This tool can be used to create a custom SmartLink for your
web page. A SmartLink is a hyperlink or drop menu that returns a set of resources when clicked or selected.
See this example page, which illustrates a SmartLink drop menu and
SmartLink hyperlinks at the top of the page.

Step 1 - Choose the type of SmartLink you would like:

SmartLink - A hyperlink that displays a set of search results when clicked (see SmartLink description) SmartLinkDropList - A drop list that contains menu selections that display a set of search results when selected
(see SmartLinkDropList description)

Step 2 - Choose a label for your SmartLink:

Step 3 - Choose the search terms and/or classifiers to map to your SmartLink:

Count with understanding and recognize 'how many' in sets of objects

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

Develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections

Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers

Connect number words and numerals to the quantities they represent, using various physical models and representations

Understand and represent commonly used fractions, such as 1/4, 1/3, and 1/2

Understand meanings of operations

Understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations

Understand the effects of adding and subtracting whole numbers

Understand situations that entail multiplication and division, such as equal groupings of objects and sharing equally

Compute fluently and make reasonable estimates

Develop and use strategies for whole-number computations, with a focus on addition and subtraction

Develop fluency with basic number combinations for addition and subtraction

Use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators

Algebra

Understand patterns, relations, and functions

Sort, classify, and order objects by size, number, and other properties

Recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from one representation to another

Analyze how both repeating and growing patterns are generated

Represent and analyze mathematical situations

Illustrate general principles and properties of operations, such as commutativity, using specific numbers

Use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations

Use mathematical models to represent and understand quantitative relationships

Model situations that involve the addition and subtraction of whole numbers, using objects, pictures, and symbols

Analyze change in various contexts

Describe qualitative change, such as a student's growing taller

Describe quantitative change, such as a student's growing two inches in one year

Geometry

Analyze characteristics and properties of two- and three-dimensional geometric shapes

Recognize, name, build, draw, compare, and sort two- and three-dimensional shapes

Describe attributes and parts of two- and three-dimensional shapes

Investigate and predict the results of putting together and taking apart two- and three-dimensional shapes

Specify locations and describe spatial relationships

Describe, name, and interpret relative positions in space and apply ideas about relative position

Describe, name, and interpret direction and distance in navigating space and apply ideas about direction and distance

Find and name locations with simple relationships such as 'near to' and in coordinate systems such as maps

Apply transformations and use symmetry to analyze mathematical situations

Recognize and apply slides, flips, and turns

Recognize and create shapes that have symmetry

Use visualization, spatial reasoning, and geometric modeling to solve problems

Create mental images of geometric shapes using spatial memory and spatial visualization

Recognize and represent shapes from different perspectives

Relate ideas in geometry to ideas in number and measurement

Recognize geometric shapes and structures in the environment and specify their location

Measurement

Understand measurable attributes of objects and the units, systems, and processes of measurement

Recognize the attributes of length, volume, weight, area, and time

Compare and order objects according to these attributes

Understand how to measure using nonstandard and standard units

Select an appropriate unit and tool for the attribute being measured

Apply appropriate techniques, tools, and formulas to determine measurements

Measure with multiple copies of units of the same size, such as paper clips laid end to end

Use repetition of a single unit to measure something larger than the unit, for instance, measuring the length of a room with a single meterstick

Use tools to measure

Develop common referents for measures to make comparisons and estimates

Data analysis and probability

Formulate questions

Pose questions and gather data about themselves and their surroundings

Sort and classify objects according to their attributes and organize data about the objects

Represent data using concrete objects, pictures, and graphs

Select and use appropriate statistical methods to analyze data

Describe parts of the data and the set of data as a whole to determine what the data show

Develop and evaluate inferences and predictions that are based on data

Discuss events related to students' experiences as likely or unlikely

Understand and apply basic concepts of probability

Understand and apply basic concepts of probability

Problem solving

Build new mathematical knowledge through problem solving

Solve problems that arise in mathematics and in other contexts

Apply and adapt a variety of appropriate strategies to solve problems

Monitor and reflect on the process of mathematical problem solving

Reasoning and proof

Recognize reasoning and proof as fundamental aspects of mathematics

Make and investigate mathematical conjectures

Develop and evaluate mathematical arguments and proofs

Select and use various types of reasoning and methods of proof

Communication

Organize and consolidate their mathematical thinking through communication

Communicate their mathematical thinking coherently and clearly to peers, teachers, and others

