics 6+ DesCartes Mathematics 6+ Report Names Operations and Algebraic Thinking Operations and Algebraic Thinking Algebraic Thinking Apply and extend previous understandings of arithmetic to algebraic expressions and equations: Solve one-variable equations and inequalities (including linear, quadratic, rational, and radical); use properties of operations to generate equivalent expressions; interpret the structure of expressions; solve real-life and mathematical problems using numerical and algebraic expressions and equations; work with radicals and integer exponents; use scientific notation; solve systems of equations; perform arithmetic operations on polynomials; represent and solve equations and inequalities graphically; understand the connections between proportional relationships, lines, and linear equations. Expressions and Equations Use functions to model relationships between quantities: Define, evaluate, and compare functions; understand the concept of a function and use function notation; interpret functions that arise in applications in terms of the context; analyze functions using different representations; build new functions from existing functions; construct and compare linear, quadratic, and exponential models and solve problems; extend the domain of trigonometric functions using the unit circle; model periodic phenomena with trigonometric functions; prove and apply trigonometric identities. Use Functions to Model Relationships The Real and Complex Number Systems The Real and Complex Number Systems Real & Complex Number Systems Measures of Academic Progress (MAP) Common Core Aligned Version 4 Page 6 of 17 Common Core Goal Structure Version 4 Created by NWEA in 2013 Using CCSSO 2010 Common Core Standards for Mathematics K-12 Mathematics 6+ Goal Structure Mathematics 6+ DesCartes Mathematics 6+ Report Names Analyze proportional relationships and use them to solve real- world and mathematical problems: Understand ratio concepts and use ratio reasoning to solve problems; use ratio and rate reasoning to solve real-world and mathematical problems; recognize and represent proportional relationships between quantities; use proportional relationships to solve multistep ratio and percent problems. Ratios and Proportional Relationships Apply and extend previous understandings of operations: Divide fractions by fractions; compute fluently with multi-digit numbers and find common factors and multiples; add, subtract, multiply, and divide rational numbers; perform arithmetic operations with complex numbers; solve real-world and mathematical problems involving the four operations with rational numbers; reason quantitatively and use units to solve problems. Perform Operations Apply and extend previous understandings of numbers to the system of rational numbers: Know that there are numbers that are not rational, and approximate them by rational numbers; extend the properties of exponents to rational exponents; use properties of rational and irrational numbers; solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Extend and Use Properties Geometry Geometry Geometry Measures of Academic Progress (MAP) Common Core Aligned Version 4 Page 7 of 17 Common Core Goal Structure Version 4 Created by NWEA in 2013 Using CCSSO 2010 Common Core Standards for Mathematics K-12 Mathematics 6+ Goal Structure Mathematics 6+ DesCartes Mathematics 6+ Report Names Solve real-world and mathematical problems involving area, circumference, surface area, volume, and angle measure: Visualize relationships between two-dimensional and three- dimensional objects understand and apply theorems about circles; find arc lengths and areas of sectors of circles; translate between the geometric description and the equation for a conic section; use coordinates to prove simple geometric theorems algebraically; solve problems involving scale drawings of geometric figures. Geometric Measurement and Relationships Understand congruence and similarity using physical models: Understand and apply the Pythagorean Theorem; experiment with transformations in the plane; understand congruence in terms of rigid motions; prove geometric theorems; understand similarity in terms of similarity transformations; use facts about the angle sum and exterior angle of triangles and about the angles created when parallel lines are cut by a transversal; prove theorems involving similarity; define trigonometric ratios and solve problems involving right triangles. Congruence, Similarity, Right Triangles, & Trig Statistics and Probability Statistics and Probability Statistics and Probability Summarize, represent, and interpret data on a single count or measurement variable and on two categorical and quantitative variables: Develop understanding of statistical variability; summarize and describe distributions; use measures of center and measures of variability; draw informal comparative inferences about two populations; investigate patterns of association in bivariate data; interpret linear models; represent data with plots on the real number line (dot plots, histograms, and box plots). Interpreting Categorical and Quantitative Data Measures of Academic Progress (MAP) Common Core Aligned Version 4 Page 8 of 17 Common Core Goal Structure Version 4 Created by NWEA in 2013 Using CCSSO 2010 Common Core Standards for Mathematics K-12 Mathematics 6+ Goal Structure Mathematics 6+ DesCartes Mathematics 6+ Report Names Use random sampling and the rules of probability: Use random sampling to draw inferences about a population; investigate chance processes and develop, use, and evaluate probability models; understand and evaluate random processes underlying statistical experiments; make inferences and justify conclusions from sample surveys, experiments, and observational studies; understand independence and conditional probability and use them to interpret data; use the rules of probability to compute probabilities of compound events in a uniform probability model. Using Sampling and Probability to Make Decisions