Board Approved - April 24, 2003 For best printing results, click here (pdf).
MATHEMATICS K-10 – Course Expectations
Integrated Algebra I	Integrated Geometry
NUMBER SENSE	NUMBER SENSE
number and numeration	number and numeration
§ understand and use rational and irrational numbers § understand the properties of positive and negative exponents § understand the value of radicals (square root, cube root, and others) § classify quantities as being discrete or continuous § find and apply common equivalents between fractions, decimals, percents and scientific notations § understand the concepts of prime and composite numbers, factors and multiples, and divisibility rules § understand and apply the concepts of ratio, direct and indirect proportion § order and compare rational numbers in various representations	§ understand negative zero and fractional exponents § understand matrix notation § understand appropriate uses for matrices § understand imaginary and complex numbers
computation	computation
§ use the properties of positive exponents to simplify expressions § recognize and interpret numbers in various formats including scientific notation § compute with real numbers, powers and roots, using a calculator to find rational approximations as appropriate § understand and apply operations with rational numbers § use order of operations to evaluate expressions § use mental arithmetic, pencil and paper, calculator or computer as appropriate to the task	§ use the quadratic formula appropriately § use rules of exponents and roots § use matrix operations § computes using imaginary and complex numbers § apply the properties of exponents and roots to simplify an expression § simplify and compute with rational numbers, integral powers, and roots in arithmetic or geometric situations § use mental arithmetic, pencil and paper, or technology as appropriate to the task involving powers and roots
estimation	estimation
§ estimate the value of radicals (square root, cube root, and others) § identify the situations in which estimation is sufficient and computation is not required § use estimation to predict computation results § use estimation to determine reasonableness of answers	§ estimate the value of radicals (square root, cube root, and others) § identify the situations in which estimation is sufficient and computation is not required § use estimation to predict computation results § use estimation to determine reasonableness of answers
MEASUREMENT	MEASUREMENT
attributes and dimensions	attributes and dimensions
§ understand and apply the concept of rate and other derived and indirect measurements (similar right triangles) § understand the concepts of the relationships among linear dimensions, area, and volume § understand how dimensional changes affect perimeter, area, surface area, and/or volume § understand the concept of rate and how to calculate rates and determine units	§ apply the concept of indirect measurements (similar triangles and trigonometric ratios for right triangles) § calculate distance, midpoint, and slope using coordinate geometry § understand how dimensional changes affect two dimensional and three dimensional figures, including spheres § use and apply formulas for surface area and volume of curved surface objects using concrete, symbolic, and technological models § use ratios and proportions to calculate the measures of objects
approximation and precision	approximation and precision
§ understand the precision and accuracy of measurement are affected by the measurements tools and calculating procedures § use appropriate number of significant digits in calculations involving measurement § know how and when to use estimation to obtain reasonable approximations § know the approximate relationship between U.S. and metric units	§ understand the precision and accuracy of measurement are affected by the measurement tools and calculating procedures § know how and when to use estimation to obtain reasonable approximations § know the approximate relationship between U.S. and metric units § use estimation to obtain reasonable approximations for volume and surface area
systems and tools	systems and tools
§ know the benefits of standard measurements § know relationships among units within each system, U.S. and metric § know the appropriate unit of measurement for linear dimensions, area, and volume § select and use tools that will provide an appropriate degree of precision	§ know relationships among units within each system, U.S. and metric § know the appropriate unit of measurement for linear dimensions, area, and volume § justify the selection of a specified unit of measure to perform a specific measurement task
GEOMETRIC SENSE	GEOMETRIC SENSE
properties and relationships	properties and relationships
§ describe shapes and figures including angles, degrees in a circle, triangles, isosceles, equilateral, or quadrilateral § understand symmetry, congruence, and similarity § identify, set up, and interpret properties between similar figures	§ construct geometric models and scale drawings in multiple perspectives using tools as appropriate § translate between 3-dimensional objects and various views of their 2-dimensional representations § solve problems related to 2-dimensional and 3-dimensional figures using concrete, symbolic, and technological models § analyze, describe, compare, and contrast geometric relationships in geometric terms § make and test conjectures about 2-dimensional and 3-dimensional figures
locations and transformations	locations and transformations
§ understand and use coordinate grids § understand and apply the Pythagorean Theorem § understand and use the properties of symmetry and similarity § analyze properties of geometric figures using the Cartesian coordinate system	§ perform complex geometric constructions using a variety of tools and technologies § use compass and straightedge and/or computer software to perform geometric constructions (perpendicular bisector, angle bisector, duplicate segments, and triangles) § understand and construct geometric transformations (translations, rotations, dilations and reflections) on a specified figure in the coordinate plane § understand and use the properties of symmetry, similarity and congruence for 2 or 3 dimensional figures § understand and apply the properties of parallel and perpendicular lines § understand and apply the properties of triangles (right, isosceles, equilateral) § understand how transformations affect properties of geometric figures § solve problems involving 2-dimensional and 3-dimensional objects represented in different coordinate systems § perform successive geometric transformations (translation, reflection, rotation, dilation) on a specified figure in the coordinated plane
PROBABILITY AND STATISTICS	PROBABILITY AND STATISTICS
probability	probability
§ discriminate whether the outcome of a first event affects the probability of a later event § determine the probability of successive events § understand, use and compare experimental and theoretical probabilities for single variable data § use knowledge of probability to find the probability of repeated events	§ understand and use appropriate counting procedures to determine probabilities (permutations and combinations) § understand the properties of dependent and independent events § construct geometric models to find or estimate probabilities
