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Subject: Math

Standard: Effectively uses a variety of strategies in the problem-solving process

Label Benchmark
Primary (K-2)
M1.1.1 Brainstorms possible approaches to take before starting a problem.
M1.1.2 Draws pictures to represent problems.
M1.1.3 Represents problems using physical objects.
M1.1.4 Clarifies problems using discussions with teacher or knowledgeable others.
M1.1.5 Makes rough estimates of answers to problems before doing them.
M1.1.6 Explains to others how she or he went about solving a numerical problem.
M1.1.7 Makes organized lists or tables of information necessary for solving a problem.
Upper Elementary (3-5)
M1.2.1 When appropriate, uses "guess and check" to solve problems.
M1.2.2 States problems in his or her own words to better understand them.
M1.2.3 Checks the reasonableness of results through estimation.
M1.2.4 Articulates similarities and differences between basic problem-solving strategies.
M1.2.5 Makes attempts to verify solutions or results in situations where it is warranted.
M1.2.6 Constructs physical representations for complex problems.
M1.2.7 Uses pictographs and graphic representations to model problems.
M1.2.8 Clarifies problems using discussions with peers.
M1.2.9 Understands that some ways of representing a problem are more helpful than others.
M1.2.10 Uses trial and error and the process of elimination to solve real-world problems.
M1.2.11 Writes answers in sentence form.
M1.2.12 Identifies a range of possible answers for a given problem situation.
M1.2.13 Distinguishes between pertinent and irrelevant information when solving problems.
M1.2.14 Determines appropriate computation method in problem-solving situation (e.g., pencil and paper, mental arithmetic, calculator).
Middle School (6-8)
M1.3.1 Identifies a similar problem type to solve a problem.
M1.3.2 Breaks complex problems into simpler parts.
M1.3.3 Works backwards from the solution to solve a problem.
M1.3.4 Represents real-world problems using geometric models.
M1.3.5 Identifies similarities and differences between a wide variety of problem types and problem-solving strategies.
M1.3.6 Effectively verifies solutions or results in situations where it is warranted.
M1.3.7 Understands that there is no one right way to solve mathematical problems but that different methods have different advantages and disadvantages.
M1.3.8 Follows a general model for solving real-world problems that includes making some basic assumptions about the problem; constructing a representation of the problem; choosing the appropriate operations or the correct formula or rule.
M1.3.9 Selects appropriate computational techniques in problem-solving situations (e.g., paper, pencil, mental, calculator, computer).
M1.3.10 Determines pertinent information required to solve a problem, methods for obtaining this information, and limits of acceptable solutions.
M1.3.11 Writes a number sentence to represent a problem situation.
M1.3.12 Uses proportional thinking (e.g., rates, scaling, similarity) to solve problems.
High School (9-12)
M1.4.1 Classifies problem-solving strategies or problem types by underlying general characteristics.
M1.4.2 Constructs and describes simple algorithms for solving problems that take several steps.
M1.4.3 Constructs direct mathematical proofs when solving problems.
M1.4.4 Constructs indirect proofs when solving problems.
M1.4.5 Uses mathematical induction when solving problems.
M1.4.6 Uses inductive reasoning to make conjectures and tests the conjectures using deductive reasoning to construct either a logical verification or a counterexample.
M1.4.7 Provides simple valid arguments as justification for solutions to specific problems and for algorithms constructed for various purposes.
M1.4.8 Writes an equation to represent a problem situation.

Standard: Understands and applies basic and advanced properties of the concept of numbers

Label Benchmark
Primary (K-2)
M2.1.1 Has a general understanding that a number is a symbol for how much of something there is.
M2.1.2 Uses counting to represent numbers.
M2.1.3 Uses number lines to describe relatively small, whole numbers.
M2.1.4 Orders relatively small sets of numbers.
M2.1.5 Understands that in sharing or measuring things there is sometimes a need to use numbers between whole numbers.
Upper Elementary (3-5)
M2.2.1 Understands the basic relationship of decimals to whole numbers.
M2.2.2 Understands the basic relationship of fractions to decimals and fractions to whole numbers.
M2.2.3 Understands the basic difference between odd and even numbers.
M2.2.4 Understands the basic characteristics of mixed numbers.
M2.2.5 Understands the basic meaning of place value.
M2.2.6 Uses number lines to model a variety of numbers.
M2.2.7 Renames, orders, and compares numbers.
M2.2.8 Understands that "0" can mean none of something or that it can represent a point on a scale.
M2.2.9 Understands that if "0" and "1" are located on a line, any other number can be depicted as a position on the line (concept of scale).
M2.2.10 Understands when one form of a number might be more useful than another.
M2.2.11 Identifies numbers pictured as shaded regions on two-dimensional or three-dimensional region models.
M2.2.12 Orders numbers presented in nonroutine forms (e.g., 12/6, 10, 4 2, 7 - 2).
Middle School (6-8)
M2.3.1 Understands the similarities and differences between rational numbers and irrational numbers.
M2.3.2 Understands the role of integers in the number system.
M2.3.3 Understands the relationship of prime numbers to other numbers.
M2.3.4 Understands the basic characteristics of and the relationships among fractions, ratios, proportions, decimals, and percents.
M2.3.5 Expresses numbers using scientific notation.
M2.3.6 Models numbers using two-dimensional regions.
M2.3.7 Expresses numbers like 100, 1,000 and 1,000,000 as powers of 10.
M2.3.8 Understands that the Arabic system is not the only system for representing numbers; the numeral system used by the Romans is still used for dates, clock faces, and ordering.
M2.3.9 Understands that number lines help demonstrate the subtraction of a bigger number from a smaller number and that the results are called negative numbers.
M2.3.10 Locates, identifies, and orders numbers on a number line, including fractions, decimals, and positive and negative integers.
M2.3.11 Understands the role of place value in whole numbers as compared to decimals.
M2.3.12 Models operations on a number line.
M2.3.13 Expresses percentages in a variety of equivalent forms or descriptions.
M2.3.14 Understands rate, proportionality, and percent, and the relationships among them.
High School (9-12)
M2.4.1 Understands the basic characteristics of the real-number system and its subsystems.
M2.4.2 Understands the basic characteristics of roots.
M2.4.3 Understands the basic characteristics of exponents.
M2.4.4 Models numbers using three-dimensional regions.
M2.4.5 Compares and contrasts elements of the real-number system.
M2.4.6 Demonstrates an understanding of relative magnitude by expressing and comparing very small and very large numbers in scientific notation.
M2.4.7 Recalls immediately the relations among 10, 100, 1000, 1 million, and 1 billion.
M2.4.8 Understands that numbers can be written in bases other than 10; the simplest base, 2, uses just two symbols ("0" and "1" or "on" and "off").
M2.4.9 Has a basic understanding of the concept of inequalities.

Standard: Uses basic and advanced procedures while performing the process of computation

Label Benchmark
Primary (K-2)
M3.1.1 Adds, subtracts, multiplies, and divides whole numbers with accuracy.
M3.1.2 Uses common, everyday fractions to count, order, and measure things encountered in everyday experiences.
M3.1.3 Understands that it is useful to estimate quantities without knowing them exactly.
M3.1.4 Solves real-world problems involving addition and subtraction of whole numbers.
M3.1.5 Understands common terms used with estimation (e.g., about, near, closer to, between, a little less than).
M3.1.6 Understands what is meant by an estimate.
Upper Elementary (3-5)
M3.2.1 Adds, subtracts, multiplies, and divides decimals with accuracy.
M3.2.2 Rounds whole numbers.
M3.2.3 Mentally adds and subtracts basic combinations of whole numbers with reasonable accuracy.
M3.2.4 Determines the effects of addition, subtraction, multiplication, and division on size and order of numbers.
M3.2.5 Adds, subtracts, multiplies, and divides whole numbers using a calculator.
M3.2.6 Accurately translates between decimals and commonly encountered fractions: halves, thirds, fourths, fifths, tenths, and hundredths (but not sixths, sevenths, and so on).
M3.2.7 When asked, accurately states the purpose for each step in basic calculations.
M3.2.8 Calculates what percentage one number is of another.
M3.2.9 Understands that choices must be made when determining which operation to use.
M3.2.10 Understands that results of computation must be judged in terms of their usefulness and whether they make sense in the real world.
M3.2.11 Carries out arithmetic computations involving dollars and cents.
M3.2.12 Solves real-world problems involving multiplication and division of whole numbers.
M3.2.13 Solves real-world problems involving decimals.
M3.2.14 Understands how close an estimate is required in a given problem situation.
Middle School (6-8)
M3.3.1 Adds, subtracts, multiplies, and divides mixed numbers and fractions.
M3.3.2 Rounds decimals and fractions.
M3.3.3 Mentally multiplies and divides basic combinations of whole numbers with reasonable accuracy.
M3.3.4 Uses basic estimation techniques effectively (e.g., overestimate, underestimate, range of estimations).
M3.3.5 Uses order of operations effectively.
M3.3.6 Understands the nature of and similarities and differences between multiples and factors.
M3.3.7 Uses a calculator to compare amounts proportionally.
M3.3.8 Understands that addition and subtraction are inverses of one another as are multiplication and division; one operation undoes what the other does.
M3.3.9 Understands the three basic meanings of the expression a/b (i.e., a is the number of units each of which has the size 1/b; a divided by b; and a compared to or in relationship to b).
M3.3.10 Converts fractions to decimals, percentages to fractions, fractions to percentages, percentages to decimals, decimals to percentages, common fractions and mixed numbers to decimal fractions, etc.
M3.3.11 Solves real-world problems involving fractions.
M3.3.12 Solves real-world problems involving ratios.
M3.3.13 Solves real-world problems involving proportions.
M3.3.14 Solves real-world problems involving percents.
M3.3.15 Selects and uses appropriate type of estimation (e.g., overestimate, underestimate, range of estimate) to solve real-world problems.
M3.3.16 Understands and describes the purpose of algorithms (e.g., regrouping with or without manipulatives, partial products, finding the greatest common divisor).
M3.3.17 Solves real-world problems involving decimals.
High School (9-12)
M3.4.1 Adds and subtracts algebraic expressions.
M3.4.2 Analyzes rounding errors using a calculator or computer.
M3.4.3 Identifies the source of any discrepancy between an estimate and a calculated answer.
M3.4.4 Understands that the reasonableness of the result of a computation can be estimated from the inputs and operations.
M3.4.5 Solves real-world problems involving roots and exponents.