Analyze and evaluate the mathematical thinking and strategies of others

Connections

Recognize and use connections among mathematical ideas

Understand how mathematical ideas interconnect and build on one another to produce a coherent whole

Recognize and apply mathematics in contexts outside of mathematics

Representation

Create and use representations to organize, record, and communicate mathematical ideas

Select, apply, and translate among mathematical representations to solve problems

Use representations to model and interpret physical, social, and mathematical phenomena

Understand the place-value structure of the base-ten number system and be able to represent and compare whole numbers and decimals

Recognize equivalent representations for the same number and generate them by decomposing and composing numbers

Develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers

Use models, benchmarks, and equivalent forms to judge the size of fractions

Recognize and generate equivalent forms of commonly used fractions, decimals, and percents

Explore numbers less than 0 by extending the number line and through familiar applications

Describe classes of numbers according to characteristics such as the nature of their factors

Understand meanings of operations

Understand various meanings of multiplication and division

Understand the effects of multiplying and dividing whole numbers

Identify and use relationships between operations, such as division as the inverse of multiplication, to solve problems

Understand and use properties of operations, such as the distributivity of multiplication over addition

Compute fluently and make reasonable estimates

Develop fluency with basic number combinations for multiplication and division and use these combinations to mentally compute related problems, such as 30 x 50

Develop fluency in adding, subtracting, multiplying, and dividing whole numbers

Develop and use strategies to estimate the results of whole-number computations and to judge the reasonableness of such results

Develop and use strategies to estimate computations involving fractions and decimals in situations relevant to students' experience

Use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals

Select appropriate methods and tools for computing with whole numbers from among mental computation, estimation, calculators, and paper and pencil according to the context and nature of the computation and use the selected method or tools

Algebra

Understand patterns, relations, and functions

Describe, extend, and make generalizations about geometric and numeric patterns

Represent and analyze patterns and functions, using words, tables, and graphs

Represent and analyze mathematical situations

Identify such properties as commutativity, associativity, and distributivity and use them to compute with whole numbers

Represent the idea of a variable as an unknown quantity using a letter or a symbol

Express mathematical relationships using equations

Use mathematical models to represent and understand quantitative relationships

Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions

Analyze change in various contexts

Investigate how a change in one variable relates to a change in a second variable

Identify and describe situations with constant or varying rates of change and compare them

Geometry

Analyze characteristics and properties of two- and three-dimensional geometric shapes

Identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes

Classify two- and three-dimensional shapes according to their properties and develop definitions of classes of shapes such as triangles and pyramids

Investigate, describe, and reason about the results of subdividing, combining, and transforming shapes

Explore congruence and similarity

Make and test conjectures about geometric properties and relationships and develop logical arguments to justify conclusions

Specify locations and describe spatial relationships

Describe location and movement using common language and geometric vocabulary

Make and use coordinate systems to specify locations and to describe paths

Find the distance between points along horizontal and vertical lines of a coordinate system

Apply transformations and use symmetry to analyze mathematical situations

Predict and describe the results of sliding, flipping, and turning two-dimensional shapes

Describe a motion or a series of motions that will show that two shapes are congruent

Identify and describe line and rotational symmetry in two- and three-dimensional shapes and designs

Use visualization, spatial reasoning, and geometric modeling to solve problems

Build and draw geometric objects

Create and describe mental images of objects, patterns, and paths

Identify and build a three-dimensional object from two-dimensional representations of that object

Identify and draw a two-dimensional representation of a three-dimensional object

Use geometric models to solve problems in other areas of mathematics, such as number and measurement

Recognize geometric ideas and relationships and apply them to other disciplines and to problems that arise in the classroom or in everyday life

Measurement

Understand measurable attributes of objects and the units, systems, and processes of measurement

Understand such attributes as length, area, weight, volume, and size of angle and select the appropriate type of unit for measuring each attribute

Understand the need for measuring with standard units and become familiar with standard units in the customary and metric systems

Carry out simple unit conversions, such as from centimeters to meters, within a system of measurement

Understand that measurements are approximations and how differences in units affect precision

Explore what happens to measurements of a two-dimensional shape such as its perimeter and area when the shape is changed in some way

Apply appropriate techniques, tools, and formulas to determine measurements

Develop strategies for estimating the perimeters, areas, and volumes of irregular shapes

