Mathematics Department Standards

 

 

1.      The student will be able to understand numbers, ways of representing numbers, relationships among numbers, and number systems.

 

2.      The student will be able to understand meanings of operations and how they relate to one another.

 

3.      The student will be able to compute fluently and make reasonable estimates.

 

4.      The student will be able to understand patterns, relations, and functions.

 

5.      The student will be able to represent and analyze mathematical situations and structures using algebraic symbols.

 

6.      The student will be able to use mathematical models to understand and represent quantitative relationships.

 

7.      The student will be able to analyze change in various contexts.

 

8.      The student will be able to analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

 

9.      The student will be able to specify locations and describe spatial relationships using coordinate geometry and other representational systems.

 

10. The student will be able to apply transformations and use symmetry to analyze mathematical situations.

 

11. The student will be able to use visualization, spatial reasoning, and geometric modeling to solve problems.

 

12. The student will be able to understand measurable attributes of objects and the units, systems, and processes of measurement.

 

13. The student will be able to apply appropriate techniques, tools, and formulas to determine measurements.

 

14. The student will be able to formulate questions that can be addressed with data.  The student will also be able to collect, organize, and display relevant data to answer them.

 

15. The student will be able to select and use appropriate statistical methods to analyze data.

 

16. The student will be able to develop and evaluate inferences and predictions that are based on data.

 

Standard #1

 

            The student will be able to understand numbers, ways of representing numbers, relationships among numbers, and number systems.

 

Benchmarks

 

        Level I            Pre - Kindergarten - Second Grade

 

1.      Counts with understanding and recognizes "how many" in sets of objects.

 

2.      Uses multiple models to develop initial understandings of place value and the base-ten number system.

 

3.      Develops understanding of the relative position and magnitude of whole numbers and of ordinal/cardinal numbers and their connections.

 

4.      Develops a sense of whole numbers and represents and uses them in flexible ways (e.g. relating, composing, decomposing numbers).

 

5.      Connects number words and numerals to the quantities they represent, using various physical models and representations.

 

6.      Understands and represents commonly used fractions (e.g. 1/4, 1/3, 1/2).

 

            Level II           Third - Fifth Grade

 

1.      Understands the place-value structure of the base-ten number system and is able to represent and compare whole numbers and decimals.

 

2.      Recognizes equivalent representations for the same number and generates them by decomposing and composing numbers.

 

3.      Develops an understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers.

 

4.      Uses models, benchmarks, and equivalent forms to judge the size of fractions.

 

5.      Recognizes and generates equivalent forms of commonly used fractions, decimals, and percents.

 

6.      Explores numbers less than zero by extending the number line and through other familiar applications.

 

7.      Describes classes of numbers according to characteristics such as the nature of their factors.

 

            Level III          Sixth - Eighth Grade

 

1.      Works flexibly with fractions, decimals, and percents to solve problems.

 

2.      Compares and orders fractions, decimals, and percents efficiently and finds their approximate location on a number line.

 

3.      Develops meaning for percents greater than one hundred (100) and less than one (1).

 

4.      Understands and uses ratios and proportions to represent quantitative relationships.

 

5.      Develops an understanding of large numbers, recognizing and appropriately using exponential, scientific, and calculator notation.

 

6.      Uses factors, multiples, prime factorization, and relatively prime numbers to solve problems.

 

7.      Develops meaning for integers and represents and compares quantities with them.

 

            Level IV         Ninth - Twelfth Grade

 

1.      Develops a deeper understanding of very large and very small numbers and their various representations.

 

2.      Compares and contrasts the properties of numbers and number systems, (e.g. rational, real numbers) and understands complex numbers as solutions to quadratic equations that do not have real solutions.

 

3.      Understands matrices as systems that have some of the properties of the real-number system.

4.      Uses number-theory arguments to justify relationships involving whole numbers.

 

 

Standard #2

 

            The student will be able to understand meanings of operations and how they relate to one another.

 

Benchmarks

 

Level I               Pre - Kindergarten - Second Grade

 

1.      Understands various meanings of addition and subtraction of whole numbers and the relationship between the two operations.

 

2.      Understands the effects of adding and subtracting whole numbers.

 

3.      Understands situations that entail multiplication and division, such as equal groupings of objects and sharing equally.