Standard: Understands and applies basic and advanced properties of the concept of measurement

Label Benchmark
Primary (K-2)
M4.1.1 Understands the relationships between length, width, and height.
M4.1.2 Understands the basic characteristics of weight and how it is measured.
M4.1.3 Has a basic understanding of the concept of time and how it is measured.
M4.1.4 Has a basic understanding of the concept of temperature and how it is measured.
M4.1.5 Makes quantitative estimates of familiar lengths, widths, and time intervals and checks them against measurements.
M4.1.6 Compares and orders objects according to a given attribute (e.g., weight, length).
Upper Elementary (3-5)
M4.2.1 Understands the basic characteristics of area and how it is measured.
M4.2.2 Understands the basic features of mass.
M4.2.3 Makes effective use of a ruler, thermometer, and scale for making measurements.
M4.2.4 Determines whether measurements of length, area, volume, weight, or time are reasonable by referring to typical values.
M4.2.5 Uses a calculator to determine the area and volume from linear dimensions.
M4.2.6 Understands the relationships among area, volume, and weight, and between time and cost.
M4.2.7 Compares the differences between any two measurements.
M4.2.8 Understands that measurements are likely to give slightly different numbers when measured multiple times.
M4.2.9 Understands that length can be thought of as units of lengths joined together.
M4.2.10 Understands that area can be thought of as a collection of unit squares.
M4.2.11 Understands that volume can be thought of as a collection of unit cubes.
M4.2.12 Approximates the area of irregular shapes using squares, rectangles, and triangles.
M4.2.13 Understands that scale drawings can be used to represent shapes and compare locations of things very different in size.
M4.2.14 Understands the basic characteristics of circumference and how it is measured.
M4.2.15 Selects and uses appropriate units of measurement, according to type and size of unit.
M4.2.16 Estimates, calculates, and compares perimeter, area, and volume.
M4.2.17 Selects appropriate methods of measurement (i.e., direct or indirect).
Middle School (6-8)
M4.3.1 Has a basic understanding of the concept of rate and how it is measured.
M4.3.2 Understands the basic characteristics of perimeter and how perimeter is measured.
M4.3.3 Makes effective use of a meter stick for making measurements.
M4.3.4 Converts from one measurement to another within the same system, i.e., customary or metric (e.g., feet to miles, minutes to hours).
M4.3.5 Determines significant digits in measurement.
M4.3.6 Determines the level of accuracy needed in measurement situations.
M4.3.7 Identifies and uses appropriate measuring tools for a variety of situations.
M4.3.8 Calculates the volumes and surface areas of rectangular solids, cylinders, cones, pyramids, prisms, and combined forms.
M4.3.9 Estimates distances and travel times from maps and the actual size of objects from scale drawings.
M4.3.10 Expresses answers using appropriate units of measurement (e.g., seconds, square inches, dollars per tankful)
M4.3.11 Reads analog and digital meters on instruments used to make direct measurements of length, volume, weight, elapsed time, rates and temperature, and chooses appropriate units for reporting various magnitudes.
M4.3.12 Uses measuring devices to determine an object's weight, length, width, or volume in metric units.
M4.3.13 Performs basic conversions between standard and metric involving weight, distance, and volume.
M4.3.14 Calculates the perimeter and area of rectangles.
M4.3.15 Calculates the perimeter and area of triangles.
M4.3.16 Calculates the circumference and area of circles.
M4.3.17 Solves real-world problems involving weight, distance, and volume.
M4.3.18 Applies given measurement formulas for perimeter, area, volume, and surface area in problem situations.
M4.3.19 Solves problems involving units of measurement and converts answers to a larger or smaller unit.
M4.3.20 Applies absolute and relative error in problem situations involving area, volume, and surface area.
M4.3.21 Given the dimensions of a shape, creates a scale drawing of the shape.
M4.3.22 Understands that the scale chosen for a graph or drawing makes a big difference in how useful it is.
High School (9-12)
M4.4.1 Understands the basic characteristics of the concept of capacity and how it is measured.
M4.4.2 Has a basic understanding of the concept of velocity and how it is measured.
M4.4.3 Has a basic understanding of the concept of acceleration and how it is measured.
M4.4.4 Determines precision and accuracy of measurements.
M4.4.5 Analyzes absolute and relative errors in measurement.
M4.4.6 Estimates the effects of measurement errors on calculations.
M4.4.7 Understands that a small error in making a measurement can lead to a large error in the result (propagation of errors).
M4.4.8 Understands that scale drawings can help one measure distances and angles that are inconvenient to measure directly.
M4.4.9 Understands the concept of rate and uses it in measurement situations.

Standard: Understands and applies basic and advanced properties of the concepts of geometry

Label Benchmark
Primary (K-2)
M5.1.1 Understands the basic properties of and similarities and differences between circles, squares, and triangles.
M5.1.2 Understands the meaning of the concepts inside, outside, between.
M5.1.3 Understands that shapes such as circles, squares, and triangles can be found in nature and in things that people make, and that these shapes can be used to describe many things.
M5.1.4 Understands that patterns can be made by putting different shapes together or taking them apart.
M5.1.5 Understands that things can move along straight, curved, circular, back-and-forth, and jagged paths.
Upper Elementary (3-5)
M5.2.1 Understands the basic characteristics of the concept of three dimensions.
M5.2.2 Understands the basic characteristics of angles.
M5.2.3 Predicts and verifies the effects of combining, subdividing, and changing basic shapes.
M5.2.4 Compares shapes in terms of such concepts as parallel, perpendicular, congruence, and symmetry.
M5.2.5 Uses motion geometry (e.g., turns, flips, slides) to investigate concepts of symmetry, similarity, and congruence.
Middle School (6-8)
M5.3.1 Understands the basic characteristics of the concept of symmetry.
M5.3.2 Understands the basic characteristics of and the relationship between distance and midpoint.
M5.3.3 Understands the basic characteristics of slope.
M5.3.4 Compares the basic characteristics of and the similarities and differences between a variety of three-dimensional shapes (e.g., pyramids and prisms, cubes and rectangular prisms).
M5.3.5 Predicts and verifies results of combining, subdividing, and changing basic shapes.
M5.3.6 Analyzes effects of basic transformations on geometric shapes.
M5.3.7 Uses the intersection of two-dimensional figures (e.g., lines, triangles, squares) to derive geometric definitions such as parallel, perpendicular, Pythagorean theorem, and midpoint.
M5.3.8 Visualizes geometric figures in various rotations.
M5.3.9 Determines ratios of measures in similar figures using properties of similarity.
M5.3.10 Understands that round shapes give the least possible boundary for a given amount of interior area.
M5.3.11 Represents problem situations with geometric models.
M5.3.12 Understands that shapes on a sphere cannot be depicted on a flat surface without some distortion.
M5.3.13 Understands that a point can be located on a map given two perpendicular distances from the point, or given an angle and a distance from the point.
M5.3.14 Solves real-world problems involving area of geometric figures.
M5.3.15 Understands the basic properties of and the similarities and differences between a trapezoid, rhombus, and quadrilateral.
High School (9-12)
M5.4.1 Understands the relationship between parallel, perpendicular, and oblique lines.
M5.4.2 Understands the basic characteristics of Pythagorean relationships.
M5.4.3 Performs synthetic transformations (e.g., translations, rotations, reflections, dilations) of basic shapes.
M5.4.4 Understands basic characteristics of vectors.
M5.4.5 Analyzes the intersection of three-dimensional figures with a plane.
M5.4.6 Classifies figures based on congruence and similarity.
M5.4.7 Describes spatial relationships in geometric terms (e.g., perpendicular, parallel, tangent, similar, congruent, symmetrical)Solves real-world problems involving vectors.
M5.4.8 Solves real-world problems involving the Pythagorean relationship.
M5.4.9 Performs algebraic transformations (e.g., translations, rotations, reflections, dilations) of geometric shapes.
M5.4.10 Constructs the image of a geometric figure under a given transformation (e.g., subdividing, dilating) and determines the relationship of the areas and perimeters of the two figures.
M5.4.11 Solves problems involving the Pythagorean theorem.
M5.4.12 Uses geometric models, diagrams, and graphs to solve real-world problems.
M5.4.13 Uses coordinates and vectors to represent geometric figures and properties algebraically.
M5.4.14 Uses properties of lines (e.g., distance, mid-point, slope, parallelism, perpendicularity) to describe figures algebraically.
M5.4.15 Knows the characteristics and properties of conic sections.
M5.4.16 Uses vectors and simple operations on vectors (e.g., addition, subtraction, scalar multiplication, dot product) to solve real-world problems.
M5.4.17 Understands that when the size of a linear shape changes by some factor, its area and volume change disproportionately: area changes in proportion to the square of the factor, and volume changes in proportion to the cube of the factor.
M5.4.18 Understands that different ways to map a curved surface onto a flat surface have different advantages and disadvantages.
M5.4.19 Understands the relationship between surface area and volume for rectangular solids.

Standard: Understands and applies basic and advanced concepts of data analysis and distributions

Label Benchmark
Primary (K-2)
M6.1.1 Understands that observations about objects or events can be organized and displayed in simple graphs.
Upper Elementary (3-5)
M6.2.1 Understands that data represents specific pieces of information about real-world objects or activities.
M6.2.2 Collects and organizes simple data sets to answer questions.
M6.2.3 Understands that tables and graphs can show how the values of one quantity are related to the values of another and that tables and graphs can make it easier to identify patterns.
M6.2.4 Understands that spreading data out on a number line helps to see what the extremes are, where the data points pile up, and where the gaps are.
M6.2.5 Understands that a summary of data should include where the middle is and how much spread there is around it.
M6.2.6 Constructs and interprets simple bar graphs, pie charts, and line graphs.
M6.2.7 Given a table of data, selects the correct graphic representation for the data.
M6.2.8 Understands that data comes in many different forms and that collecting, organizing, and displaying data can be done in many ways.
Middle School (6-8)
M6.3.1 Understands basic characteristics of and calculates measures of central tendency (i.e., mean, median, mode).
M6.3.2 Understands similarities and differences between tables, bar graphs, and circle graphs.
M6.3.3 Identifies basic trends in tables and graphs including varying rates of change, gaps, and clusters, and uses these trends to make predictions about the phenomena being graphed.
M6.3.4 Understands that comparison of data from two groups involves comparing their middles and the spreads around them (i.e., dispersion of data).
M6.3.5 Interpolates or extrapolates from data presented in various forms.
M6.3.6 Constructs, reads, and interprets data in charts, tables, plots (e.g., stem-and-leaf, box-and-whiskers, scatter), and graphs (e.g., bar, circle, line).
High School (9-12)
M6.4.1 Understands the basic features of data sets (matrices).
M6.4.2 Understands the basic measures of dispersion (i.e., standard deviation, variance).
M6.4.3 Understands the basic features of outliers and procedures to deal with them.
M6.4.4 Represents data using stem-and-leaf plots and scatter plots.
M6.4.5 Understands that the same set of data can be represented using a variety of tables, graphs, and symbols and that different modes of representation often convey different messages.
M6.4.6 Understands that the middle of a distribution may be misleading under certain circumstances (e.g., when data are not distributed symmetrically, when extreme high or low values exist, when the distribution is not reasonably smooth).
M6.4.7 Calculates measures of central tendency (i.e., mean, median, mode) for complex sets of data and analyzes the relative merits of those measures for the various data sets.
M6.4.8 Solves real-world problems involving data matrices.
M6.4.9 Understands basic generalizations about the nature of graphs: the position of any point on a surface can be described by two numbers; a graph represents all the values that satisfy an equation.