Select and apply appropriate standard units and tools to measure length, area, volume, weight, time, temperature, and the size of angles

Select and use benchmarks to estimate measurements

Develop, understand, and use formulas to find the area of rectangles and related triangles and parallelograms

Develop strategies to determine the surface areas and volumes of rectangular solids

Data analysis and probability

Formulate questions

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

Collect data using observations, surveys, and experiments

Represent data using tables and graphs such as line plots, bar graphs, and line graphs

Recognize the differences in representing categorical and numerical data

Select and use appropriate statistical methods to analyze data

Describe the shape and important features of a set of data and compare related data sets, with an emphasis on how the data are distributed

Use measures of center, focusing on the median, and understand what each does and does not indicate about the data set

Compare different representations of the same data and evaluate how well each representation shows important aspects of the data

Develop and evaluate inferences and predictions that are based on data

Propose and justify conclusions and predictions that are based on data and design studies to further investigate the conclusions or predictions

Understand and apply basic concepts of probability

Describe events as likely or unlikely and discuss the degree of likelihood using such words as certain, equally likely, and impossible

Predict the probability of outcomes of simple experiments and test the predictions

Understand that the measure of the likelihood of an event can be represented by a number from 0 to 1

Problem solving

Build new mathematical knowledge through problem solving

Solve problems that arise in mathematics and in other contexts

Apply and adapt a variety of appropriate strategies to solve problems

Monitor and reflect on the process of mathematical problem solving

Reasoning and proof

Recognize reasoning and proof as fundamental aspects of mathematics

Make and investigate mathematical conjectures

Develop and evaluate mathematical arguments and proofs

Select and use various types of reasoning and methods of proof

Communication

Organize and consolidate their mathematical thinking through communication

Communicate their mathematical thinking coherently and clearly to peers, teachers, and others

Analyze and evaluate the mathematical thinking and strategies of others

Use the language of mathematics to express mathematical ideas precisely

Connections

Recognize and use connections among mathematical ideas

Understand how mathematical ideas interconnect and build on one another to produce a coherent whole

Recognize and apply mathematics in contexts outside of mathematics

Representation

Create and use representations to organize, record, and communicate mathematical ideas

Select, apply, and translate among mathematical representations to solve problems

Use representations to model and interpret physical, social, and mathematical phenomena

Work flexibly with fractions, decimals, and percents to solve problems

Compare and order fractions, decimals, and percents efficiently and find their approximate locations on a number line

Develop meaning for percents greater than 100 and less than 1

Understand and use ratios and proportions to represent quantitative relationships

Develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation

Use factors, multiples, prime factorization, and relatively prime numbers to solve problems

Develop meaning for integers and represent and compare quantities with them

Understand meanings of operations

Understand the meaning and effects of arithmetic operations with fractions, decimals, and integers

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

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

Compute fluently and make reasonable estimates

Select appropriate methods and tools for computing with fractions and decimals from among mental computation, estimation, calculators or computers, and paper and pencil, depending on the situation, and apply the selected methods

Develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use

Develop and use strategies to estimate the results of rational-number computations and judge the reasonableness of the results

Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios

Algebra

Understand patterns, relations, and functions

Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules

Relate and compare different forms of representation for a relationship

Identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations

Represent and analyze mathematical situations

Develop an initial conceptual understanding of different uses of variables

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

Use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships

Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations

Use mathematical models to represent and understand quantitative relationships

Model and solve contextualized problems using various representations, such as graphs, tables, and equations

Analyze change in various contexts

Use graphs to analyze the nature of changes in quantities in linear relationships

Geometry

Analyze characteristics and properties of two- and three-dimensional geometric shapes

Precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties

Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects

Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship

Specify locations and describe spatial relationships

Use coordinate geometry to represent and examine the properties of geometric shapes

Use coordinate geometry to examine special geometric shapes, such as regular polygons or those with pairs of parallel or perpendicular sides

Apply transformations and use symmetry to analyze mathematical situations

Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling

Examine the congruence, similarity, and line or rotational symmetry of objects using transformations

Use visualization, spatial reasoning, and geometric modeling to solve problems

Draw geometric objects with specified properties, such as side lengths or angle measures

Use two-dimensional representations of three-dimensional objects to visualize and solve problems such as those involving surface area and volume

