|
1.
|
Students
will apply a wide variety of mathematical concepts, processes, and
skills to solve a broad range of problems in various content areas
and everyday situations. |
By the end of grade 3:
a. Formulate a problem, determine information required to solve the
problem, choose methods for obtaining this information, and set limits
for acceptable solutions.
b. Demonstrate that there may be multiple ways to solve a problem and
explain why this is so.
c. Understand that there is no one right way to solve mathematical
problems but that different methods (e.g., working backward from a solution,
using a similar problem type, identifying a pattern) have different
advantages and disadvantages.
d. Transfer strategies from a prior problem to a new situation.
e. Use trial and error and the process of elimination to solve problems.
f. Verify the correctness and reasonableness of simple mathematical
results.
By the end of grade 5:
a. Know how to select and use mathematical tools and methods (such
as manipulatives, mental math, calculator, computer, and paper-and-pencil
techniques) as a part of the problem-solving process.
b. Develop and apply a variety of problem-solving strategies (for example,
make an organized list, guess-and-check) and justify choice of strategies.
c. Interpret results in the context of the problem being solved (for
example, when determining the number of buses necessary to transport
students, the remainder must be rounded up).
d. Differentiate between relevant and irrelevant information
e. Understand how to break a complex problem into simpler parts.
By the end of grade 8:
a. Pose, explore, and solve a variety of problems, including those
that are non-routine or have a variety of possible strategies or solutions
or both, in order to build new mathematical knowledge.
b. Develop, modify, and apply an increasing variety of problem-solving
techniques to solve problems (for example, working backward, information
organizers, or solving a similar but simpler problem).
c. Try various problem-solving approaches before selecting and using
a strategy and reflect on different strategies used when a task is complete.
By the end of grade 12:
a. Explore the validity and efficiency of various problem-posing and
problem-solving strategies; develop alternative strategies and generalizations
as needed.
b. Monitor progress toward solutions.
c. Generalize strategies and reflect on their proficiency and merit.
|
2.
|
Students
will apply mathematical reasoning skills to investigate, evaluate,
justify, and connect approaches and solutions to situations in mathematics
and in other disciplines. |
By the end of grade 3:
a. Make, check, and verify predictions about the quantity, size, and
shape of objects and groups of objects.
b. Find examples that support or refute mathematical statements.
c. Explain why a prediction, estimation, or solution is reasonable.
d. Make and describe connections linking conceptual and procedural knowledge
using a variety of strategies (manipulative, pictorial, symbolic).
By the end of grade 5:
a. Describe the connections and translate between various representations
of equivalent numbers (such as 3/3 = 1, 10% of a dollar = 1 dime).
b. Use models, spreadsheets, number facts, properties,
and relationships to check and verify predictions and explain reasoning.
c. Given a rule or generalization, determine whether
the example fits.
d. Draw logical conclusions about mathematical situations using informal
inductive and deductive reasoning (e.g., observing that the angles of
several triangles add up to 180 degrees and concluding that the angles
of all triangles add up to 180 degrees; concluding that since all rectangles
have 4 90-degree corners, a square must be a rectangle).
e. Interpret statements made with the precise language of logic (such
as all, every, none, some).
f. Independently apply mathematical concepts to other content areas
such as science, geography, and music.
By the end of grade 8:
a. Make and investigate mathematical conjectures.
b.
Use "ifthen" statements to
construct simple valid arguments.
c. Use inductive and deductive reasoning appropriately.
d. Apply proportional and spatial thinking.
e. Develop and evaluate mathematical arguments and informal proofs.
f. Identify and use connections between various mathematical topics
to build upon existing knowledge.
g. Use mathematical ideas from one area of mathematics (e.g., an equation
or formula from algebra) to explain an idea from another area of mathematics
(e.g., the area of a triangle) and to demonstrate how mathematical ideas
are a coherent whole.
h. Apply mathematical skills and processes to other disciplines and
to everyday situations.