Standard: Understands and applies basic and advanced concepts of probability and statistics

Label Benchmark
Primary (K-2)
M7.1.1 Understands that some events are more likely to happen than others.
M7.1.2 Understands that some events can be predicted fairly well but others cannot because we do not always know everything that may affect an event.
M7.1.3 Understands that one can find out about a group of things by studying just a few of them.
Upper Elementary (3-5)
M7.2.1 Understands that the word "chance" refers to the likelihood of an event.
M7.2.2 Understands that when predictions are based on what is known about the past, one must assume that conditions stay the same from the past event to the predicted future event.
M7.2.3 Understands that statistical predictions are better for describing what proportion of a group will experience something (e.g., what proportion of automobiles will be involved in accidents).
M7.2.4 Understands that summary predictions about large collections of events are usually more accurate than summary predictions about just a few events.
M7.2.5 Understands that even unlikely events may occur fairly often in very large populations.
M7.2.6 Understands that a small part of something may have unique characteristics but not be an accurate representation of the whole, and that how useful a sample is depends on how it is chosen.
M7.2.7 Understands that when choosing a sample, one must guard against choosing only the data that show what is expected.
M7.2.8 Given a sample space for an experiment involving different outcomes, identifies the probabilities associated with each outcome.
Middle School (6-8)
M7.3.1 Understands the basic features of a sample and sampling error.
M7.3.2 Designs a simulation to estimate the probability for given event.
M7.3.3 Identifies common errors in the presentation of statistics.
M7.3.4 Estimates probabilities of events in familiar situations using data from the past or by making rough calculations.
M7.3.5 Understands that how probability is estimated depends on what is known about the situation.
M7.3.6 Understands that estimates of probability can be based on data from similar situations in the past or on the assumption that all possible situations and events are known.
M7.3.7 Understands that data from the past may no longer be applicable to a current problem.
M7.3.8 Understands that probabilities are ratios that can be expressed as fractions, percentages, or odds.
M7.3.9 Understands that the larger a well-chosen sample is, the more likely it is to represent the whole, and that many ways of choosing a sample can make it unrepresentative of the whole.
M7.3.10 Understands that events can be described in terms of being more or less likely, impossible, or certain.
M7.3.11 Understands procedures for selecting an unbiased sample.
M7.3.12 Understands the relationship between the numerical expression of a probability and the events that produce these numbers (e.g., 3/5 as it relates to the probability of pulling a green chip from a hat).
High School (9-12)
M7.4.1 Has a basic understanding of the concept of random variables.
M7.4.2 Understands the similarities and differences between joint and conditional probability.
M7.4.3 Understands the concept of independent and dependent events.
M7.4.4 Understands the basic features of a statistic.
M7.4.5 Determines probabilities using counting procedures, tables, trees, area models, and formulas for permutations and combinations.
M7.4.6 Compares experimental results with mathematical expectations of probabilities.
M7.4.7 Compares data for two groups by representing their averages and spreads graphically.
M7.4.8 Understands that when estimating a statistic, one should also estimate how far off he or she may be (estimates expected error).
M7.4.9 Understands that the larger and more well-chosen a sample of a population is, the better it estimates the population summary statistics.
M7.4.10 Understands that a physical or mathematical model can be used to estimate the probability of real-world events.
M7.4.11 Understands that when comparing percentages and proportions, one must also consider the number of cases on which those percentages are based.
M7.4.12 Designs and carries out statistical experiments.
M7.4.13 Solves real-world problems involving conditional probability and joint probability.
M7.4.14 Understands the concepts of independent and dependent events and their relationship to compound events and conditional probability
M7.4.15 Determines probability for given independent events.
M7.4.16 Determines probability for given dependent events.
M7.4.17 Uses the properties of the normal curve to answer questions about sets of data that are assumed to be normally distributed.

Standard: Understands and applies basic and advanced properties of functions and algebra

Label Benchmark
Primary (K-2)
M8.1.1 Recognizes basic number patterns.
Upper Elementary (3-5)
M8.2.1 Interpolates simple patterns of numbers.
M8.2.2 Extrapolates simple patterns of numbers and geometric shapes.
M8.2.3 Understands that at a very basic level, mathematics is the study of many kinds of patterns, including numbers and shapes, and operations applied to them.
M8.2.4 Uses patterns and relationships to represent mathematical situations.
M8.2.5 Given general constraints, constructs a pattern and articulates why the pattern works (or, "the rule of the pattern").
Middle School (6-8)
M8.3.1 Understands that an algebraic expression contains a variable which is a symbol representing an unknown quantity.
M8.3.2 Understands the basic features of coordinates.
M8.3.3 Has a basic understanding of the concept of equation.
M8.3.4 Understands that a variable can be used as a placeholder for a specific unknown (e.g., x + 8 = 13), and as a representative of a range of values (e.g., 4t + 7).
M8.3.5 Understands that mathematical statements can be used to describe functional relationships for which one quantity changes when another changes.
M8.3.6 Computes rates of change from magnitudes and magnitudes from rates of change.
M8.3.7 Understands the common relationships that can exist between two variables and the various ways these relationships will look on a graph.
M8.3.8 Cross-tabulates the occurrence of variables and makes a general determination whether they co-vary.
M8.3.9 Uses substitution within given formulas and expressions with real-world problems.
M8.3.10 Solves real-world problems involving rectangular coordinates.
M8.3.11 Solves real-world problems involving formulas with one variable.
M8.3.12 Simplifies algebraic expressions involving numbers and variables.
M8.3.13 Solves simple systems of equations graphically.
High School (9-12)
M8.4.1 Uses appropriate terminology and notation to define functions and their properties, including domain, range, function composition, and inverses.
M8.4.2 Understands the characteristics and uses of basic trigonometric functions.
M8.4.3 Investigates the effects of parameter changes on the graphs of functions.
M8.4.4 Has a basic understanding of polynomial equations.
M8.4.5 Has a basic understanding of polar coordinates.
M8.4.6 Determines the maximum and minimum points on a graph.
M8.4.7 Fits a line or curve to a set of data and uses this line or curve to make predictions.
M8.4.8 Compares and applies the numerical, symbolic, and graphical properties of a variety of functions.
M8.4.9 Solves systems of equations and inequalities graphically, algebraically, and using matrices.
M8.4.10 Uses a variety of algebraic and graphical methods to solve polynomial equations with real and complex roots.
M8.4.11 Understands functional relationships for which the rate of change of one variable is dependent on how much there is of another variable (e.g., the rate of change of speed is proportional to the amount of force acting on it).
M8.4.12 Understands that symbolic statements in mathematics can be manipulated by rules of mathematical logic to produce other statements that preserve the basic relationships but are more easily interpreted.
M8.4.13 Understands that symbolic statements can be combined to look for values of variables that will satisfy all of them at the same time.
M8.4.14 Understands that any graphic or algebraic mathematical model is limited in how well it represents the world by uncertainties in measurement, neglect of some important influences, or by requiring too much computation.
M8.4.15 Understands that when a relationship between variables is represented in symbols, numbers can be substituted for all but one of the symbols and the possible value of the remaining symbol computed.
M8.4.16 Understands that mathematical modeling is a tool that can be used to simulate how a proposed system might behave.
M8.4.17 Understands that mathematical modeling aids in technological design by simulating how a proposed system would theoretically behave.
M8.4.18 Understands that the basic process of creating a mathematical model involves the following components: (1) abstractions; (2) manipulating abstractions; (3) checking results; and (4) creating a new model if necessary.
M8.4.19 Understands that it may not be easy to determine which mathematical model to use to describe data even when plenty of data is available, and that the mathematical model one chooses may require more computing power than is available.
M8.4.20 Understands that determining the correlation between two variables involves inspecting their distributions using two-way tables or scatter plots; a correlation between two variables does not mean that one variable causes another.
M8.4.21 Uses the technique of spatial sampling to determine the extent to which two variables have a relationship.
M8.4.22 Constructs scatter plots for data representing two variables and makes a qualitative analysis of the relationship between the two variables.
M8.4.23 Identifies and analyzes linear and nonlinear patterns in data using line graphs.
M8.4.24 Constructs linear mathematical models for real-world phenomena.
M8.4.25 Constructs nonlinear mathematical models for real-world phenomena.
M8.4.26 Understands the formal differences between the terms "correlates with" and "causes".
M8.4.27 Solves real-world problems involving linear programming.
M8.4.28 Represents real-world problems using algebraic functions and graphs of those functions.
M8.4.29 Solves real-world problems involving polar coordinates.
M8.4.30 Approximates solutions of equations (e.g., bisection, sign changes, successive approximations).

Standard: Understands the general nature and uses of mathematics

Label Benchmark
Primary (K-2)
M9.1.1 Not appropriate for this level
Upper Elementary (3-5)
M9.2.1 Understands that numbers and the operations performed on them can be used to describe things in the real world and predict what might occur.
M9.2.2 Understands that mathematical ideas and concepts can be represented concretely, graphically, and symbolically.
Middle School (6-8)
M9.3.1 Understands that mathematics has been helpful in practical ways for many centuries.
M9.3.2 Understands that mathematicians often represent real things using abstract ideas like numbers or lines; they then work with these abstractions to learn about the things they represent.
High School (9-12)
M9.4.1 Understands that mathematics is the study of any pattern or relationship, but natural science is the study of those patterns that are relevant to the observable world.
M9.4.2 Understands that mathematics began long ago to help solve practical problems; however, it soon focused on abstractions drawn from the world and then on abstract relationships among those abstractions.
M9.4.3 Understands that in mathematics, as in other sciences, simplicity is one of the highest values; some mathematicians try to identify the smallest set of rules from which many other propositions can be logically derived.
M9.4.4 Understands that theories in mathematics are greatly influenced by practical issues; real-world problems sometimes result in new mathematical theories and pure mathematical theories sometimes have highly practical applications.
M9.4.5 Understands that new mathematics continues to be invented even today, along with new connections between various components of mathematics.
M9.4.6 Understands that science and mathematics operate under common principles: belief in order, ideals of honesty and openness, the importance of review by colleagues, and the importance of imagination.
M9.4.7 Understands that mathematics provides a precise system to describe objects, events, and relationships and to construct logical arguments.
M9.4.8 Understands that the development of computers has opened many new doors to mathematics just as other advances in technology can open up new areas to mathematics.
M9.4.9 Understands that mathematics often stimulates innovations in science and technology.
M9.4.10 Understands that mathematicians commonly operate by choosing an interesting set of rules and then playing according to those rules; the only limit to those rules is that they should not contradict each other.