 

            Level II           Third - Fifth Grade

 

1.      Understands various meanings of multiplication and division.

 

2.      Understands the effects of multiplying and dividing whole numbers.

 

3.      Identifies and uses relationships between operations, such as division as the inverse of multiplication, to solve problems.

 

4.      Understands and uses properties of operations, such as the distributivity of multiplication over addition.

 

            Level III          Sixth - Eighth Grade

 

1.      Understands the meaning and effects of arithmetic operations with fractions, decimals, and integers.

 

2.      Uses the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition to simplify computations with integers, fractions, and decimals.

3.      Understands and uses inverse relationships (e.g. addition and subtraction, multiplication and division, squaring and finding square roots) to simplify computations and solve problems.

 

            Level IV         Ninth - Twelfth Grade

 

1.      Judges the effects of such operations as multiplication, division, and computing powers and roots on the magnitudes of quantities.

 

2.      Develops an understanding of properties of ,and representations for, the addition and multiplication of matrices

 

 

Standard #3

 

            The student will be able to compute fluently and make reasonable estimates.

 

Benchmarks

 

        Level I            Pre - Kindergarten - Second Grade

 

1.      Develops and uses strategies for whole-number computations; with a focus on addition and subtraction.

 

2.      Develops fluency with basic number combinations for addition and subtraction.

 

3.      Uses a variety of methods and tools to compute (e.g. objects, mental computation, estimation, paper-and-pencil, calculators).

 

            Level II           Third - Fifth Grade

 

1.      Develops fluency with basic number combinations for multiplication and division and uses these combinations to mentally compute related problems, such as 30 x 50.

 

2.      Develops fluency in adding, subtracting, multiplying, and dividing whole numbers.

 

3.      Develops and uses strategies to estimate the results of whole-number computations and to judge the rationality of such results.

 

4.      Develops and uses strategies to estimate computations involving fractions and decimals in situations relevant to students' experience.

 

5.      Uses visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals.

 

6.      Selects and uses appropriate methods/tools for computing with whole numbers (e.g. mental computation, estimation, calculators, and paper-and-pencil) according to the context and nature of the computation.

 

            Level III          Sixth - Eighth Grade

 

1.      Selects and applies appropriate methods and tools for computing with fractions and decimals (e.g. mental computation, estimation, calculators/computers, paper-and-pencil) depending on the situation.

 

2.      Develops and analyzes algorithms for computing with fractions, decimals, and integers developing fluency in their use.

 

3.      Develops and uses strategies to estimate the results of rational-number computations and judges the rationality of the results.

 

4.      Develops, analyzes, and explains methods for solving problems involving proportions (e.g. scaling, finding equivalent ratios).

 

            Level IV         Ninth - Twelfth Grade

 

1.      Develops fluency in operations with real numbers and matrices (e.g. using mental computation or paper-and-pencil calculations for simple cases, technology for more complicated cases).

 

2.      Judges the reasonableness of numerical computations and their results.

 

 

Standard #4

 

            The student will be able to understand patterns, relations, and functions.

 

Benchmarks

 

        Level I            Pre - Kindergarten - Second Grade

 

1.      Sorts, classifies, and orders objects by size, number, and other properties.

 

2.      Recognizes, describes, and extends patterns (e.g. sequences of sounds and shapes, simple numeric patterns) translating them from one representation to another.

 

3.      Analyzes how both repeating and growing patterns are generated.

 

            Level II           Third - Fifth Grade

 

1.      Describes, extends, and makes generalizations about geometric and numeric patterns.

 

2.      Represents and analyzes patterns and functions; using words, tables, and graphs.

 

            Level III          Sixth - Eighth Grade

 

1.      Represents, analyzes, and generalizes a variety of patterns; using tables, graphs, words, and, when possible, symbolic rules.

 

2.      Relates and compares different forms of representation for a relationship.

 

3.      Identifies functions as linear/nonlinear and contrasts their properties from tables, graphs, or equations.

 

            Level IV         Ninth - Twelfth Grade

 

1.      Generalizes patterns using explicitly and recursively defined functions.

 

2.      Understands, selects, converts flexibly among, and uses various representations of relations and functions.

3.      Analyzes functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local/global behavior.

 

4.      Understands and performs transformations by arithmetically combining, composing, and inverting commonly used functions; or using technology to perform more complicated symbolic expressions.

 

5.      Understands and compares the properties of classes of functions (e.g. exponential, polynomial, rational, logarithmic, periodic functions).