By the end of grade 12:
a. Construct, follow and evaluate arguments, judging their validity
using reasoning and logic.
b. Use a variety of methods of proofs (for example, direct, indirect,
informal, truth tables, paragraph) to validate conjectures.
c. Relate procedures in one representation of a problem to procedures
in an equivalent representation.
d. Use the connections among mathematical topics to develop multiple
approaches to problems.
e. Demonstrate how graphs can be used to model real-world situations
and to determine solutions to numerous problems involving algebraic
functions.
|
3.
|
Students
will understand mathematical information presented and obtained in
a variety of ways and will accurately and clearly present and justify
mathematical ideas in diverse formats. |
By the end of grade 3:
a. Listen
to and read about mathematical strategies and solutions, and communicate
them to others using everyday language
and correct mathematical
terms (e.g., sum, product) and symbols (e.g., +, =, >).
b. Recognize that certain words give clues to specific operations (e.g.,
sum means addition, difference means subtraction, of means multiplication
and per means division).
c. Communicate mathematical ideas using concrete, pictorial and symbolic
representations.
d. Understand and demonstrate that some ways of representing a problem
are more helpful than others.
By the end of grade 5:
a. Identify, communicate, and model key mathematical
concepts and situations using oral, written, concrete, pictorial, and
graphic methods, making certain that the situation is represented
clearly and accurately.
b. Explain and justify mathematical ideas, strategies, and solutions
to others, using the correct mathematical vocabulary.
c. Demonstrate an ability to understand others' strategies or explanations.
By the end of grade 8:
a. Demonstrate a repertoire of mathematical representations and use
them purposefully, flexibly, and appropriately.
b. Use mathematical language, notation, and symbols as a precise means
of expressing problem situations and mathematical ideas.
c. Analyze, evaluate, and explain mathematical arguments and conclusions
presented by others.
By the end of grade 12:
a. Formulate questions, conjectures, and generalizations about data,
information, and problem situations.
b. Present complete and convincing arguments and justifications adapted
to be effective for various audiences.
c. Use technology (such as graphics calculators, spreadsheets, graphing
programs) to present information and ideas.
d. Use properties, models, known facts, and relationships to explain
and defend thinking.
|
4.
|
Students
will select and use a wide variety of tools and technology to support
and validate mathematical results, when appropriate. |
By the end of grade 3:
a. Represent and examine mathematical situations using concrete materials
and computers.
b. Use a four-function or fraction calculator to confirm computations
and to explore patterns.
c. Use a variety of standard tools (e.g., rulers, clocks, measuring
tapes, thermometers) and non-standard objects (e.g., counters, sticks,
bolts), to measure mathematical and physical objects in the environment.
By the end of grade 5:
a. Use calculators or software to verify estimations and in problem-solving
situations.
b. Use technology such as spreadsheets, cameras, science probe, or
calculators to gather, analyze, and display mathematical data and information.
By the end of grade 8:
a. Use a variety of technologies, including computers, scientific calculators,
graphing calculators, science probes, and digital cameras to evaluate
and validate problem solutions.
b. Recognize situations when calculator use is not appropriate (for
example, when solving a simple quadratic equation which could be factored)
or when it yields misleading results (for example, when a non-linear
curve appears linear).
By the end of grade 12:
a. Use graphing calculators and computer software effectively and efficiently
to define and solve various types of problems.
|
5.
|
Students
will understand and apply numbers, ways of representing numbers, relationships
among numbers, and number systems. |
By the end of grade 3:
a. Connect physical, verbal, and symbolic representations of whole
numbers, fractions and mixed numbers.
b. Use drawings, diagrams, and models to show the concept of fractions
as part of a whole and part of a set.
c. Explain how numbers are used in various ways, including counting,
ordering, representing quantities, measuring, labeling, and indicating
location.
d. Apply place-value concepts and numeration to describe, compare,
count, order, and group numbers.
e. Explain the connections between operations.
f. Use concrete objects to count, order, group, and demonstrate one-to-one
correspondence with whole numbers beyond 100.
g. Identify patterns in number sequences (identify even and odd numbers,
count by 2s, 3s, 5s, 10s, and 25s).
h. Read, write, and order numbers to 10,000.
By the end of grade 5:
a. Model and connect physical, verbal, and symbolic representations
of fractions, decimals, percentages, whole numbers, and mixed numbers.
b. Order fractions, decimals, and whole numbers using physical, verbal,
and symbolic representations.
c. Recognize the relationship among fractions, decimals, and percentages.
d. Use concepts of negative numbers in concrete situations (such as
on a number line, with temperature).
e. Identify and describe different uses for the same numerical representation
(for example, 1/4 can represent a fraction, a division problem, or a
ratio) and different representations for the same number (for example,
2,343 is the same as 2,000 + 300 + 40 + 3; and 1 equals 16/16).
f. Use, model, and identify place value and describe its relationship
to magnitude.
g. Demonstrate that mathematical operations can represent a variety
of problem situations (for example, multiplication can represent repeated
addition and a model for finding area).
h. Explain the relative effect of operations with fractions and decimals
(for example, what happens to 10 when you divide by 1/2 or multiply
by .75).
i. Explain, derive, compare, and use properties of operations and relationships
among operations.
j. Explain and apply number theory concepts (such as primes, multiples,
and composites).
k. Read, write, and order numbers to a million.