Subject: Science

Standard: Understands basic features of the Earth

Label Benchmark
Primary (K-2)
S1.1.1 Knows that Earth materials consist of solid rocks and soils, liquid water and the gases of the atmosphere.
S1.1.2 Knows that water can be a liquid (e.g., rain) or a solid (ice) and can be made to go back and forth from one form to the other, but the amount of water stays the same.
S1.1.3 Knows that weather changes some from day to day, but things like temperature and rain (or snow) tend to be high, low or medium in the same months every year (weather vs. climate).
Upper Elementary (3-5)
S1.2.1 Knows that when liquid water disappears, it turns into gas (vapor) in the air and can reappear as a liquid when cooled.
S1.2.2 Knows the major differences between fresh and ocean waters.
S1.2.3 Knows that clouds, like fog and steam from a kettle, are made of tiny droplets of water.
S1.2.4 Knows that air is a substance that surrounds us, takes up space and whose movement we feel as wind.
S1.2.5 Knows that the rotation of the Earth on its axis every 24 hours produces the night and day cycle.
S1.2.6 Knows that the Sun provides the light and heat necessary to maintain the temperature of the Earth.
Middle School (6-8)
S1.3.1 Knows that the Earth is the only body in our solar system that appears able to support life.
S1.3.2 Knows that the solid Earth is layered with a thin brittle crust, hot convecting mantle and dense metallic core; three-fourths of the Earth's surface is covered by a thin layer of water; and the entire planet is surrounded by a blanket of air.
S1.3.3 Knows the composition and structure of the Earth's atmosphere.
S1.3.4 Knows that clouds, which are formed by the condensation of water vapor, affect weather and climate; some do so by reflecting much of the sunlight that reaches Earth from the Sun; others hold heat energy emitted from the Earth's surface.
S1.3.5 Knows that because of the tilt of the Earth's axis, sunlight and, hence, heat fall more intensely on one part or another of the Earth during its one-year revolution around the Sun; the difference in heating of the Earth's surface produces the planet's seasons and weather patterns.
S1.3.6 Knows that the Earth's climate sometimes changes radically in response to the effects of geological shifts (e.g., the advance or retreat of glaciers over centuries, a series of huge volcanic eruptions in a short time).
S1.3.7 Knows that even relatively small changes of atmospheric content or ocean temperature can have widespread effects on climate if the change lasts long enough.
S1.3.8 Knows that the cycling of water in and out of the atmosphere plays an important role in determining climatic patterns: water evaporates from the surface of the Earth, rises and cools, condenses into rain or snow and falls to the surface where it forms rivers and lakes and collects in porous layers of rock.
S1.3.9 Knows that water is a solvent; as it passes through the water cycle it dissolves minerals and gases and carries them to the oceans.
S1.3.10 Knows that the Sun is the major source of energy for phenomena on the Earth's surface, such as winds, ocean currents, the water cycle and the growth of plants.
High School (9-12)
S1.4.1 Knows that Earth systems have both internal and external sources of energy, both of which create heat; although the Sun is the major external source of energy, the decay of radioactive isotopes and gravitational energy from the Earth's original formation are primary sources of internal heat.
S1.4.2 Knows that weather (in the short run) and climate (in the long run) involve the transfer of energy in and out of the atmosphere.
S1.4.3 Knows that solar radiation heats the land masses, oceans and air, and that transfer of heat energy at the boundaries (between the atmosphere, the land masses and the oceans) results in layers at different temperatures and densities in both the ocean and atmosphere; the action of gravitational force on layers of different densities causes them to rise or fall, and such circulation (influenced by the rotation of the Earth) produces winds and ocean currents.
S1.4.4 Knows how life is adapted to conditions on the Earth, including the force of gravity that enables the planet to retain an adequate atmosphere and the intensity of radiation from the Sun that allows water to cycle between liquid and vapor.

Standard: Understands basic concepts about the structure and properties of matter

Label Benchmark
Primary (K-2)
S10.1.1 Knows that objects can be described and classified by their composition (wood, metal) and their physical properties (color, size, shape).
S10.1.2 Knows that things can be done to materials to change some of their properties, but not all materials respond the same way to what is done to them.
Upper Elementary (3-5)
S10.2.1 Knows that things have properties (e.g., magnetism, conductivity, density, solubility) that can be used to tell them apart and to find out which of them are alike.
S10.2.2 Knows that materials may be composed of parts that are too small to be seen without magnification.
S10.2.3 Knows how an object's properties can be measured using tools such as rulers, balances and thermometers.
S10.2.4 Knows that materials have different states (solid, liquid, gas), and some common materials such as water can be changed from one state to another by heating or cooling.
S10.2.5 Knows that the mass of a material is conserved whether it is together, in parts or in a different state.
Middle School (6-8)
S10.3.1 Knows that there are more than 100 known elements that combine in a multitude of ways to produce compounds, which account for the living and nonliving substances that we encounter; chemical elements do not break down by normal laboratory reactions such as heating, electric current or reaction with acids.
S10.3.2 Knows that many elements can be grouped according to similar properties, such as highly reactive metals, less-reactive metals, highly reactive nonmetals (chlorine, fluorine, oxygen) and some almost completely nonreactive gases (helium, neon); some elements, such as carbon and hydrogen, do not fit into any of the categories.
S10.3.3 Knows methods used to separate mixtures into their component parts (boiling, filtering, chromatography, screening).
S10.3.4 Knows that different arrangements of atoms into groups compose all substances; atoms are far too small to see directly through a microscope.
S10.3.5 Knows that atoms in solids are close together and don't move about easily; in liquids, atoms are close together and stick to each other, but move about easily; atoms in gas are quite far apart and move about freely.
S10.3.6 Knows that atoms often combine to form a molecule (or crystal), the smallest particle of a substance that retains its properties.
S10.3.7 Understands that no matter how substances within a closed system interact with one another, or how they combine or break apart, the total weight of the system remains the same; the same number of atoms weighs the same, no matter how the atoms are arranged.
S10.3.8 Knows that the temperature and acidity of a solution influence reaction rates; many substances dissolve in water, which may greatly facilitate reactions between them.
S10.3.9 Knows that oxidation involves the combining of oxygen with something else as in burning or rusting.
S10.3.10 Knows that substances react chemically in characteristic ways with other substances to form new substances (compounds) with different characteristic properties; however, in chemical reactions the total mass is conserved.
High School (9-12)
S10.4.1 Knows that an element is composed of a single type of atom; when elements are listed in order according to the number of protons (called the atomic number), repeating patterns of physical and chemical properties identify families of elements with similar properties (as seen in the periodic table).
S10.4.2 Knows that atoms interact with one another by transferring or sharing electrons that are furthest from the nucleus; these outer electrons govern the chemical properties of the element.
S10.4.3 Knows that atoms may be bonded together into molecules or crystalline solids; when two or more kinds of atoms bind together chemically, a compound is formed.
S10.4.4 Knows that the properties of a compound reflect the nature of the interactions among its molecules, which are determined by the structure of the molecule (the kinds of atoms and the distances and angles between them).
S10.4.5 Knows that atoms consist of negative electrons, which occupy most of the space in the atom, and very tiny nuclei consisting of neutrons and positive protons, each almost two thousand times heavier than an electron; the electric force between the nucleus and electrons holds the atom together.
S10.4.6 Knows that usually the number of electrons will equal the number of protons, and the neutron has no electric charge, so the atom, overall, is electrically neutral; but an atom may acquire an unbalanced charge by gaining or losing electrons.
S10.4.7 Knows that when an element has atoms that differ in the number of neutrons, these atoms are called different isotopes of the element; although neutrons have little effect on how an atom interacts with others, they do affect the mass and stability of the nucleus.
S10.4.8 Knows that scientists continue to investigate atoms and have discovered even smaller constituents of which electrons, neutrons and protons are made.
S10.4.9 Knows that radioactive isotopes are unstable and undergo spontaneous nuclear reactions, emitting particles and/or wavelike radiation; the decay of any one nucleus cannot be predicted, but a large group of identical nuclei decay at a predictable rate, andthis predictability can be used to estimate the age of materials that contain radioactive isotopes.
S10.4.10 Knows that chemical reactions can take place in time periods ranging from the few femtoseconds required for an atom to move a fraction of a chemical bond distance to geologic time scales; reaction rates depend on how often the reacting atoms and molecules encounter one another, the temperature and the properties (including shape) of the reacting species.
S10.4.11 Knows that catalysts, such as metal surfaces, accelerate chemical reactions; chemical reactions in living systems are often catalyzed by protein molecules called enzymes.
S10.4.12 Knows that carbon atoms can bond to one another in chains, rings and branching networks to form a variety of structures, including synthetic polymers, oils and the large molecules essential to life; complex chemical reactions involving carbon-based molecules take place constantly in every cell in our bodies.
S10.4.13 Knows that a large number of important reactions involve the transfer of either electrons (oxidation/reduction reactions) or hydrogen ions (acid/base reactions) between reacting ions, molecules or atoms; in other reactions, chemical bonds are broken by heat or light to form very reactive radicals with electrons ready to form new bonds.
S10.4.14 Knows that radical reactions control many processes such as the ozone and green house gases in the atmosphere, burning and processing of fossil fuels, formation of polymers and explosions.

Standard: Understands energy types, sources and conversions, and their relationship to heat and temperature

Label Benchmark
Primary (K-2)
S11.1.1 Knows that the Sun applies heat and light to Earth.
S11.1.2 Knows that heat can be produced in many ways (e.g., burning, rubbing, mixing chemicals).
S11.1.3 Knows that electricity in circuits can produce light, heat, sound and magnetic effects.
Upper Elementary (3-5)
S11.2.1 Knows that things that give off light often also give off heat.
S11.2.2 Knows that mechanical and electrical machines give off heat.
S11.2.3 Knows that heat can move from one object to another by conduction.
S11.2.4 Knows that some materials conduct heat better than others; materials that do not conduct heat well can reduce heat loss.
S11.2.5 Knows that electrical circuits require a complete loop through which the electrical current can pass.
Middle School (6-8)
S11.3.1 Knows that energy comes in different forms, such as light, heat, chemical, nuclear, mechanical and electrical.
S11.3.2 Understands that energy cannot be created or destroyed but only changed from one form to another.
S11.3.3 Knows that the Sun is a major source of energy for changes on the Earth's surface; the Sun's energy arrives as light with a range of wavelengths consisting mainly of visible light with significant amounts of infrared and ultraviolet radiation.
S11.3.4 Knows that heat energy moves in predictable ways, flowing from warmer objects to cooler ones until both objects are at the same temperature.
S11.3.5 Knows that heat can be transferred through materials by the collisions of atoms or across space by radiation; if the material is fluid, currents will be set up in it that aid the transfer of heat.
S11.3.6 Knows that electrical circuits provide a means of converting electrical energy into heat, light, sound, chemical or other forms of energy.
S11.3.7 Knows that in most chemical reactions energy is released or added to the system in the form of heat, light, electrical or mechanical energy.
High School (9-12)
S11.4.1 Knows that although energy can be transferred by collisions or waves and converted from one form to another, it can never be created or destroyed, so the total energy of the universe is constant.
S11.4.2 Knows that all energy can be considered to be either kinetic energy (energy of motion), potential energy (depends on relative position) or energy contained by a field (electromagnetic waves).
S11.4.3 Knows that heat energy consists of random motion and the vibrations of atoms, molecules and ions; the higher the temperature, the greater the atomic or molecular motion.
S11.4.4 Knows that energy tends to move spontaneously from hotter to cooler objects by conduction, convection or radiation; similarly, any ordered state tends to spontaneously become less ordered over time.
S11.4.5 Knows that the energy of waves (electromagnetic and material) can be changed into other forms of energy (e.g., chemical and electrical), just as other forms of energy (chemical and nuclear) can be transformed into wave energy.
S11.4.6 Knows that some changes of atomic or molecular configuration require an input of energy, whereas others release energy.
S11.4.7 Knows that each kind of atom or molecule can gain or lose energy only in particular discrete amounts and thus can absorb and emit light only at wavelengths corresponding to these amounts; these wavelengths can be used to identify the substance.
S11.4.8 Knows that fission is the splitting of a large nucleus into smaller pieces, and fusion is the joining of two nuclei at extremely high temperature and pressure; nuclear reactions convert a fraction of the mass of interacting particles into energy.