 

6.      Interprets the representations of functions of two variables.

 

 

Standard #5

 

            The student will be able to represent and analyze mathematical situations and structures using algebraic symbols.

 

Benchmarks

 

            Level I            Pre - Kindergarten - Second Grade

 

1.      Illustrates general principles and properties of operations (e.g. commutativity) using specific numbers.

 

2.      Uses concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations.

 

            Level II           Third - Fifth Grade

 

1.      Identifies such properties as commutativity, associativity, and distributivity and uses them to compute with whole numbers.

 

2.      Represents the idea of a variable as an unknown quantity using a letter or symbol.

 

3.      Expresses mathematical relationships using equations.

 

            Level III          Sixth - Eighth Grade

 

1.      Develops an initial conceptual understanding of different uses of variables.

 

2.      Explores relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope.

 

3.      Uses symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships.

 

4.      Recognizes and generates equivalent forms for simple algebraic expressions and solves linear equations.

 

            Level IV         Ninth - Twelfth Grade

 

1.      Understands the meaning of equivalent forms of expressions, equations, inequalities, and relations. The student also writes equivalent forms of equations, inequalities, and systems of equations and solves them with fluency (e.g. mentally or with paper-and-pencil in simple cases, using technology in other cases).

 

2.      Uses symbolic algebra to represent and explain mathematical relationships.

 

3.      Uses a variety of symbolic representations (e.g. equations) for functions and relations.

 

4.      Judges the meaning, utility, and reasonableness of the results of symbol manipulations; including those carried out by technology.

 

 

Standard #6

 

            The student will be able to use mathematical models to understand and represent quantitative relationships.

 

Benchmarks

 

            Level I            Pre - Kindergarten - Second Grade

 

1.      Models situations that involve the addition and subtraction of whole numbers with objects, pictures, and symbols.

 

 

 

 

            Level II           Third - Fifth Grade

 

1.      Models problem situations with objects and uses representations (e.g. graphs, tables, and equations) to draw conclusions.

 

            Level III          Sixth - Eighth Grade

 

1.      Models and solves contextualized problems using various representations (e.g. graphs, tables, equations).

 

            Level IV         Ninth - Twelfth Grade

 

1.      Identifies essential quantitative relationships in a situation and determines the class/classes of functions that might model the relationships.

 

2.      Uses symbolic expressions (e.g. iterative and recursive forms) to represent relationships arising from various contexts.

 

3.      Draws reasonable conclusions about a situation being modeled.

 

 

Standard #7

 

            The student will be able to analyze change in various contexts.

 

Benchmarks

 

            Level I            Pre - Kindergarten - Second Grade

 

1.      Describes qualitative change (e.g. a student growing taller).

 

2.      Describes quantitative change (e.g. a student growing two inches in one year).

 

            Level II           Third - Fifth Grade

 

1.      Investigates how a change in one variable relates to a change in a second variable.

 

2.      Identifies and describes situations with constant/varying rates of change and compares them.

 

            Level III          Sixth - Eighth Grade

 

1.      Uses graphs to analyze the nature of changes in quantities in linear relationships.

 

            Level IV         Ninth - Twelfth Grade

 

1.      Approximates and interprets rates of change from graphical and numerical data.

 

 

Standard #8

 

            The student will be able to analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

 

Benchmarks

 

            Level I            Pre - Kindergarten - Second Grade

 

1.      Recognizes, names, builds, draws, compares, and sorts two- and three-dimensional shapes.

 

2.      Describes attributes and parts of two- and three-dimensional shapes.

 

3.      Investigates and predicts the results of putting together and taking apart two- and three-dimensional shapes.

 

            Level II           Third - Fifth Grade

 

1.      Identifies, compares, and analyzes attributes of two- and three-dimensional shapes, developing vocabulary to describe the attributes.

 

2.      Classifies two- and three-dimensional shapes according to their properties and develops definitions of classes of shapes (e.g. triangles and pyramids).

 

3.      Investigates, describes, and reasons about the results of subdividing, combining, and transforming shapes.

 

4.      Explores congruence and similarity.

 

5.      Makes and tests conjectures about geometric properties and relationships, developing logical arguments to justify conclusions.

            Level III          Sixth - Eighth Grade

 

1.      Precisely describes, classifies, and understands relationships among types of two- and three-dimensional objects using their defining properties.