Use visual tools such as networks to represent and solve problems

Use geometric models to represent and explain numerical and algebraic relationships

Recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life

Measurement

Understand measurable attributes of objects and the units, systems, and processes of measurement

Understand both metric and customary systems of measurement

Understand relationships among units and convert from one unit to another within the same system

Understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume

Apply appropriate techniques, tools, and formulas to determine measurements

Use common benchmarks to select appropriate methods for estimating measurements

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

Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes

Develop strategies to determine the surface area and volume of selected prisms, pyramids, and cylinders

Solve problems involving scale factors, using ratio and proportion

Solve simple problems involving rates and derived measurements for such attributes as velocity and density

Data analysis and probability

Formulate questions

Formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population

Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots

Select and use appropriate statistical methods to analyze data

Find, use, and interpret measures of center and spread, including mean and interquartile range

Discuss and understand the correspondence between data sets and their graphical representations, especially histograms, stem-and-leaf plots, box plots, and scatterplots

Develop and evaluate inferences and predictions that are based on data

Use observations about differences between two or more samples to make conjectures about the populations from which the samples were taken

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

Use conjectures to formulate new questions and plan new studies to answer them

Understand and apply basic concepts of probability

Understand and use appropriate terminology to describe complementary and mutually exclusive events

Use proportionality and a basic understanding of probability to make and test conjectures about the results of experiments and simulations

Compute probabilities for simple compound events, using such methods as organized lists, tree diagrams, and area models

Problem solving

Build new mathematical knowledge through problem solving

Solve problems that arise in mathematics and in other contexts

Apply and adapt a variety of appropriate strategies to solve problems

Monitor and reflect on the process of mathematical problem solving

Recognize reasoning and proof as fundamental aspects of mathematics

Reasoning and proof

Make and investigate mathematical conjectures

Develop and evaluate mathematical arguments and proofs

Select and use various types of reasoning and methods of proof

Communication

Organize and consolidate their mathematical thinking through communication

Communicate their mathematical thinking coherently and clearly to peers, teachers, and others

Analyze and evaluate the mathematical thinking and strategies of others

Use the language of mathematics to express mathematical ideas precisely

Connections

Recognize and use connections among mathematical ideas

Understand how mathematical ideas interconnect and build on one another to produce a coherent whole

Recognize and apply mathematics in contexts outside of mathematics

Representation

Create and use representations to organize, record, and communicate mathematical ideas

Select, apply, and translate among mathematical representations to solve problems

Use representations to model and interpret physical, social, and mathematical phenomena

Develop a deeper understanding of very large and very small numbers and of various representations of them

Compare and contrast the properties of numbers and number systems, including the rational and real numbers, and understand complex numbers as solutions to quadratic equations that do not have real solutions

Understand vectors and matrices as systems that have some of the properties of the real-number system

Use number-theory arguments to justify relationships involving whole numbers

Understand meanings of operations

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

Develop an understanding of properties of, and representations for, the addition and multiplication of vectors and matrices

Develop an understanding of permutations and combinations as counting techniques

Compute fluently and make reasonable estimates

Develop fluency in operations with real numbers, vectors, and matrices, using mental computation or paper-and-pencil calculations for simple cases and technology for more-complicated cases

Judge the reasonableness of numerical computations and their results

Algebra

Understand patterns, relations, and functions

Generalize patterns using explicitly defined and recursively defined functions

Understand relations and functions and select, convert flexibly among, and use various representations for them

Analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior

Understand and perform transformations such as arithmetically combining, composing, and inverting commonly used functions, using technology to perform such operations on more-complicated symbolic expressions

Understand and compare the properties of classes of functions, including exponential, polynomial, rational, logarithmic, and periodic functions

Interpret representations of functions of two variables

Represent and analyze mathematical situations

Understand the meaning of equivalent forms of expressions, equations, inequalities, and relations

Write equivalent forms of equations, inequalities, and systems of equations and solve them with fluency, mentally or with paper and pencil in simple cases and using technology in all cases

Use symbolic algebra to represent and explain mathematical relationships

Use a variety of symbolic representations, including recursive and parametric equations, for functions and relations

Judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by technology

Use mathematical models to represent and understand quantitative relationships

Identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationships

Use symbolic expressions, including iterative and recursive forms, to represent relationships arising from various contexts