Standard: Understands motion and the principles that explain it

Label Benchmark
Primary (K-2)
S12.1.1 Knows that vibrating objects produce sound.
S12.1.2 Knows that light travels in a straight line unless it strikes an object.
S12.1.3 Knows that the position of an object can be described by locating it relative to another object or the background.
S12.1.4 Knows that the varieties of motion include straight line, zigzag, vibrational or circular.
S12.1.5 Knows that an object's motion can be changed by a push or a pull by people or by other objects.
Upper Elementary (3-5)
S12.2.1 Knows that properties of sound such as pitch and loudness can be altered by changing the properties of the sound's source (e.g., by changing the rate of vibration).
S12.2.2 Knows that light can be reflected by a mirror, refracted by a lens or absorbed by the object.
S12.2.3 Knows that an object's motion can be described by indicating the change in its position over time.
S12.2.4 Knows that when a force is applied to an object, the object either speeds up, slows down or goes in a different direction.
S12.2.5 Knows that the greater the force that is applied to an object, the greater the change in motion the object will have; the more massive the object is, the smaller the effect a given force will have.
Middle School (6-8)
S12.3.1 Knows that vibrations (e.g., sounds, earthquakes) move at different speeds in materials, have different wavelengths and set up wave-like disturbances that spread away from the source.
S12.3.2 Knows that light interacts with matter by transmission (including refraction), absorption or scattering (including reflection); to see an object, light from that object (emitted by or scattered from it) must enter the eye.
S12.3.3 Knows that only a narrow range of wavelengths of electromagnetic radiation can be seen by the human eye; differences of wavelength within that range of visible light are perceived as differences in color.
S12.3.4 Knows that an object's motion can be described and represented graphically according to its position, direction of motion and speed.
S12.3.5 Knows that the motion of an object is always judged with respect to some other object or point, and so the idea of absolute motion or rest is misleading.
S12.3.6 Knows that whenever an object is seen to speed up, slow down or change direction, we know that an unbalanced force (e.g., friction) acts on it.
S12.3.7 Knows that if more than one force acts on an object, then the forces can reinforce or cancel one another, depending on their direction and magnitude; unbalanced forces will cause changes in the speed and/or direction of an object's motion.
S12.3.8 Knows that an object that is not being subjected to a force will continue to move at a constant speed and in a straight line.
High School (9-12)
S12.4.1 Knows that waves, including sound and seismic waves, waves on water and light waves, carry energy and can interact with matter.
S12.4.2 Knows that electromagnetic waves include radio waves (the longest wavelength), microwaves, infrared radiation (radiant heat), visible light, ultraviolet radiation, x-rays and gamma rays; electromagnetic waves result when a charged object is accelerated ordecelerated; and each wavelength of light delivers energy in packets whose sizes are inversely proportional to the wavelength.
S12.4.3 Knows that apparent changes in wavelength can provide information about changes in motion because the observed wavelength of a wave depends upon the relative motion of the source and the observer; if either the source or observer is moving toward the other, the observed wavelength is shorter; if either is moving away, the wavelength is longer.
S12.4.4 Knows that the theory of special relativity suggests that in contrast to other moving things, the speed of light is the same for all observers, no matter how they or the light source happen to be moving, and that nothing can travel faster than the speed of light.
S12.4.5 Knows that because the light we see from almost all distant galaxies has longer wavelengths than the same light here on Earth, astronomers believe that the whole universe is expanding.
S12.4.6 Knows that objects change their motion only when a net force is applied; whenever one object exerts force on another, an equal amount of force is exerted back on the first object.
S12.4.7 Knows that laws of motion are used to calculate precisely the effects of forces on the motion of objects; the magnitude of the change in motion can be calculated using the relationship F=ma.

Standard: Knows the kinds of forces that exist between objects and within atoms

Label Benchmark
Primary (K-2)
S13.1.1 Knows that magnets can be used to make some things move without being touched.
S13.1.2 Knows that things near the Earth fall to the ground unless something holds them up.
Upper Elementary (3-5)
S13.2.1 Knows that material that has been electrically charged pulls on all other materials and can attract or repel other charged materials.
S13.2.2 Knows that magnets attract and repel each other and certain kinds of metals.
S13.2.3 Knows that the Earth's gravity pulls any object toward it without touching it.
Middle School (6-8)
S13.3.1 Knows that just as electric current can produce magnetic forces, magnets can cause electric currents.
S13.3.2 Knows that every object exerts gravitational force on every other object; this force depends on the mass of the objects and their distance from one another; gravitational force is hard to detect unless at least one of the objects (e.g., the Earth) has a lot of mass.
High School (9-12)
S13.4.1 Knows that different kinds of materials respond differently to electric forces; in some materials, such as metals, electrons flow easily, whereas in insulating materials, such as glass, they can hardly flow at all; semiconducting materials have intermediate behavior, and at low temperatures some materials become superconductors and offer no resistance to the flow of electrons.
S13.4.2 Knows that materials contain almost exactly equal proportions of positive and negative charges, making the materials as a whole electrically neutral; a very small excess or deficit of negative charges in a material produces noticeable electric forces.
S13.4.3 Knows that magnetic forces are very closely related to electric forces and can be thought of as different aspects of a single electromagnetic force: moving electric charges produce magnetic forces and moving magnets produce electric forces; the interplayof these forces is the basis for electric motors, generators, radio, television and many other modern technologies.
S13.4.4 Knows that at the atomic level, electric forces between oppositely charged electrons and protons hold atoms and molecules together and thus are involved in all chemical reactions; on a larger scale, electric forces hold solid and liquid materials togetherand act between objects when they are in contact.
S13.4.5 Knows that electromagnetic forces acting within and between atoms are vastly stronger than the gravitational forces acting between them, and the forces that hold the nucleus of atoms together are much stronger than the electromagnetic force; this explains why great amounts of energy are released from the nuclear reactions in atomic or hydrogen bombs, and in the Sun and other stars.
S13.4.6 Knows that gravity is a universal force that each mass exerts on any other mass; the strength of the gravitational attractive force between two masses is proportional to the masses and inversely proportional to the square of the distance between them.
S13.4.7 Knows that the electric force is a universal force that exists between any two charged objects opposite charges attract whereas like charges repel; as with gravitation, the strength of the force is proportional to the charges and inversely proportional to the square of the distance between them.

Standard: Understands the nature of scientific knowledge

Label Benchmark
Primary (K-2)
S14.1.1 Knows that science experiments normally have reproducible results; that is, science experiments generally work the same way in different places.
Upper Elementary (3-5)
S14.2.1 Knows that the same scientific investigation often gives slightly different results when it is carried out by different persons, or at different times or places; however, if the results of repeated experiments are very different, something must be wrong with the design of the investigation.
Middle School (6-8)
S14.3.1 Knows that scientists often repeat an experiment many times before accepting a consistent result as true.
S14.3.2 Knows that scientists formulate and test their explanations of nature using observation, experiments and theoretical and mathematical models; although all scientific ideas are tentative and subject to change and improvement in principle, for most core ideas in the sciences there is much experimental and observational confirmation.
S14.3.3 Knows that in areas where active research is being pursued and in which there is not a great deal of experimental or observational evidence and understanding, it is normal for scientists to differ with one another about the evidence or theory being considered; until evidence is available that supports one position over another, scientists acknowledge that a conflict exists.
S14.3.4 Knows that scientists evaluate the results of scientific investigations and the explanations proposed by other scientists by reviewing experimental procedures, examining evidence, identifying faulty reasoning, pointing out statements that go beyond the evidence and suggesting alternative explanations for the same observations.
S14.3.5 Knows that although scientists may disagree about certain aspects of an investigation or explanation, they do agree that skepticism, questioning and open communication are essential to progress in science.
High School (9-12)
S14.4.1 Knows that science distinguishes itself from other ways of knowing and from other bodies of knowledge through the use of empirical standards, logical arguments and skepticism, as scientists strive for certainty of their proposed explanations.
S14.4.2 Knows that scientific explanations must meet certain criteria: they must be consistent with experimental and observational evidence about nature, and they must include a logical structure, rules of evidence, openness to criticism, reporting methods and procedures and a commitment to making knowledge public.
S14.4.3 Knows that because all scientific ideas depend on experimental and observational confirmation, all scientific knowledge is, in principle, subject to change as new evidence becomes available; in areas where data, information or understanding is incomplete, it is normal for scientific ideas to be incomplete, but this is also where the opportunity for making advances may be greatest.
S14.4.4 Knows that from time to time, major shifts occur in the scientific view of how the world works, but usually the changes that take place in the body of scientific knowledge are small modifications of prior knowledge; change and continuity are persistent features of science.
S14.4.5 Knows that in science, the testing, revising and occasional discarding of theories, new and old, never ends; this ongoing process leads to an increasingly better understanding of how things work in the world, but not to absolute truth.