 

2.      Understands relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.

 

            Level IV         Ninth - Twelfth Grade

 

1.      Creates and critiques inductive and deductive arguments concerning geometric ideas and relationships (e.g. congruence, similarity, the Pythagorean relationship).

 

2.      Analyzes properties and determines attributes of two- and three-dimensional objects. The student also explores relationships (e.g. congruence and similarity) among classes of two- and three-dimensional geometric objects, making and testing conjectures about them, and solving problems involving them.

 

3.      Establishes the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by others.

 

4.      Uses trigonometric relationships to determine lengths and angle measures.

 

 

Standard #9

 

            The student will be able to specify locations and describe spatial relationships using coordinate geometry and other representational systems.

 

Benchmarks

 

          Level I            Pre - Kindergarten - Second Grade

 

1.      Describes, names, and interpret relative positions in space and applies ideas about relative position.

 

2.      Describes, names, and interprets direction and distance in navigating space and applies ideas about direction and distance.

 

3.      Finds and names locations with simple relationships (e.g. "near to") and in coordinate systems (e.g. maps).

 

            Level II           Third - Fifth Grade

 

1.      Describes location and movement using common language and geometric vocabulary.

 

2.      Makes and uses coordinate systems to specify locations and to describe paths.

 

3.      Finds the distance between points along horizontal and vertical lines of a coordinate system.

 

          Level III      Sixth - Eighth Grade

 

1.      Uses coordinate geometry to represent and examine the properties of geometric shapes.

 

2.      Uses coordinate geometry to examine special geometric shapes (e.g. regular polygons or those with pairs of parallel/perpendicular sides).

 

          Level IV      Ninth - Twelfth Grade

 

1.      Uses Cartesian coordinates and other coordinate systems to analyze geometric situations.

 

2.      Investigates conjectures and solves problems involving two- and three-dimensional objects represented with Cartesian coordinates.

 

 

Standard #10

 

            The student will be able to apply transformations and use symmetry to analyze mathematical situations.

 

Benchmarks

 

            Level I            Pre - Kindergarten - Second Grade

 

1.      Recognizes and applies slides, flips, and turns.

 

2.      Recognizes and creates shapes that have symmetry.

 

            Level II           Third - Fifth Grade

 

1.      Predicts and describes the results of sliding, flipping, and turning two-dimensional shapes.

 

2.      Describes a motion or a series of motions that will show that two shapes are congruent.

 

3.      Identifies and describes line and rotational symmetry in two- and three-dimensional shapes and designs.

 

            Level III          Sixth - Eighth Grade

 

1.      Describes sizes, positions, and orientations of shapes under informal transformations (e.g. flips, turns, slides, scaling).

 

2.      Examines the congruence, similarity, and line/rotational symmetry of objects using transformations.

 

            Level IV         Ninth - Twelfth Grade

 

1.      Understands and represents translations, reflections, rotations, and dilations of objects in the plane by using sketches, coordinates, and function notation.

 

2.      Uses various representations to help understand the effects of simple transformations and their compositions.

 

3.      Examines the congruence, similarity, and line/rotational symmetry of objects using transformations.

 

 

Standard #11

 

            The student will be able to use visualization, spatial reasoning, and geometric modeling to solve problems.

 

Benchmarks

 

            Level I            Pre - Kindergarten - Second Grade

 

1.      Creates mental images of geometric shapes using spatial memory and spatial visualization.

 

2.      Recognizes and represents shapes from different perspectives.

 

3.      Relates ideas in geometry to ideas in number and measurement.

 

4.      Recognizes geometric shapes and structures in the environment and specifies their location.

 

          Level II        Third - Fifth Grade

 

1.      Builds and draws geometric objects.

 

2.      Creates and describes mental images of objects, patterns, and paths.

 

3.      Identifies and builds a three-dimensional object from a two-dimensional representation of that object.

 

4.      Identifies and draws a two-dimensional representation of a three-dimensional object.

 

5.      Uses geometric models to solve problems in other areas of mathematics (e.g. number and measurement).

 

6.      Recognizes geometric ideas and relationships and applies them to other disciplines and to problems that arise in the classroom or in everyday life.

 

            Level III          Sixth - Eighth Grade

 

1.      Draws geometric objects with specified properties (e.g. side lengths, angle measures).

 

2.      Uses two-dimensional representations of three-dimensional objects to visualize and solve problems, such as those involving surface area and volume.

