Arkansas K–6 mathematics standards

Use objects, fingers, mental images, drawings, sounds, acting out situations, or verbal explanations to represent addition and subtraction from 0 to 10.

Use objects or drawings to decompose numbers less than or equal to 10 into pairs in more than one way, recording each decomposition.

Use a drawing or equation to find the number that makes 10 when added to a given number.

Use manipulatives and various strategies to fluently add and subtract within 10.

Solve real-world problems involving addition and subtraction within 10, using objects, drawings, or equations to represent the problem.

Collect, sort, and organize data into two or three categories, using real-object graphs and picture graphs.

Describe the positions of objects and geometric shapes in the environment.<ul><li>Terms include: inside, outside, between, above, below, near, far, under, over, up, down, behind, in front of, next to, to the left of, and to the right of</li></ul>

Name shapes correctly regardless of their orientation or overall size.<ul><li>Shapes include: squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres</li></ul>

Identify two-dimensional attributes of three-dimensional objects.

Analyze and sort a variety of two and three-dimensional shapes using informal language to describe their similarities, differences, and other attributes.

Compose and draw shapes found in the world using objects (e.g., straws, toothpicks, clay balls).

Make direct comparisons of the length, capacity, weight, and temperature of objects, recognizing which object is shorter/longer, lighter/heavier, warmer/cooler, or holds more.

Understand concepts of time, recognizing that clocks and calendars are tools that measure time.<ul><li>Concepts of time include: morning, afternoon, evening, today, yesterday, tomorrow, day, week, month, and year</li></ul>

Identify pennies and dimes by name and value.

Count to 100 by ones and tens; count forward by ones from any given number up to 100.

Count a set of objects up to 20 using one-to-one correspondence, demonstrating that the last number stated indicates the number of objects in the set regardless of the arrangement.

Identify the position of objects in a set using ordinal numbers (first, second, third, etc.).

Identify quickly a number of items in a set from 0 to 10 without counting.

Read, write, and represent whole numbers from 0 to 20.

Show equivalent forms of whole numbers up to 20 as groups of tens and ones, using manipulatives and drawings.

Use matching and counting strategies to compare the number of objects in one group to the number of objects in another group (0 to 10) using the terms greater than, less than, or equal.

Compare two whole numbers, using the terms greater than, less than, or equal.

Add and subtract fluently within 10 with mastery by the end of first grade.

Use computational fluency to add and subtract within 20 using manipulatives and/or a variety of strategies.

Apply properties of operations to add and subtract within 20.

Use concrete models or drawings to add within 100, including a two-digit number and a one-digit number as well as a two-digit number and a multiple of ten; relate strategy used to a written expression or equation and explain reasoning.

Demonstrate the relationship between addition and subtraction by solving problems, using an inverse operation.

Solve real-world problems involving addition and subtraction within 20.<ul><li>Problem types include: adding to, taking from, putting together, taking apart, and comparing with unknowns present throughout the addition and subtraction problem.</li></ul>

Solve real-world problems involving addition of three whole numbers whose sum is less than or equal to 20.

Apply understanding of the equal sign to determine if equations involving addition and subtraction are true or false.

Determine the unknown whole number in an addition or subtraction equation relating three whole numbers.

Organize, represent, and interpret data with up to three categories (e.g., tally tables, picture graphs, bar graphs).

Ask and answer questions about the total number represented such as how many in each category and how many more or less in one category compared to another.

Understand the difference between defining attributes (e.g., triangles are closed and three-sided shapes) and non-defining attributes (e.g., color, orientation, overall size), using that understanding to build and draw shapes that exhibit defining attributes.

Create a composite shape using two-dimensional or three-dimensional shapes.<ul><li>Two-dimensional include: rectangle, square, trapezoid, triangle, hexagon, half circle, and quarter circle</li><li>Three-dimensional include: cube, rectangular prism, cone, and cylinder</li></ul>

Express the length of an object as a whole number of units by laying multiple copies of a shorter object end-to-end, understanding that the length of one object is equal to the number of same-size units that span the object with no gaps or overlaps.

Order three objects by their length, indirectly comparing the lengths of two objects by using a third object.

Tell and write time to the nearest hour and half hour using analog clocks; understand how to read hours and minutes using digital clocks.

Identify coins by name and value, including penny, nickel, dime, and quarter.

Count collections of like coins including pennies, nickels, and dimes to determine their total value up to 100 cents.

Count forward and back within 120 by ones and tens from any given whole number.

Skip count forward by multiples of fives within 120.

Explain the place value of ones and tens in two-digit numbers, using concrete models, diagrams, numbers, or words.