Standard: Understands the nature of scientific inquiry

Label Benchmark
Primary (K-2)
S15.1.1 Knows that learning can come from careful observations and simple experiments.
S15.1.2 Knows that tools like thermometers, magnifiers, rulers and balances add to information from our senses.
Upper Elementary (3-5)
S15.2.1 Knows that scientific investigations involve asking and answering a question and comparing the answer to what scientists already know about the world.
S15.2.2 Knows that scientists use different kinds of investigations (e.g., naturalistic observation of things or events, data collection, controlled experiments) depending on the questions they are trying to answer.
S15.2.3 Plans and conducts a simple investigation (e.g., systematic observations, simple experiments to answer questions).
S15.2.4 Uses simple equipment and tools to gather scientific data and extend the senses (e.g., rulers, thermometers, magnifiers, microscopes, calculators).
S15.2.5 Knows that scientists develop explanations using observations (evidence) and what they already know about the world (scientific knowledge); good explanations are based on evidence from investigations.
S15.2.6 Knows that scientists make the results of their investigations public; they describe the investigations in ways that enable others to repeat the investigations.
S15.2.7 Knows that scientists review and ask questions about the results of other scientists' work.
Middle School (6-8)
S15.3.1 Knows that there is no fixed procedure called "the scientific method," but that investigations involve carefully collected, relevant evidence, logical reasoning and some imagination in developing hypotheses and explanations.
S15.3.2 Designs and conducts a scientific investigation (e.g., formulates questions, designs and executes investigations, interprets data, synthesizes evidence into explanations, proposes alternative explanations, critiques explanations and procedures).
S15.3.3 Uses appropriate tools (including computers) and techniques to gather, analyze and interpret scientific data.
S15.3.4 Establishes relationships based on evidence and logical argument (e.g., provides causes for effects).
S15.3.5 Knows that scientific explanations use evidence and logically consistent arguments to propose, modify or elaborate principles, models and theories in science; the scientific community accepts and uses such explanations until displaced by better scientificexplanations; when the latter occurs, science advances.
S15.3.6 Knows that scientific investigations sometimes result in new ideas, objects and phenomena for study, new methods or procedures for an investigation, or new technologies to improve the collection of data; all of these results lead to new investigations.
High School (9-12)
S15.4.1 Knows that scientists usually base their investigations on existence questions or causal-functional questions; causal-functional questions lead to investigations of how physical, living or designed systems function.
S15.4.2 Knows that hypotheses are widely used in science for choosing what data to pay attention to and what additional data to seek, and for guiding the interpretation of the data (both new and previously available).
S15.4.3 Formulates a testable hypothesis.
S15.4.4 Designs and conducts scientific investigations by identifying and clarifying the question, method, controls and variables; organizing and displaying data; revising methods and explanations; presenting the results; and receiving critical response from others.
S15.4.5 Knows that conceptual principles and knowledge guide scientific inquiries; historical and current scientific knowledge influence the design and interpretation of investigations and the evaluation of proposed explanations made by other scientists.
S15.4.6 Knows that scientists conduct investigations for a variety of reasons, such as exploration of new areas, discovery of new aspects of the natural world, confirmation of prior investigations, prediction of current theories and comparison of models and theories.
S15.4.7 Knows that results of scientific inquiry new knowledge and methods emerge from different types of investigations and public communication among scientists; the nature of communicating and defending the results of scientific inquiry is guided by criteria of being logical and empirical and by connections between natural phenomena, investigations and the historical body of scientific knowledge.

Standard: Understands the scientific enterprise

Label Benchmark
Primary (K-2)
S16.1.1 Understands that in science it is helpful to work with a team and share findings with others.
Upper Elementary (3-5)
S16.2.1 Knows that women and men of all ages, backgrounds and groups participate in the various areas of science and technology as they have for many centuries.
S16.2.2 Knows that although men and women doing scientific inquiry have learned much about the objects, events and phenomena in nature, there is still much more to be understood.
Middle School (6-8)
S16.3.1 Knows that women and men of diverse interests, talents, qualities and motivations and of various social and ethnic backgrounds, engage in the activities of science, engineering and related fields; some scientists work in teams, some work alone, but all communicate with others.
S16.3.2 Knows that doing science requires different abilities depending on such factors as the field of study, type of inquiry and cultural context; the work of science relies on human qualities (e.g., reasoning, insight, skill, creativity) and habits of mind (e.g., intellectual honesty, tolerance of ambiguity, skepticism, openness to new ideas).
S16.3.3 Knows that scientists and engineers work in many different settings including colleges and universities, business and industry, specific research institutes and government agencies.
S16.3.4 Understands that the ethics of science require that potential subjects be fully informed of the risks and benefits associated with the research and their right to refuse to participate; this ethic extends to informing potential subjects of the possible risks to community and property.
S16.3.5 Knows that tracing the history of science can show how difficult it was for scientific innovators to break through their preconceptions of their time to reach conclusions which today seem obvious.
High School (9-12)
S16.4.1 Knows that Western as well as non-Western cultures (e.g., Egyptian, Chinese, Hindu, Arabic) have developed scientific ideas and solved human problems through technology.
S16.4.2 Knows that progress in science and technology can relate to social issues and challenges (e.g., funding priorities, health problems).
S16.4.3 Knows that individuals and teams have contributed and will continue to contribute to the scientific enterprise; doing science or engineering can be as simple as an individual conducting field studies or as complex as hundreds of people working on a major scientific question or technological problem.
S16.4.4 Knows that scientists have ethical traditions, including commitment to peer review, truthful reporting of the methods and outcomes of investigations and publication of the results of work; violations of ethical traditions such as these rarely occur, but if violations do occur, the scientists responsible are strongly condemned.
S16.4.5 Knows that science and technology are essential social enterprises, but alone from other information they can only indicate what can happen, not what should happen.
S16.4.6 Knows that scientists in different disciplines ask different questions, use different methods of investigation, and accept different types of evidence to support their explanations; many scientific investigations require the contributions of individuals from different disciplines (including engineering) and new disciplines of science often emerge at the interface of two older disciplines (e.g., geophysics, biochemistry).
S16.4.7 Knows that scientists and engineers can only conduct research on human subjects if they have the consent of the subjects.
S16.4.8 Knows that creativity, imagination and a good knowledge base are all required in the work of science and engineering.

Standard: Understands the nature of technological design

Label Benchmark
Primary (K-2)
S17.1.1 Knows that some objects occur in nature, whereas others have been designed and made by people to solve human problems.
Upper Elementary (3-5)
S17.2.1 Categorizes items into groups of natural objects and designed objects.
S17.2.2 Knows that designing a solution to a simple problem may have constraints, such as cost, materials, time, space and safety.
S17.2.3 Implements proposed solutions using suitable tools, techniques and quantitative measurements where appropriate.
S17.2.4 Evaluates a product or design based on constraints.
Middle School (6-8)
S17.3.1 Identifies appropriate problems for technological design (e.g., identifies a specific need, considers its various aspects, considers criteria for a suitable product).
S17.3.2 Knows that for some technological needs, the cultural backgrounds and beliefs of different groups can affect the criteria for a suitable product.
S17.3.3 Designs a solution or product, taking into account needs and constraints (e.g., cost, time, trade-offs, materials needed).
S17.3.4 Implements a proposed design (e.g., organizes materials and other resources, plans one's work, makes use of group collaboration, chooses suitable tools and techniques, works with appropriate measurement methods).
S17.3.5 Knows that a technological design should meet criteria established in the original purpose (e.g., developed measures of quality).
High School (9-12)
S17.4.1 Proposes designs and chooses between alternatives (e.g., models, simulations).
S17.4.2 Implements a proposed solution (e.g., construction of artifacts for intended users or beneficiaries).
S17.4.3 Knows that a solution and its consequences must be tested against the needs or criteria the solution was designed to meet.

Standard: Understands the interactions of science, technology and society

Label Benchmark
Primary (K-2)
S18.1.1 Not appropriate at this level
Upper Elementary (3-5)
S18.2.1 Knows that scientists and engineers often work in teams with different individuals doing different things that contribute to the results.
S18.2.2 Knows that tools help scientists make better observations, measurements and equipment for investigations.
S18.2.3 Knows that people have always had questions about their world; science is one way of answering questions and explaining the natural world.
S18.2.4 Knows that people have always had problems and invented tools and techniques (ways of doing something) to solve problems; trying to determine the effects of various solutions helps people avoid some new problems.
S18.2.5 Knows that people continue inventing new ways of doing things, solving problems and getting work done; these new ideas and inventions often affect other people sometimes the effects are good and sometimes they are bad.
S18.2.6 Knows that science and technology have improved transportation, health, sanitation and communication; however, the benefits of science and technology are not available to all people.
Middle School (6-8)
S18.3.1 Knows that scientific inquiry and technological design have similarities and differences (e.g., scientists propose explanations for questions about the natural world and engineers propose solutions relating to human problems, needs and aspirations; technological solutions are temporary; technologies exist within nature and they cannot contravene biological or physical principles; technological solutions have side effects).
S18.3.2 Knows that science and technology have advanced through the contributions of many different people, in different cultures and at different times in history; science and technology have contributed to the economic growth and productivity of societies and this, in turn, results in social changes with different effects on societies and groups within societies.
S18.3.3 Knows that a person's gender, race or national origin should not influence the acceptance or rejection of his or her proposed contributions to science or technology.
S18.3.4 Knows that science helps drive technology, as it provides knowledge for better understanding, instruments and techniques.
S18.3.5 Knows that technology is essential to science because it enables observations of phenomena that are far beyond the capabilities of scientists due to factors such as distance, location, size and speed.
S18.3.6 Knows that technological solutions have trade-offs, such as safety, cost, efficiency and appearance; engineers often build in back-up systems to provide safety, but risk is part of living in a highly technological world.
S18.3.7 Knows that technological designs have constraints; some constraints are unavoidable (e.g., properties of materials, gravity, effects of weather and friction), and other constraints limit choices in the design (e.g., environmental protection, human safety,aesthetics).
S18.3.8 Knows that technological solutions have intended benefits and unintended consequences; some consequences can be predicted, but others cannot.
S18.3.9 Knows that scientific knowledge and the procedures used by scientists influence the way many individuals in society think about themselves, others and the natural environment; societal challenges often inspire questions for scientific research and social priorities often influence research priorities through funding.
S18.3.10 Knows that technology influences society through its products and processes, and technological changes are often accompanied by social, political and economic changes that may be beneficial or detrimental to individuals and to society; social needs, attitudes and values influence the direction of technological development.
S18.3.11 Knows that science cannot answer all questions and technology cannot solve all human problems and meet all human needs.
High School (9-12)
S18.4.1 Knows that science often advances with the introduction of new technologies and solving technological problems often results in new scientific knowledge; new technologies often extend the current levels of scientific understanding and introduce new arenas of research.
S18.4.2 Knows that science and technology are pursued for different purposes: scientific inquiry is driven by the desire to understand the natural world and seeks to answer questions that may or may not directly influence humans; technological design is driven bythe need to meet human needs and solve human problems and has a more direct effect on society than science because its purpose is to solve human problems, help humans adapt and fulfill human aspirations.
S18.4.3 Knows that individuals and society must decide on proposals involving new research and technologies; decisions involve assessment of alternatives, risks, costs and benefits, and consideration of who benefits and who suffers, who pays and gains and what are the risks and who bears them.
S18.4.4 Knows that technological knowledge is often not made public because of patents and the financial potential of the idea or inventions; scientific knowledge is made public through presentations at professional meetings and publication in scientific journals.