 

3.      Uses visual tools, such as networks, to represent and solve problems. 

 

4.      Recognizes and applies geometric ideas and relationships in areas outside the mathematics classroom (e.g. art, science, everyday life).

          Level IV         Ninth - Twelfth Grade

 

1.      Uses geometric models to represent and explain numerical and algebraic relationships.

 

2.      Draws and constructs representations of two- and three-dimensional geometric objects using a variety of tools.

 

3.      Visualizes three-dimensional objects and spaces from different perspectives and analyzes their cross sections.

 

4.      Uses vertex-edge graphs to model and solve problems.

 

5.      Uses geometric models to gain insights into, and answer questions in, other areas of mathematics. 

 

6.      Uses geometric ideas to solve problems in, and gain insights into, other disciplines and other areas of interest (e.g. art, architecture).

 

 

Standard #12

 

            The student will be able to understand measurable attributes of objects and the units, systems, and processes of measurement.

 

Benchmarks

 

            Level I            Pre - Kindergarten - Second Grade

 

1.      Recognizes the attributes of length, volume, weight, area, and time.  The student also compares and orders objects according to these attributes.

 

2.      Understands how to measure using nonstandard and standard units. 

 

3.      Selects an appropriate unit and tool for the attribute being measured.

 

            Level II           Third - Fifth Grade

 

1.      Understands attributes (e.g. length, area, weight, time, volume, size of angle) and selects the appropriate type of unit for measuring each attribute. 

 

2.      Understands the need for measuring with standard units and becomes familiar with standard units in the customary and metric systems.

 

3.      Carries out simple unit conversions (e.g. centimeters to meters) within a system of measurement.

 

4.      Understands that measurements are approximations and how differences in units affect precision.

 

5.      Explores what happens to measurements of a two-dimensional shape (e.g. perimeter, area) when the shape is changed in some way.

 

            Level III          Sixth - Eighth Grade

 

1.      Understands both metric and customary systems of measurement. 

 

2.      Understands relationships among units and converts from one unit to another within the same system. 

 

3.      Understands, selects, and uses units of appropriate size and type to measure angles, perimeter, area, surface area, and volume.

 

            Level IV         Ninth - Twelfth Grade

 

1.      Makes decisions about units and scales that are appropriate for problem situations involving measurement. 

 

 

Standard #13

 

            The student will be able to apply appropriate techniques, tools, and formulas to determine measurements.

 

Benchmarks

 

            Level I            Pre - Kindergarten - Second Grade

 

1.      Measures with multiple copies of units of the same size (e.g. paper clips laid end to end). 

 

2.      Uses repetition of a single unit to measure something larger than the unit (e.g. measuring the length of a room with a single meter stick).

 

3.      Uses tools to measure. 

 

4.      Develops common referents for measures to make comparisons and estimates.

 

            Level II           Third - Fifth Grade

 

1.      Develops strategies for estimating the perimeters, areas, and volumes of irregular shapes. 

 

2.      Selects and applies appropriate standard units and tools to measure length, area, volume, weight, time, temperature, and the size of angles.

 

3.      Selects and uses benchmarks to estimate measurements. 

 

4.      Develops, understands, and uses formulas to find the area of rectangles, related triangles, and parallelograms. 

 

5.      Develops strategies to determine the surface areas and volumes of rectangular solids.

 

            Level III          Sixth - Eighth Grade

 

1.      Uses common benchmarks to select appropriate methods for estimating measurements. 

 

2.      Select and applies techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision. 

 

3.      Develops and uses formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles, developing strategies to find the area of more-complex shapes.

 

4.      Solves problems involving scale factors, using ratio and proportion. 

 

            Level IV         Ninth - Twelfth Grade

 

1.      Analyzes precision, accuracy, and approximates error in measurement situations. 

 

2.      Understands and uses formulas for the area, surface area, and volume of geometric figures (e.g. cones, spheres, cylinders). 

 

3.      Applies informal concepts of successive approximation, upper and lower bounds, and limit in measurement situations. 

 

4.      Uses unit analysis to check measurement computations.

 

5.      Solves simple problems involving rates and derived measurements for such attributes as velocity and density

 

Standard #14

 

            The student will be able to formulate questions that can be addressed with data.  The student will also be able to collect, organize, and display relevant data to answer them.