Read, write, and represent whole numbers up to 120, using concrete models or drawings, word form, base ten numerals, and expanded form.

Use concrete models or drawings to subtract multiples of 10 from multiples of 10 (within the range of 10-90), relate the strategy to a written expression or equation, and explain the reasoning used to solve.

Use mental strategies to find 10 more or 10 less than a given two-digit number.

Compare two two-digit numbers using symbols (<, =, >) based on the value of tens and ones in the given numbers.

Partition circles and rectangles into two and four equal shares, describing the shares using the words halves, fourths, and quarters; understand that decomposing into more equal pieces creates smaller pieces.

Use mental strategies to fluently add and subtract within 20 with mastery by the end of second grade.

Use computational fluency to add and subtract within 100 using strategies based on place value, properties of operations, or the relationship between addition and subtraction.

Add up to four two-digit numbers with sums not exceeding 100 using strategies based on place value and properties of operations.

Use a number line to solve addition and subtraction problems within 100.

Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

Use concrete models, drawings, or equations to solve addition and subtraction problems within 1000.

Solve one and two-step real-world problems involving addition and subtraction within 100 in situations of adding to, taking from, putting together, taking apart, and comparing unknowns in all positions.

Determine whether a group of objects up to 20 has an odd or even number of members; write an equation to express an even number as a sum of two equal addends.

Use bar graphs, picture graphs, and line plots to organize and represent data, interpreting data with up to four categories.

Ask and answer simple put together, take apart, and compare problems, using information presented in the bar graphs, picture graphs, and line plots.

Identify, describe, and draw two-dimensional shapes.<ul><li>Shapes include: triangles, regular pentagons, regular hexagons, and quadrilaterals (square, rectangle, trapezoid, parallelogram, rhombus)</li></ul>

Identify and describe three-dimensional shapes based on the shape, number of faces, number of edges, and number of vertices.<ul><li>Shapes include: rectangular prisms, cubes, and square-based pyramids</li></ul>

Select appropriate measurement tools to estimate and measure the length of an object to the nearest whole inch or whole centimeters.

Demonstrate how the length of an object does not change, regardless of the units used to measure it, by measuring the length of an object twice; use two different length units, describing how the two measurements relate to the size of the chosen unit.

Measure to determine how much longer or shorter one object is than another, expressing the length difference in terms of a standard length whole unit.

Solve real-world problems involving lengths of the same units, using addition and subtraction within 100.

Solve real-world and mathematical problems to find the perimeter of polygons.

Partition a rectangle into rows and columns of same-size squares, counting the total number of squares to find the area.

Using an analog clock, tell and write time to the nearest five minutes using colon notation and indicate a.m. or p.m.

Describe relationships of time.<ul><li>Times include: seconds in a minute; minutes in an hour; hours in a day; days in a week; and days, weeks, and months in a year</li></ul>

Solve real-world problems involving addition and subtraction of time intervals in half hours or hours.

Count collections of mixed coins and solve real-world problems involving quarters, dimes, nickels, and pennies within 99¢ and whole dollar amounts.

Count within 1,000 forwards and backwards by ones, tens, and hundreds from any given number.

Identify the value of hundreds, tens, and ones place in a three-digit number.

Read, write, and represent whole numbers up to 1,000 using concrete models or drawings, number names, and a variety of expanded forms.

Mentally add 10 or 100 to a given number in the range of 100-900 and mentally subtract 10 or 100 from a given number in the range of 100-900.

Compare two three-digit numbers using symbols (<, =, >) based on the value of hundreds, tens, and ones in the given numbers.

Partition circles and rectangles into two, three, or four equal shares, describing the shares using the words halves, thirds, and fourths (or quarters).

Recognize that equal shares of identical wholes need not have the same shape.

Use computational fluency to add and subtract three-digit whole numbers, using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

Use basic fact fluency to multiply and divide whole numbers with mastery by the end of third grade.<ul><li>Knowing all products with factors up to and including 12 and the corresponding division facts from the products with factors up to and including 12.</li><li>Using strategies such as the relationship between multiplication and division (e.g., Knowing that 8∙5=40, one knows 40 ÷ 5 =8) or properties of operations.</li></ul>

Apply properties of operations as strategies to multiply and divide.<ul><li>Properties include: Distributive, Commutative, and Associative Properties of Multiplication</li></ul>

Use strategies to multiply one-digit numbers by multiples of 10 ranging from 10-90; strategies are based on place value and properties of operations (e.g., 9∙80,5∙60).

Identify arithmetic patterns including, but not limited to, patterns in an addition or multiplication table, explaining use of properties of operations appropriate to the pattern.

