2. Number
Core Concept AThe real numbers include the rational numbers and are in one-to-one correspondence with the points on the number line. Example Task 1 2. Number
Core Concept BQuantities can be compared using division, yielding rates and ratios. Example Task 1 2. Number
Core Concept CA fraction can represent the result of dividing the numerator by the denominator; equivalent fractions have the same value. Example Task 1 2. Number
Core Concept DPlace value and the rules of arithmetic form the foundation for efficient algorithms. Example Task 1 3. Quantity
Core Concept AThe value of a quantity is not specified unless the units are named or understood from the context. 3. Quantity
Core Concept BQuantities can be added and subtracted only when they are of the same type (length, area, speed, etc.). 3. Quantity
Core Concept CQuantities can be multiplied or divided to create new types of quantities, called derived quantities. 4. Expressions
Core Concept AExpressions are constructions built up from numbers, variables, and operations, which have a numerical value when each variable is replaced with a number. Example Task 1 4. Expressions
Core Concept CThe rules of arithmetic can be applied to transform an expression without changing its value. 4. Expressions
Core Concept DRewriting expressions in equivalent forms serves a purpose in solving problems. Example Task 1 5. Equations
Core Concept BThe solutions of an equation are the values of the variables that make the resulting numerical statement true. 5. Equations
Core Concept CThe steps in solving an equation are guided by understanding and justified by logical reasoning. 5. Equations
Core Concept DEquations not solvable in one number system may have solutions in a larger number system. 6. Functions
Core Concept AA function is a rule, often defined by an expression, that assigns a unique output for every input. Example Task 1 6. Functions
Core Concept BThe graph of a function f is a set of ordered pairs (x, f(x)) in the coordinate plane.
Example Task 1 6. Functions
Core Concept CFunctions model situations where one quantity determines another. Example Task 1 6. Functions
Core Concept DCommon functions occur in families where each member describes a similar type of dependence. Example Task 1 7. Modeling
Core Concept AMathematical models involve choices and assumptions that abstract key features from situations to help us solve problems. 8. Shape
Core Concept AShapes and their parts, attributes, and measurements can be analyzed deductively. In this document, deductive analysis aligns with the notion of adaptive reasoning as defined in Adding it Up, and includes empirical exploration, informal justification, and formal proof. Example Task 1 8. Shape
Core Concept BCongruence, similarity, and symmetry can be analyzed using transformations. Example Task 1 8. Shape
Core Concept CMathematical shapes model the physical world, resulting in practical applications of geometry. Example Task 1 8. Shape
Core Concept DRight triangles and the Pythagorean theorem are central to geometry and its applications, including trigonometry. Example Task 1 9. Coordinates
Core Concept ALocations in the plane or in space can be specified by pairs or triples of numbers called coordinates. Example Task 1 9. Coordinates
Core Concept BCoordinates link algebra with geometry and allow methods in one domain to solve problems in the other. Example Task 1 9. Coordinates
Core Concept CThe set of solutions to an equation in two variables forms a curve in the coordinate plane—such as a line, parabola, circle—and the solutions to systems of equations correspond to intersections of these curves. Example Task 1 10. Probability
Core Concept AProbability models outcomes for situations in which there is inherent randomness, quantifying the degree of uncertainty in terms of relative frequency of occurrence. Example Task 1 10. Probability
Core Concept BThe law of large numbers provides the basis for estimating certain probabilities by use of empirical relative frequencies. Example Task 1 10. Probability
Core Concept CThe laws of probability govern the calculation of probabilities of combined events. Example Task 1 10. Probability
Core Concept DInterpreting probabilities contextually is essential to rational decision-making in situations involving randomness. Example Task 1 11. Statistics
Core Concept AStatistical methods take variability into account to support making informed decisions based on quantitative studies designed to answer specific questions. Example Task 1 11. Statistics
Core Concept BVisual displays and summary statistics condense the information in data sets into usable knowledge. Example Task 1 |