 

Benchmarks

 

            Level I            Pre - Kindergarten - Second Grade

 

1.      Poses questions and gathers data about themselves and their surroundings. 

 

2.      Sorts and classifies objects according to their attributes and organizes data about the objects. 

 

3.      Represents data using concrete objects, pictures, and graphs.

 

            Level II           Third - Fifth Grade

 

1.      Designs investigations to address a question and consider how data-collection methods affect the nature of the data set. 

 

2.      Collects data using observations, surveys, and experiments. 

 

3.      Represents data using tables and graphs (e.g. line plots, bar graphs, line graphs).

 

4.      Recognizes the differences in representing categorical and numerical data. 

 

            Level III          Sixth - Eighth Grade

 

1.      Formulates questions, designs studies, and collects data about a characteristic shared by two populations or different characteristics within one population. 

 

2.      Selects, creates, and uses appropriate graphical representations of data (e.g. histograms, box plots, scatterplots).

 

            Level IV         Ninth - Twelfth Grade

 

1.      Understands the differences among various kinds of studies and which types of inferences can legitimately be drawn from each.

 

2.      Knows the characteristics of well-designed studies, including the role of randomization in surveys and experiments.

 

3.      Understands the meaning of measurement data, categorical data, univariate/bivariate data, and of the term variable.

 

4.      Understands histograms, parallel box plots, and scatterplots; and uses them to display data.

 

5.      Computes basic statistics and understands the distinction between a statistic and a parameter.

 

 

Standard #15

 

            The student will be able to select and use appropriate statistical methods to analyze data.

 

Benchmarks

 

            Level I            Pre - Kindergarten - Second Grade

 

1.      Describes parts of data and the set of data as a whole to determine what the data shows.

 

            Level II           Third - Fifth Grade

 

1.      Describes the shape and important features of a set of data and compares related data sets; with an emphasis on how the data are distributed. 

 

2.      Uses measures of center, focusing on the median, and understands what each does and does not indicate about the data set.

 

3.      Compares different representations of the same data and evaluates how well each representation shows important aspects of the data.

 

            Level III          Sixth - Eighth Grade

 

1.      Finds, uses, and interprets measures of center and spread, including mean and interquartile range.

 

2.      Discusses and understands the correspondence between data sets and their graphical representations, especially histograms, stem-and-leaf plots, box plots, and scatterplots.

 

            Level IV         Ninth - Twelfth Grade

 

1.      Is able to display the distribution of univariate measurement data; describing its shape, selecting, and calculating summary statistics.

 

2.      Is able to display a scatterplot for bivariate measurement data, using technological tools to describe its shape.

 

3.      Recognizes how linear transformations of univariate data affect shape, center, and spread.

 

4.      Identifies trends in bivariate data and finds functions that model the data or transform the data so that they can be modeled.

 

 

Standard #16

 

          The student will be able to develop and evaluate inferences and predictions that are based on data.

 

Benchmarks

 

            Level I            Pre - Kindergarten - Second Grade

 

1.      Discusses events related to students' experiences as likely or unlikely. 

 

            Level II           Third - Fifth Grade

 

1.      Proposes and justifies conclusions and predictions that are based on data and design studies to further investigate the conclusions or predictions.

 

            Level III          Sixth - Eighth Grade

 

1.      Uses observations about differences between two or more samples to make conjectures about their populations from which they were taken.

 

            Level IV         Ninth - Twelfth Grade

 

1.      Makes conjectures about possible relationships between two characteristics of a sample on the basis of scatterplots of the data and approximate lines of fit. 

 

2.      Uses conjectures to formulate new questions and plan new studies to answer them.

 

3.      Uses simulations to explore the variability of sample statistics from a known population and constructs sampling distributions. 

 

4.      Understands how sample statistics reflect the values of population parameters and uses sampling distributions as the basis for informal inference.

 

5.      Evaluates published reports that are based on data by examining the design of the study, the appropriateness of the data analysis, and the validity of conclusions.

 

6.      Understands how basic statistical techniques are used to monitor process characteristics in the workplace.

 

 

 

Fundamental Mathematics Department Standards

Instructional programs from prekindergarten through grade 12 should enable all students to—

 

Standard:  Problem Solving

 

 

Standard:  Reasoning and Proof

 

 

Standard:  Communication

 

 

Standard:  Connections

 

 

Standard:  Representation