Standard: Understands basic Earth processes

Label Benchmark
Primary (K-2)
S2.1.1 Knows that animals and plants sometimes cause changes in their surroundings.
S2.1.2 Knows that chunks of rocks come in all sizes, from boulders to grains of sand and even smaller.
Upper Elementary (3-5)
S2.2.1 Knows that smaller rocks come from the breakage and weathering of bedrock and larger rocks.
S2.2.2 Knows that rock is composed of different combinations of minerals.
S2.2.3 Knows that soil is made up of weathered rock and products of plants and animals, and also contains many living organisms.
S2.2.4 Knows that waves, wind, water and ice constantly change the Earth's land surface by eroding rock and soil in some areas and depositing them in other areas, sometimes in seasonal layers.
S2.2.5 Knows that the surface of the Earth changes; some changes are due to slow processes (e.g., erosion, weathering), and some changes are due to rapid processes (e.g., landslides, volcanoes, earthquakes).
S2.2.6 Knows that fossils provide evidence about the plants and animals that lived long ago and the nature of the environment at that time.
Middle School (6-8)
S2.3.1 Knows that the composition and texture of the soil and its fertility and resistance to erosion are greatly influenced by plant roots and debris, bacteria, fungi, worms, rodents and other animals as they break up the soil and add organic material to it.
S2.3.2 Knows that rock contains evidence of the minerals, temperatures and forces that created it.
S2.3.3 Knows that sediments of sand and smaller particles (sometimes containing the remains of organisms) are gradually buried, cemented together by dissolved minerals and eventually turned into rock again.
S2.3.4 Knows how land forms are created through a combination of constructive and destructive forces: constructive forces include crustal deformation, volcanoes and deposition of sediment; destructive forces include weathering and erosion.
S2.3.5 Knows that thousands of layers of sedimentary rock confirm the long history of the Earth and the long history of changing life forms whose remains are found in successive layers of sedimentary rock; the newest layers may not always be found on top because of the folding, breaking and uplifting of layers.
S2.3.6 Knows that fossils provide important evidence of how life and environmental conditions have changed on the Earth over time (e.g., changes in atmospheric composition, movement of crustal plates, impact of an asteroid or comet).
High School (9-12)
S2.4.1 Knows that the Earth is a system containing a fixed amount of each stable chemical atom or element; each element moves among reservoirs in the solid Earth, oceans, atmosphere and living things, as part of geochemical cycles (e.g., carbon cycle, nitrogen cycle).
S2.4.2 Knows that the "rock cycle" consists of the formation, weathering, sedimentation and reformation of rock; in this cycle, the total amount of material stays the same as its form changes.
S2.4.3 Knows that the solid crust of the Earth including both the continents and the ocean basins consists of separate plates that ride on a denser, hot, gradually deformable layer of the Earth; the crust sections move very slowly, pressing against one another in some places and pulling apart in other places.
S2.4.4 Knows that the slow movement of material within the Earth results from heat flowing out from the deep interior and from the action of gravitational forces on regions of different density.
S2.4.5 Knows that earthquakes often occur along the boundaries between colliding plates.
S2.4.6 Knows that molten rock from below the Earth's surface creates pressure that is released by volcanic eruptions; under the ocean basins, molten rock may well up between separating plates to create new ocean floor; and volcanic activity along the ocean floor may form undersea mountains, which may eventually become islands.
S2.4.7 Knows that geologic time can be estimated by observing rock sequences and using fossils to correlate the sequences at various locations; recent methods use the predictability of decay rates of radioactive isotopes in rock formation to determine geologic time.
S2.4.8 Knows that evidence for simple, one-celled forms of life, such as bacteria and algae, extends back more than 3.5 billion years; the evolution of life resulted in dramatic changes in the composition of the Earth's atmosphere, which did not originally contain oxygen.

Standard: Understands essential ideas about the composition and structure of the universe and the Earth's place in it

Label Benchmark
Primary (K-2)
S3.1.1 Knows that the stars are innumerable, unevenly dispersed and of unequal brightness.
S3.1.2 Knows that the Sun can be seen only in daytime, whereas the Moon is out sometimes at night and sometimes during the day.
S3.1.3 Knows that the Moon looks a little different every day, but looks the same again about every four weeks.
Upper Elementary (3-5)
S3.2.1 Knows that the Earth is one of several planets that orbit the Sun, and the Moon orbits around the Earth.
S3.2.2 Knows that over time, planets change their position in the sky relative to the general pattern of stars.
S3.2.3 Knows that the patterns of stars in the sky stay the same, although they appear to move across the sky nightly, and different stars can be seen in different seasons.
S3.2.4 Understands that although telescopes magnify distant objects in the sky (such as the Moon and planets) and dramatically increase the number of stars we can see, some objects are so distant, small or dim that they do not appear in a telescope.
S3.2.5 Understands that astronomical objects in interstellar space are unimaginably distant from the Earth and each other: stars are like our Sun but so distant they look like points of light; galaxies, though very large, are so distant they look like a single star.
Middle School (6-8)
S3.3.1 Knows that the Sun is a medium-sized star, located at the edge of a disk-shaped galaxy, part of which can be seen on a clear night as a glowing band of light.
S3.3.2 Knows that nine planets of differing sizes and surface features and with differing compositions move around the Sun in nearly circular orbits; some planets have a variety of moons and rings of particles orbiting around them (e.g., the Earth is orbited by one moon, many artificial satellites and debris).
S3.3.3 Knows that we live on a fairly small planet, the third from the Sun in the only system of planets definitely known to exist, although other, similar systems might yet be discovered in the universe.
S3.3.4 Knows that the Sun's gravitational pull keeps the Earth and other planets in their orbits, just as the gravitational pull of planets keeps their moons in orbit around them.
S3.3.5 Knows that many pieces of rock and ice orbit our Sun: some meet the Earth in its orbit, glow and disintegrate from friction as they plunge through our atmosphere; other objects have long, off-center orbits that bring them close to the Sun, whose radiation boils off material and pushes it into a long, illuminated tail.
S3.3.6 Knows that the Moon's orbit around the Earth once in some 28 days changes how much of the Moon is lighted by the Sun and how much of that part can be seen from the Earth, resulting in the phases of the Moon.
S3.3.7 Knows that the universe contains many billions of galaxies, each containing many billions of stars.
S3.3.8 Knows that light travels from the Sun to the Earth in a few minutes, from the next nearest star in four years, and from very distant stars in several billion years; the distance light travels in a few years would take the fastest rocket thousands of years to travel.
High School (9-12)
S3.4.1 Knows that current theory states that about ten billion years ago, the entire contents of the universe expanded explosively into existence from a single, hot, dense chaotic mass; our solar system formed from a nebular cloud of dust and gas about 4.6 billion years ago.
S3.4.2 Knows that at the beginning of the universe, stars formed out of clouds of the lightest elements and became hot as the material condensed and began releasing energy from the nuclear fusion of light elements into heavier ones in their extremely hot, dense cores; some stars eventually exploded, producing clouds of material from which other stars and planets would condense; this process of star formation and destruction continues.
S3.4.3 Understands that stars differ from each other in size, temperature and age, but appear to be made up of the same elements and to behave according to the same principles; however, unlike our Sun, most stars are in systems of two or more stars orbiting around a common point.
S3.4.4 Knows that life is adapted to conditions on Earth, including the strength of gravity to hold an adequate atmosphere and an intensity of radiation from the Sun that allows water to cycle between liquid and vapor.
S3.4.5 Knows that the scientific account of the universe comes from studying evidence about its contents and imagining, with the help of mathematical models and computer simulations, how the contents got to be the way they are.

Standard: Knows about the diversity and unity that characterize life

Label Benchmark
Primary (K-2)
S4.1.1 Knows that plants and animals have external features that help them thrive in different environments.
Upper Elementary (3-5)
S4.2.1 Knows that living things can be sorted into groups in many ways using various properties to decide which things belong to which group; features used for grouping depend on the purpose of the grouping.
S4.2.2 Knows that plants and animals have life cycles which include birth, growth and development, reproduction and death; the details of this life cycle are different for different organisms.
Middle School (6-8)
S4.3.1 Knows that major categories of living organisms are plants, which get their energy directly from sunlight, and animals, which consume energy-rich foods; some kinds of organisms cannot be neatly classified as either plants or animals.
S4.3.2 Knows that all organisms, including the human species, are part of and depend on two main global food webs: one global food web starts with microscopic ocean plants and seaweed and includes the animals that feed on them and the animals that feed on those animals; the other global food web begins with land plants and includes the animals that feed on them and so forth.
S4.3.3 Knows that organisms can be classified according to the function they serve in a food chain (producer, consumer and/or decomposer of organic matter) and by the details of their internal and external features.
S4.3.4 Knows that animals and plants have a great variety of body plans and internal structures that contribute to their being able to make or find food and reproduce.
S4.3.5 Knows that for sexually reproducing organisms, a species comprises all organisms that can mate with one another to produce fertile offspring.
S4.3.6 Knows that although different species look very different, the unity among organisms becomes apparent from an analysis of internal structures, observation of the similarity of their chemical processes and the evidence of common ancestry.
High School (9-12)
S4.4.1 Knows that organisms are classified into a hierarchy of groups and subgroups based on their similarities and reflecting their evolutionary relationships; the similarity of organisms inferred from similarity in their molecular structure closely matches the classification based on anatomical similarities.
S4.4.2 Knows that the variation of organisms within a species increases the likelihood that at least some members of the species will survive under changed environmental conditions, and a great diversity of species increases the chance that at least some living things will survive in the face of large changes in the environment.

Standard: Understands the genetic basis for the transfer of biological characteristics from one generation to the next

Label Benchmark
Primary (K-2)
S5.1.1 Knows that plants and animals closely resemble their parents.
S5.1.2 Knows that there is variation among individuals within a population.
Upper Elementary (3-5)
S5.2.1 Knows that many characteristics of an organism are inherited from the parents of the organism (e.g., eye color in human beings, fruit or flower color in plants), but other characteristics result from an individual's interactions with the environment (e.g. , people's table manners, ability to play a musical instrument).
S5.2.2 Knows that for offspring to resemble their parents, there must be a reliable way to transfer information from one generation to the next.
Middle School (6-8)
S5.3.1 Knows that reproduction is a characteristic of all living systems; since no individual organism lives forever, reproduction is essential to the continuation of species.
S5.3.2 Knows that in some kinds of organisms, all the genes come from a single parent, whereas in organisms that have sexes, typically half of the genes come from each parent.
S5.3.3 Knows that in sexual reproduction, an egg from a female unites with a sperm from a male to begin the development of a new individual that has an equal contribution of information from its mother and its father; sexually produced offspring are never identical to either of their parents.
S5.3.4 Knows that the characteristics of an organism can be described in terms of a combination of traits; some traits are inherited and others result from interactions with the environment.
S5.3.5 Knows that hereditary information is contained in genes, located in the chromosomes of each cell; each gene carries a single unit of information, and an inherited trait of an individual can be determined by either one or many genes.
S5.3.6 Knows that selective breeding can cause small differences between parents and offspring to accumulate in successive generations so that descendants are very different from their ancestors; selective breeding for particular traits has resulted in new varieties of cultivated plants and domestic animals.
High School (9-12)
S5.4.1 Knows that in all organisms, the instructions for specifying the characteristics of the organism are carried in DNA; the chemical and structural properties of DNA explain how the genetic information that underlies heredity is both encoded in genes (as a string of molecular "letters") and replicated (by a templating mechanism).
S5.4.2 Knows that genes are segments of DNA molecules, and that inserting, deleting or substituting portions of the DNA can alter genes; changes in DNA (mutations) can also occur when a cell is exposed to certain kinds of radiation or chemical substances.
S5.4.3 Knows that the sorting and recombination of genes in sexual reproduction results in a great variety of possible gene combinations from the offspring of any two parents.
S5.4.4 Knows that most of the cells in a human contain two copies of each of 22 chromosomes; in addition, there is a pair of chromosomes that determines sex: a female contains two X chromosomes and a male contains one X and one Y chromosome.
S5.4.5 Knows that the fact that the human body is formed from cells that contain two copies of each chromosome (and, therefore, two copies of each gene), explains many features of human heredity, such as how variations that are hidden in one generation can be expressed in the next.