Draw reasonable conclusions about a situation being modeled

Analyze change in various contexts

Approximate and interpret rates of change from graphical and numerical data

Geometry

Analyze characteristics and properties of two- and three-dimensional geometric shapes

Analyze properties and determine attributes of two- and three-dimensional objects

Explore relationships (including congruence and similarity) among classes of two- and three-dimensional geometric objects, make and test conjectures about them, and solve problems involving them

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

Use trigonometric relationships to determine lengths and angle measures

Specify locations and describe spatial relationships

Use Cartesian coordinates and other coordinate systems, such as navigational, polar, or spherical systems, to analyze geometric situations

Investigate conjectures and solve problems involving two- and three-dimensional objects represented with Cartesian coordinates

Apply transformations and use symmetry to analyze mathematical situations

Understand and represent translations, reflections, rotations, and dilations of objects in the plane by using sketches, coordinates, vectors, function notation, and matrices

Use various representations to help understand the effects of simple transformations and their compositions

Use visualization, spatial reasoning, and geometric modeling to solve problems

Draw and construct representations of two- and three-dimensional geometric objects using a variety of tools

Visualize three-dimensional objects and spaces from different perspectives and analyze their cross sections

Use vertex-edge graphs to model and solve problems

Use geometric models to gain insights into, and answer questions in, other areas of mathematics

Use geometric ideas to solve problems in, and gain insights into, other disciplines and other areas of interest such as art and architecture

Measurement

Understand measurable attributes of objects and the units, systems, and processes of measurement

Make decisions about units and scales that are appropriate for problem situations involving measurement

Apply appropriate techniques, tools, and formulas to determine measurements

Analyze precision, accuracy, and approximate error in measurement situations

Understand and use formulas for the area, surface area, and volume of geometric figures, including cones, spheres, and cylinders

Apply informal concepts of successive approximation, upper and lower bounds, and limit in measurement situations

Use unit analysis to check measurement computations

Data analysis and probability

Formulate questions

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

Know the characteristics of well-designed studies, including the role of randomization in surveys and experiments

Understand the meaning of measurement data and categorical data, of univariate and bivariate data, and of the term variable

Understand histograms, parallel box plots, and scatterplots and use them to display data

Compute basic statistics and understand the distinction between a statistic and a parameter

Select and use appropriate statistical methods to analyze data

For univariate measurement data, be able to display the distribution, describe its shape, and select and calculate summary statistics

For bivariate measurement data, be able to display a scatterplot, describe its shape, and determine regression coefficients, regression equations, and correlation coefficients using technological tools

Display and discuss bivariate data where at least one variable is categorical

Recognize how linear transformations of univariate data affect shape, center, and spread

Identify trends in bivariate data and find functions that model the data or transform the data so that they can be modeled

Develop and evaluate inferences and predictions that are based on data

Use simulations to explore the variability of sample statistics from a known population and to construct sampling distributions

Understand how sample statistics reflect the values of population parameters and use sampling distributions as the basis for informal inference

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

Understand how basic statistical techniques are used to monitor process characteristics in the workplace

Understand and apply basic concepts of probability

Understand the concepts of sample space and probability distribution and construct sample spaces and distributions in simple cases

Use simulations to construct empirical probability distributions

Compute and interpret the expected value of random variables in simple cases

Understand the concepts of conditional probability and independent events

Understand how to compute the probability of a compound event

Problem solving

Build new mathematical knowledge through problem solving

Solve problems that arise in mathematics and in other contexts

Apply and adapt a variety of appropriate strategies to solve problems

Monitor and reflect on the process of mathematical problem solving

Reasoning and proof

Recognize reasoning and proof as fundamental aspects of mathematics

Make and investigate mathematical conjectures

Develop and evaluate mathematical arguments and proofs

Select and use various types of reasoning and methods of proof

Communication

Organize and consolidate their mathematical thinking through communication

Communicate their mathematical thinking coherently and clearly to peers, teachers, and others

Analyze and evaluate the mathematical thinking and strategies of others

Use the language of mathematics to express mathematical ideas precisely

Connections

Recognize and use connections among mathematical ideas

Understand how mathematical ideas interconnect and build on one another to produce a coherent whole

Recognize and apply mathematics in contexts outside of mathematics

Representation

Create and use representations to organize, record, and communicate mathematical ideas

Select, apply, and translate among mathematical representations to solve problems

Use representations to model and interpret physical, social, and mathematical phenomena