By the end of grade 8:
a. Demonstrate a conceptual understanding of irrational numbers and
be able to solve problems involving rational numbers (e.g., area of
circles, working with radicals).
b. Describe how percent, ratio, and proportion apply to mathematical
situations (such as rate, similar triangles).
c. Recognize and apply multiple representations of rational and irrational
numbers, exponents, absolute values, and scientific notation; compare
these numbers accurately, find their approximate locations on a number
line, and choose appropriate forms of these numbers.
d. Demonstrate an understanding of numbers that represent large and
small values, including the use of benchmarks to comprehend their magnitude;
and recognize, understand, and appropriately use various representations
for large numbers.
e. Represent and explain the effect of operations on positive and negative
numbers.
f. Add, subtract, multiply, and divide fractions, decimals, percents,
integers, and nonnegative whole number exponents.
g. Understand and use the inverse relationships of addition and subtraction,
multiplication and division, and squaring and finding square roots to
simplify computations and solve problems.
h. Use factors, multiples, and prime factorization to solve problems.
i. Recognize and use the associative and commutative properties of
addition and multiplication, and the distributive property of multiplication
over addition to simplify computations with rational numbers.
j. Model and connect physical, verbal, and symbolic representations
of real numbers by hand and/or with a graphing calculator.
By the end of grade 12:
a. Explain the effect of operations on measurements (for example, the
imprecise nature of measurement is amplified with multiplication).
b. Understands the concept of infinity.
|
6.
|
Students
will estimate, compute, and assess reasonableness of solutions. |
By the end of grade 3:
a. Demonstrate proficiency with and memorize addition and subtraction
facts through 20 and multiplication facts through 10.
b. Add and subtract single- and multi-digit whole numbers with regrouping.
c. Apply addition and subtraction in a variety of situations (such
as computing perimeter, extending functions).
d. Multiply multi-digit whole numbers by single-digit numbers.
e. Divide two-digit whole numbers by single-digit numbers.
f. Demonstrate the concept of multiplication as repeated addition and
arrays; demonstrate the concept of division as repeated subtraction
and as sharing.
g. Understand and appropriately use the vocabulary of estimation (such
as about, near, between).
h. Use a variety of mental computational methods, strategies, and estimation
skills to find solutions and to determine the reasonableness of calculated
answers, including those involving concrete and abstract items and situations,
such as time and money.
i. Determine the value of a set of host country currency and U.S. currency.
j. Read, write, add, and subtract with decimal notation in situations
involving money.
By the end of grade 5:
a. Demonstrate proficiency with and memorize multiplication and division
facts through 12.
b. Select and use the most efficient computational methods, choosing
among concrete materials, paper and pencil, estimation, mental computation,
and calculators.
c. Create and solve practical problems involving addition, subtraction,
multiplication, and division of whole numbers, fractions, and mixed
numbers.
d. Develop, analyze, and compare algorithms for computing with fractions,
decimals, percents, and integers and compute with them efficiently and
accurately, including in multi-step problems that require application
of order of operations.
e. Know and convert among fractions, decimals, and percents for 1/10,
1/5, 1/4, 1/2, and 3/4.
f. Apply beginning number theory including identifying
and using multiples, factors, divisibility, properties of identity (zero
and one), and prime and composite numbers.
g. Apply, explain, and assess the appropriateness of a variety of estimation
strategies (such as rounding to compatible numbers).
h. Use various forms of estimation, including rounding, to determine
the reasonableness of calculated answers; determine if an estimate is
too high or too low.
i. Use a variety of strategies to make change and
solve problems using U.S. and host country's currency, and to convert
between host country and U.S. currency.
By the end of grade 8:
a. Solve problems using rates and understand rate as a unit of measure.
b. Use algorithms for computing with fractions, decimals, percents,
and integers and compute them efficiently and accurately with and without
a calculator.
c. Use multi-step computational procedures with rational and irrational
numbers.
d. Estimate the value of irrational numbers.
e. Develop, analyze, and explain methods to solve problems involving
proportions and percents (such as scaling, finding equivalent ratios).
f. Compute circumference, area, surface area, and
volume of geometric figures; find missing dimensions of right triangles
using the Pythagorean theorem.
g. Estimate the value of tips, discounts, and taxes using host country
and U.S. currency.
h. Explain and apply the rules of divisibility, square numbers, prime
factorization, and the properties of zero with the order of operations.
i. Determine what a reasonable degree of accuracy would be in particular
situations (e.g., great precision is required in scientific experiments,
but much less is required in estimating a grocery bill).