Standard: Knows the general structure and functions of cells in organisms

Label Benchmark
Primary (K-2)
S6.1.1 Knows that animals require air, water and food; plants require air, water and light.
Upper Elementary (3-5)
S6.2.1 Knows that each plant or animal has different structures which serve different functions in growth, survival and reproduction (e.g., humans have distinct structures of the body for walking, holding, seeing and talking).
S6.2.2 Knows that microscopes make it possible to see that living things are made mostly of cells; some organisms are made of a collection of similar cells that benefit from cooperating, whereas other organisms' cells vary greatly in appearance and perform very different roles in the organism.
Middle School (6-8)
S6.3.1 Knows that living systems at all levels of organization demonstrate complementarity of structure and function; the major levels of organization for structure and function include cells, tissues, organs, organ systems, whole organisms and eco-systems.
S6.3.2 Knows that all organisms are composed of cells, which are the fundamental units of life; most organisms are single cells, but other organisms (including humans) are multicellular.
S6.3.3 Knows that cells carry on the many functions needed to sustain life and that cells are able to grow and divide; this requires that cells take in nutrients, which they use to power their work and to make the materials that a cell or an organism needs.
S6.3.4 Knows that specialized cells perform specialized functions in multicellular organisms; each type of cell, tissue and organ has a distinct structure and set of functions that serve the organism as a whole.
S6.3.5 Knows that disease represents a breakdown in structures or functions of an organism; some diseases are the result of intrinsic failures of the system, whereas others are the result of infection by other organisms.
High School (9-12)
S6.4.1 Knows that every cell is covered by a membrane that separates it from the outside world and controls what molecules can enter and leave the cell; in all but quite primitive cells, a complex network of proteins provides organization and shape and, for animal cells, movement.
S6.4.2 Knows that inside the cell is a concentrated mixture of thousands of different molecules which form a variety of specialized structures that carry out such cell functions as energy production, transport of molecules, waste disposal, synthesis of new molecules and the storage of genetic material.
S6.4.3 Knows that initially most cells have the ability to become any kind of cell because they contain the same genetic information; through the process of their growth and development, they differentiate and specialize in structure and function (e.g., to become blood or leaf cells), but they retain the basic information that also allows them to reproduce themselves.
S6.4.4 Knows that most cell functions involve chemical reactions; food molecules taken into cells are broken down to provide the chemical constituents needed to synthesize other molecules; both breakdown and synthesis are made possible by a large set of protein catalysts called enzymes.
S6.4.5 Knows that cell functions are regulated; regulation of cells occurs both through changes in the activity of the functions performed by proteins and the selective expression of individual genes, allowing cells to respond to their environment and to control and coordinate the synthesis and breakdown of specific molecules, cell growth and division.
S6.4.6 Knows that cells store and use information to guide their functions; the genetic information stored in DNA is used to direct the synthesis of the thousands of proteins that each cell requires.
S6.4.7 Knows that proteins are long, usually folded chain molecules made from 20 different kinds of smaller amino acid molecules; the function of each molecule depends on the sequence of amino acids in it, and the chain's shape is a consequence of attractions between the chain's parts.
S6.4.8 Knows that multicellular animals have nervous systems to generate behavior; nervous systems are formed from specialized cells that conduct signals rapidly through the long cell extensions that make up nerves, and the nerve cells communicate with each other by secreting specific excitatory and inhibitory molecules.

Standard: Understands how species depend on one another and on the environment for survival

Label Benchmark
Primary (K-2)
S7.1.1 Knows that living things are found almost everywhere in the world; different types of plants and animals live in different places.
Upper Elementary (3-5)
S7.2.1 Knows that the behavior of individual organisms is influenced by internal cues such as hunger and external cues such as environmental change; humans and other organisms have senses that help them detect internal and external cues.
S7.2.2 Knows that an organism's patterns of behavior are related to the nature of that organism's environment, including the kinds and numbers of other organisms present, the availability of food and resources and the physical characteristics of the environment.
S7.2.3 Knows that when an environment changes, some plants and animals survive and reproduce and others die or move to new locations.
S7.2.4 Knows that all organisms (including humans) cause changes in the environment where they live; some of these changes are detrimental to themselves or other organisms and others are beneficial.
Middle School (6-8)
S7.3.1 Knows that all organisms must be able to obtain and use resources, grow, reproduce and maintain a relatively stable internal environment while living in a constantly changing external environment; regulation of an organism's internal environment involves sensing external changes and changing physiological activities to keep within the range required to survive.
S7.3.2 Knows that behavior is one kind of response an organism may make to an internal or environmental stimulus, and may be determined by heredity or from past experience; a behavioral response requires coordination and communication at many levels including cells, organ systems and whole organisms.
S7.3.3 Knows that all species ultimately depend on one another; interactions between two types of organisms include producer/consumer, predator/prey, parasite/host and relationships that can be mutually beneficial or competitive.
S7.3.4 Knows that populations consist of all individuals of a species that occur together at a given place; all of the populations living together (community) and the physical factors with which they interact compose an ecosystem.
S7.3.5 Knows that the number and types of organisms an ecosystem can support depend on the resources available and abiotic factors such as quantity of light and water, range of temperatures and the soil composition; limitations of resources and other factors such as predation and climate limit the growth of populations in specific niches in the ecosystem.
High School (9-12)
S7.4.1 Knows that organisms both cooperate and compete in ecosystems; the interrelationships and interdependencies of these organisms may generate ecosystems that are stable for hundreds or thousands of years.
S7.4.2 Knows that like many complex systems, ecosystems have cyclic fluctuations around a state of rough equilibrium.
S7.4.3 Knows that humans are increasingly modifying ecosystems as a result of population growth, technology and consumption; human destruction of habitats through direct harvesting, pollution, atmospheric changes and other factors is threatening global stability, and if not addressed, ecosystems will be irreversibly damaged.

Standard: Understands the cycling of matter and flow of energy through the living environment

Label Benchmark
Primary (K-2)
S8.1.1 Knows that plants and animals both need water, animals need food to eat and plants need light
S8.1.2 Knows that animals eat plants or other animals for food and may also use plants or other animals for shelter and nesting.
Upper Elementary (3-5)
S8.2.1 Knows that some source of "energy" is needed for organisms to live and grow.
S8.2.2 Knows that all animals depend on plants; some animals eat plants for food while other animals eat animals that eat the plants.
S8.2.3 Knows that over the whole Earth, organisms are growing, dying and decaying, and new organisms are being produced by the old ones.
Middle School (6-8)
S8.3.1 Knows that almost all food energy ultimately comes from the Sun as plants convert light into stored chemical energy; that energy can change from one form to another in living things; and that animals get energy from oxidizing their food, releasing some ofits energy as heat.
S8.3.2 Knows how matter is transferred from one organism to another repeatedly and between organisms and their physical environment; as in all material systems, the total amount of matter remains constant, even though its form and location change.
High School (9-12)
S8.4.1 Knows that as matter and energy flow through different levels of organization of living systems (e.g., cells, organs, organisms, communities), and between living systems and the physical environment, chemical elements are transformed and recombined in different ways; each transformation results in storage and dissipation of energy into the environment as heat, and matter and energy are conserved in each transformation.
S8.4.2 Knows that because all matter tends toward more disorganized states, living systems require a continuous input of energy to maintain their chemical and physical organizations; the energy for life ultimately derives from the Sun and energy flows through ecosystems in one direction, from photosynthetic organisms to herbivores to carnivores and decomposers.
S8.4.3 Knows that plant cells contain chloroplasts, the sites of photosynthesis, which provide the vital connection between the Sun and the energy needs of living systems; plants, and some other organisms, use solar energy to combine molecules of carbon dioxide and water into complex, energy-rich organic compounds.
S8.4.4 Knows that the complexity and organization of organisms accommodates the need for obtaining, transforming, transporting, releasing and eliminating the matter and energy used to sustain the organism.
S8.4.5 Knows that the amount of life any environment can support is limited by the available energy, water, oxygen and materials, and by the ability of ecosystems to recycle the residue of dead organic materials.

Standard: Understands the basic concepts of the evolution of species

Label Benchmark
Primary (K-2)
S9.1.1 Knows that some kinds of things that live today still resemble once-living things that have completely disappeared.
Upper Elementary (3-5)
S9.2.1 Knows that living things of the same kind vary among individuals, and sometimes the differences give individuals an important advantage in surviving and reproducing.
S9.2.2 Knows that fossils provide evidence that some organisms living long ago are now extinct, and fossils can be compared to one another and to living organisms to observe their similarities and differences.
Middle School (6-8)
S9.3.1 Knows how the fossil record, through geologic evidence, documents the appearance, diversification and extinction of many life forms; millions of species of animals, plants and micro-organisms living today differ from those that lived in the remote past, and each species lives in a specific and fairly uniform environment.
S9.3.2 Knows that extinction of a species occurs when the environment changes and the adaptive characteristics of a species do not enable it to survive in competition with its neighbors; extinction of species is common most of the species that have lived on theEarth no longer exist.
S9.3.3 Knows that biological evolution accounts for a diversity of species developed through gradual processes over many generations; species acquire many of their unique characteristics through biological adaptation (e.g., changes in structure, behavior or physiology that enhance reproductive success), which involves the selection of naturally occurring variations in populations.
High School (9-12)
S9.4.1 Knows that new heritable characteristics can only result from new combinations of existing genes or from mutations of genes in an organism's sex cells; other changes in an organism cannot be passed on.
S9.4.2 Knows that heritable characteristics, which can be biochemical and anatomical, largely determine what capabilities an organism will have, how it will behave and, hence, how likely it is to survive and reproduce.
S9.4.3 Knows that the basic idea of evolution is that the Earth's present-day life forms have evolved from earlier, distinctly different species as a consequence of the interactions of (1) the potential for a species to increase its numbers, (2) the genetic variability of offspring due to mutation and recombination of genes, (3) a finite supply of the resources required for life and (4) the ensuing selection by the environment of those offspring better able to survive and leave offspri
S9.4.4 Knows that life on Earth is thought to have begun about four billion years ago as simple, one-celled organisms; during the first two billion years, only microorganisms existed, but once cells with nuclei developed about a billion years ago, increasingly complex multicellular organisms evolved.
S9.4.5 Knows that natural selection leads to organisms that are well suited for survival in particular environments, so that when an environment changes, some inherited characteristics become more or less advantageous or neutral, and chance alone can result in characteristics having no survival or reproductive value.
S9.4.6 Knows that natural selection and its evolutionary consequences provide a scientific explanation for the fossil record of ancient life forms, as well as for the striking molecular similarities observed among the diverse species of living organisms; the millions of different species that live on the Earth today are related by descent from common ancestors.

PUMAS Train