statistics	statistics
§ understand the significance of the interpretations of data and how statistics can be used and misused to support differing points of view or arguments § organize and display data in tables, charts, and graphs as appropriate, using appropriate technology including scatter plots, box and whisker plots § develop a conclusion about trends in data from examining a graph § understand, calculate, and use the different measures of central tendency and range as appropriate in describing sets of data § identify how statistics can be used to support different points of view	§ understand the significance of the interpretations of data and how statistics can be used and misused to support differing points of view or arguments § understand the different ways to obtain a samples § understand and use appropriate methods and technology for collecting data § display and interpret data in an appropriate form
prediction and inference	prediction and inference
§ understand how to design and conduct experiments to verify or disprove predictions § use scatter plots and lines of best fit to make predictions § understand and make inferences based on analysis of experimental results, statistical data, and simple graphical representations	§ draw supportable inferences from a given set of data, citing the basis for the generalizations drawn § use an experiment to simulate the results of a survey and to justify or disprove predictions § use a sample to predict the results for a population § demonstrate an understanding of how statistical techniques are used to make predictions about real world situations § use conjectures to formulate new questions to plan new studies
ALGEBRAIC SENSE	ALGEBRAIC SENSE
patterns	patterns
§ represent and extend a wide variety of complex numerical patterns, including combinations of addition, multiplication and exponents § understand the concepts of independent and dependent variables § develop and express rules describing patterns	§ recognize, create and extend series and sequences e.g., iterations and fractals § develop and express rules describing patterns to find specified terms in the pattern
representations	representations
§ translate among tabular, symbolic, and graphical representations of relations § use graphs to model and solve problems of equalities and inequalities § understand and apply the components of equations of the form y=mx + b § represent situations with expressions, formulas, equations, and inequalities § understand that using algebraic equations can facilitate problem solving § recognize and use the direct variation model § use the standard form of a quadratic equation to find the line of symmetry, vertex, and y intercepts	§ develop symbolic and graphical representations for situations involving variable quantities § translate among tabular, symbolic, and graphical representations of relations § represent situations with expressions, formulas, equations, and inequalities § understand that using algebraic equations can facilitate problem solving § recognize and interpret graphs of functions § recognize and use appropriate variation model for a give situations § use the standard and vertex form of a quadratic equations to find the line of symmetry, vertex, and x intercepts
operations	operations
§ set up and solve linear equations and inequalities and interpret the answer in the context of the problem § understand how to evaluate and simplify expressions § solve, estimate, and interpret the solution to a system of linear equations using graphs, symbolic representations or technology	§ set up and solve linear, quadratic, and rational equations using a variety of methods (graphically, symbolically, etc.) § set up and solve a system of linear equations using a variety of methods (graphically, symbolically, and suing matrices) § understand how to evaluate and simplify expressions § set up and solve a system of linear, inequalities graphically
PROBLEM SOLVING	PROBLEM SOLVING
investigate situations	investigate situations
§ investigate complex situations that involve more than one step or variable in order to reach a solution § develop, use, and explain a variety of strategies and approaches (e.g. work backwards, draw diagrams, make charts, graphs, and tables, use formulas and technology) § recognize when a problem can’t be solved and state the needed information in order to solve it § recognize when an approach is unproductive and try a new approach	§ investigate complex situations that involve more than one step or variable in order to reach a solution § develop, use, and explain a variety of strategies and approaches (e.g. work backwards, draw diagrams, make charts, graphs, and tables, use formulas and technology) § recognize when a problem can’t be solved and state the needed information in order to solve it § recognize when an approach is unproductive and try a new approach
formulate questions and define the problem	formulate questions and define the problem
§ define problems and determine which questions need to be answered in complex situations § identify the unknowns in complex, open-ended problem situations	§ define problems and determine which questions need to be answered in complex situations § identify the unknowns in complex, open-ended problem situations
construct solutions	construct solutions
§ determine which materials, information, strategies, and variables could be used to solve complex, open-ended problems § select and use tools that are appropriate to solve a complex problem § organize relevant information in a manner consistent with solving problems	§ determine which materials, information, strategies, and variables could be used to solve complex, open-ended problems § select and use tools that are appropriate to solve a complex problem § organize relevant information in a manner consistent with solving problems
MATHEMATICAL REASONING	MATHEMATICAL REASONING
analyze information	analyze information
§ compare, contrast, and interpret information from a variety of sources § evaluate the validity of statements by providing support or creating a counter-example	§ compare, contrast, and interpret information from a variety of sources § evaluate the validity of statements by providing support or creating a counter-example
predict results and make inferences	predict results and make inferences
§ make conjectures, predictions, and inferences based on analysis of new problem situations	§ make conjectures, predictions, and inferences based on analysis of new problem situations
draw conclusions and verify results	draw conclusions and verify results
§ defend the validity of a conclusion by citing multiple sources § analyze results of others and determine if they are correct § reflect on and evaluate procedures and results in a problem situation	§ defend the validity of a conclusion by citing multiple sources § analyze results of others and determine if they are correct § reflect on and evaluate procedures and results in a problem situation