By the end of grade 12:
a. Manipulate algebraic procedures with real and complex numbers.
b. Apply factorials, exponents, and matrices to
solve practical problems.
c. Compute permutations and combinations.
d. Assess the error resulting from estimation and rounding, using both
customary and metric units.
e. Estimate algebraic solutions.
f. Determine when to use exact value solutions and distinguish between
exact value and approximate values.
|
7.
|
Students
will estimate and measure to a required degree of accuracy and precision
by selecting and using appropriate units, tools, and technologies. |
By the end of grade 3:
a. Estimate before measuring to determine the reasonableness of a solution.
b. Estimate and measure length, time, temperature, and weight to the
nearest unit using customary, metric, and nonstandard measurement.
c. Compare and order measurable characteristics (for example, time,
temperature, length, weight, capacity, area, perimeter) of different
objects on the same dimensions.
d. Tell time to the minute with both analog and digital clocks.
e. Determine elapsed time to the hour using AM and PM.
f. Find the perimeter and area of rectangles with direct methods, including
using concrete objects as tools.
g. Recognize the need for a uniform unit of measure.
By the end of grade 5:
a. Select and use appropriate instruments and customary and metric
units for measuring quantities, including perimeter, volume, area, weight,
time, and temperature, with specified accuracy; match tools with the
attribute they measure (for example, rulers measure length, thermometers
measure temperature).
b. Understand and apply formulas for finding perimeter, volume of simple
solids (excluding cylinders), and area.
c. Add
and subtract measurements (e.g., 12 m. – 6.2
m.).
d. Identify and use equivalent measurements as required by the situation
(for example, 60 minutes = 1 hour, 7 days = 1 week).
e. Identify the approximate size of basic standard units of measurement
and the relationship between them (for example, there are 100 centimeters
in a meter).
f. Solve calendar problems involving days, weeks, months, and years.
g. Determine and compare elapsed time using AM and PM and a 24-hour
clock.
By the end of grade 8:
a. Estimate and measure angles and use formulas to find perimeter,
area, and circumference of plane figures and the volume and surface
area of prisms, pyramids, and cylinders to a specified degree of accuracy.
b. Select and use appropriate units and tools to measure length, area,
volume, angle, and weight to appropriate levels of precision.
c. Convert measurements within and between monetary systems and within
and between metric and customary systems and demonstrate an understanding
of the relationship between units in metric and customary systems.
d. Select and apply indirect methods of measurement including formulae,
geometric ideas and relationships (such as congruence, similarity and
the Pythagorean theorem) and algorithms for mathematical relationships
(such as scale, proportions, rate).
e. Select and use a variety of methods and tools
to construct and compare plane figures of given measures.
f. Apply information about time zones and elapsed time to solve problems.
By the end of grade 12:
a. Incorporate units into all aspects of measurement problems and determine
the appropriateness of a solution based upon dimensional analysis.
b. Explain the relationship among error, precision, and accuracy in
measurement, including the compounding of errors in calculations.
c. Evaluate the accuracy and precision of measurements resulting from
the measuring tools and methods chosen.
d. Apply indirect methods, such as ratios and trigonometry,
to find missing dimensions.
e. Interpret various international measurement systems (such as the
Richter Scale, decibels) to describe phenomena and solve problems.
|
8.
|
Students
will use algebraic methods to represent, analyze, and solve abstract
and practical mathematical situations involving patterns and functional
relationships. |
By the end of grade 3:
a. Recognize, reproduce, extend, create, and describe repeating and
increasing patterns and sequences using a variety of materials.
b. Use tables, graphic organizers, verbal rules, and open sentences
to describe patterns and other relationships.
c. Generate and solve simple functions by identifying and applying
addition and subtraction patterns.
d. Generate, write, and solve open sentences using informal methods
(such as using manipulatives, drawing, or acting out the solution).
e. Use concrete objects and symbols to model the concepts of variables,
expressions, equations, and inequalities (for example, find the missing
number, symbol, or operation sign).
f. Identify and describe numeric patterns and make predictions based
on them (e.g., 1 bicycle = 2 wheels, so 6 bicycles = how many wheels).
By the end of grade 5:
a. Use patterns and their extensions to make predictions and solve
problems.
b. Use rules and variables to describe patterns, functions, and other
relationships and to solve equations.
c. Generate and solve simple functions by identifying and applying
multiplication and division patterns.
d. Find solutions to inequalities from a given replacement set.
e. Solve simple equations using methods such as inverse operations,
mental math, and guess-and-check.
f. Use concrete objects and combinations of symbols and numbers to
create expressions that model mathematical situations.
g. Understand the basic characteristics of a 2-dimensional coordinate
system.
By the end of grade 8:
a. Analyze, create, and generalize numeric and visual patterns.
b. Describe relationships between symbolic expressions
and graphs on the coordinate plane, with particular attention to the
horizontal and vertical intercepts, points of intersection, and slope
(for linear relations).
c. Analyze functional relationships to explain
how a change in one quantity results in a change in another (for example,
the relationship among length, area, and volume).
d. Find the value of a variable by evaluating formulas
and algebraic expressions for given values (for example, if an object
has a length of 4 and an area of 28, what is the object's width?).
e. Rewrite
formulas in terms of the missing variable (for example, "if an object has a length of 4 and an area of 28, what is the
object's width?" can be expressed as 4W=28 or as W=28/4).
f. Create expressions, equations, and inequalities
to represent problem situations and to solve problems involving linear
relationships.
g. Demonstrate fluency in generating equivalent expressions for simple
algebraic expressions and in solving linear equations and inequalities.
h. Demonstrate a basic understanding of rate of change, including connections
between slope of a line and constant rate of change and their meaning
in context.
By the end of grade 12:
a. Define functions and their properties and find the inverse of a
function; understand the relationship between a function and its inverse.
b. Create and solve linear and quadratic equations and inequalities.
c. Add, subtract, multiply, divide, and simplify rational and irrational
expressions; add, subtract, multiply and divide polynomials.
d. Identify, graph, and describe the graphs of
basic families of functions including linear, absolute value, quadratic,
exponential, and trigonometric functions and explain why a variety of
phenomena can be modeled by the same type of function.
e. Solve systems of equations and inequalities.
f. Formulate expressions, equations, inequalities,
systems of equations, systems of inequalities, and matrices to model
problem situations.
g. Use matrices to organize and manipulate data,
including matrix addition, subtraction, multiplication, and scalar multiplication.
|
9.
|
Students
will use spatial reasoning and apply the properties and relationships
of geometric figures to represent, investigate, analyze, and solve
problems. |
By the end of grade 3:
a. Use comparative directional and positional words (such as above,
inside, left, horizontal, middle).
b. Describe, name, and label related geometric two- and three-dimensional
shapes (such as circle and sphere, square and cube, triangle and pyramid,
rectangle and prism).
c. Draw two-dimensional geometric shapes and construct rectangles,
squares, and triangles using tools (such as geoboards, grid paper, ruler,
compass), including representation of side, top, and bottom views of
the object.
d. Construct three-dimensional geometric shapes, including boxes and
triangular prisms.
e. Identify and describe geometric figures in the environment.
f. Identify and create examples of line symmetry.
g. Order simple geometric figures by size.
h. Estimate and determine the perimeter and area of geometric figures
using manipulatives; demonstrate conservation of area.
i. Describe, identify, and model slides, flips, and turns with geometric
figures.
By the end of grade 5:
a. Locate and describe objects in terms of their position with and
without compass directions; identify coordinates for a given point or
locate points of given coordinates on a single quadrant grid.
b. Compare, contrast, and describe plane and solid figures and shapes
using their attributes (such as number of sides, parallel or perpendicular
sides, number of vertices, classification of angles).
c. Sketch and identify line segments, midpoint, intersections, and
parallel and perpendicular lines.
d. Identify, draw, and measure, using a protractor, right, obtuse,
and acute angles and their parts, including rays, points, and vertices.
e. Identify and model geometric figures that are congruent, similar,
or symmetrical or some combination of these properties.
f. Identify the diameter, radius, chord, and circumference of a circle.
g. Determine area and perimeter, finding both using
a variety of methods.
h. Analyze and model transformations of geometric
figures and rotations of line segments, describing the motions as slides,
flips, or rotations.
By the end of grade 8:
a. Describe the relationship between an equation and its graph.
b. Use coordinate geometry to represent and interpret relationships
defined by equations and formulas (for example, distance, mid-point),
translating among ordered pairs, graphs, and equations.
b. Model, classify, compare, and sketch a variety of two- and three-dimensional
regular and irregular figures.
c. Apply properties of equality and proportionality to solve problems
involving congruent or similar shapes.
d. Describe and apply geometric properties and relationships (such
as congruence, perpendicularity).
e. Describe and apply a variety of strategies for determining circumference,
perimeter, area, surface area, angle measure, and volume.
f. Explain and apply the Pythagorean theorem.
g. Draw and describe the results of transformations,
including translations, rotations, reflections, and dilations (shrinking
or enlarging), using proper notation.
By the end of grade 12:
a. Be familiar with the graphs of the following equations and be able
to apply them to problem solving: y = sinx; y = cosx; y = tanx.
b. Use coordinate geometry to graph linear and
quadratic equations, determine slopes of lines, identify parallel and
perpendicular lines, and find possible solutions to sets of equations.
c. Create two-dimensional representations of three-dimensional objects
(e.g., draw a basic cube).
d. Construct geometric models, transformations,
and scale drawings using a variety of methods and tools (such as paper
folding or protractor).
e. Identify congruent and similar figures; apply this information to
solve problems.
f. Use basic trigonometric ratios and trigonometric laws (triangle
trigonometry) to solve problems involving indirect measurement.
g. Use vector methods, matrices, and transformations.
|
10.
|
Students
will pose a question, collect, organize, analyze, and represent data
in order to make decisions and predictions. |
By the end of grade 3:
a.
Pose a question and collect data by observing, measuring, surveying,
and counting.
b. Construct, read, interpret, and label
graphs, including pictographs, simple bar and line graphs, and pie charts.
c. Interpret data by looking for patterns and relationships, determining
range, considering cause and effect, then drawing conclusions and answering
related questions.
By the end of grade 5:
a. Solve problems that involve systematically collecting, organizing,
and analyzing data.
b. Discuss the appropriateness of different types
of data displays, and use a variety of displays (such as tables, histograms,
graphs).
c. Interpret data, using the arithmetic
mean, median, mode, range, and make convincing arguments based on data
analysis and previous experiences.
d. Find all possible outcomes of a simple experiment
using straightforward methods (such as organized lists, tree diagrams).
By the end of grade 8:
a. Formulate and solve problems by collecting,
organizing, analyzing (including comparing and contrasting), and displaying
data in a variety of ways (including stem and leaf plots, histograms,
whisker plots, surveys, circle graphs) by hand and with technology.
b. Find, describe, and interpret the arithmetic mean, median, and mode
as measures of the center of a data set; select the appropriate measure
in particular situations to most accurately and fairly represent the
data.
c. Describe ways to define a sample group; analyze a sample to make
inferences about a population.
d. Design and conduct a simulation to study a problem
and communicate the results.
By the end of grade 12:
a. Describe the attributes of several common distributions (e.g., normal,
uniform, Poisson, exponential), indicating data sets that would be expected
to follow each type of distribution.
b. Determine regression equations to model and
draw inferences from data; summarize and interpret single-variable data
by choosing measures of central tendency and dispersion.
c. Analyze the validity of statistical conclusions and the use, misuse,
and abuse of data caused by choices of scale, inappropriate choices
of central tendency, incorrect curve fitting, or inappropriate use of
control groups.
d. Pose questions; collect, organize, and represent data to answer
those questions.
|
11.
|
Students
will understand and apply basic concepts of probability. |
By the end of grade 3:
a. Predict and measure the outcome of events, and explain why the results
of an experiment may not match predicted outcomes.
b. Use concepts of certainty, fairness, and chance to discuss the probability
of actual events.
By the end of grade 5:
a. Make predictions based on intuitive, experimental, and theoretical
probabilities.
b. Conduct simple probability experiments using concrete materials
(e.g. tossing one or more coins, spinning a spinner of even or uneven
divisions, drawing objects from a container with and without replacement)
and represent the results using fractions and probability.
By the end of grade 8:
a. Determine theoretical probability using a variety of methods, including
creating a sample space; compare theoretical expectations to experimental
results.
b. Design, conduct, and analyze the results of probability experiments.
By the end of grade 12:
a. Describe the normal curve in general terms and use
its properties to answer questions about sets of data.
b. Find the probability of simple events, compound events,
and independent events using a variety of methods including the fundamental
counting principle.
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