Solve real-world problems using multiplication and division within 100 involving equal groups, arrays, partitive and measurement division.

Solve two-step real-world situations using addition, subtraction, multiplication, and division, representing these problems using equations with a symbol standing for an unknown quantity.

Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

Understand division as an unknown-factor problem.

Represent a data set with multiple categories, using a scaled picture graph, scaled bar graph, and a line plot.

Solve one and two-step problems, using categorical data represented with a scaled picture graph, scaled bar graph, and a line plot.

Understand that quadrilaterals in different categories may share attributes; those attributes (e.g., four equivalent sides) can define a larger category (e.g., quadrilaterals) or subcategory (e.g., rhombus and square).

Identify perpendicular and parallel lines, as well as right angles in two-dimensional shapes and real-world surroundings or objects.

Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, identifying and/or drawing examples of quadrilaterals that do not belong to any of these subcategories.

Measure lengths of objects to the nearest half and quarter inch, using a ruler.

Describe area as the number of unit squares that cover a plane figure without gaps and overlaps.

Find the area of a rectangle with whole number side lengths by modeling with unit squares and multiplying the side lengths to show the results are the same.

Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real-world and mathematical problems.

Measure and estimate liquid volumes and masses of objects using standard units.

Solve one-step real-world problems involving liquid volumes and masses of objects in the same units, using all four operations.

Tell and write time to the nearest minute, using analog clocks.

Solve word problems involving addition and subtraction of time intervals in minutes.

Round four-digit whole numbers to the nearest 10 or 100, using place value understanding.

Identify the value of thousands, hundreds, tens, and ones place in a four-digit number.

Read and write whole numbers up to 10,000, using base ten numerals, word form, and a variety of expanded forms.

Compare two four-digit numbers using symbols (<, =, >) based on the value of thousands, hundreds, tens, and ones in the given numbers.

Compare two fractions with the same numerator or denominator by reasoning about their size based on the same whole; use symbols (<, =, >) and justify the conclusion using visual fraction models, concrete objects, or words.

Identify fractions as parts of a whole and parts of a collection or set.<ul><li>Fractions include: denominators 2, 3, 4, 6, and 8</li></ul>

Partition squares, regular hexagons, and equilateral triangles into parts with equal shares, explaining the shares of each part as a unit fraction of the whole.<ul><li>Fractions include: denominators 2, 3, 4, 6, and 8</li></ul>

Identify and represent a unit fraction as a number on the number line.<ul><li>Fractions include: denominators 2, 3, 4, 6, and 8</li></ul>

Identify and represent a non-unit fraction as a number on the number line, including fractions greater than one.<ul><li>Fractions include: denominators 2, 3, 4, 6, and 8</li></ul>

Decompose and compose a non-unit fraction a/b as the quantity formed by the sum of unit fractions.<ul><li>Fractions include: denominators 2, 3, 4, 6, and 8</li></ul>

Use number lines and visual models to recognize and generate equivalent fractions, explaining how they are equivalent in real-world and mathematical situations.<ul><li>Fractions include: denominators 2, 3, 4, 6, and 8</li></ul>

Find the factor pairs for a given number in the range of 1-100, identifying whether a number is prime or composite; determine whether a given whole number in the range of 1-100 is a multiple of a given one-digit number.

Use computational fluency to add and subtract whole numbers up to 1,000,000 by using strategies and algorithms, including the standard algorithm, with mastery by the end of fourth grade.

Use strategies based on place value and the properties of operations to multiply four-digit by one-digit whole numbers and two two-digit whole numbers.

Use strategies based on place value, the properties of operations, and the relationship between multiplication and division to divide whole numbers with four-digits by one-digit divisors; quotients should be with and without whole number remainders.

Add and subtract fractions, including mixed numbers, with like denominators, using visual fraction models and equations.<ul><li>Fractions include: denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100</li></ul>

Multiply a fraction by a whole number using visual fraction models and equations.<ul><li>Fractions include: denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100</li></ul>

Solve real-world problems involving multiplicative comparison, using drawings and/or equations with a symbol for the unknown number, and distinguish between multiplicative comparison and additive comparison.

Solve multi-step, real-world problems posed with whole numbers and having whole-number answers, using addition, subtraction, multiplication, and division; include problems in which remainders must be interpreted and represent these problems using equations with symbols standing for the unknown quantity.

Solve real-world problems involving the addition and subtraction of fractions; include mixed numbers with like denominators, using visual fraction models or equations.<ul><li>Fractions include: denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100</li></ul>

Solve real-word problems involving the multiplication of a fraction by a whole number using visual fraction models or equations.<ul><li>Fractions include: denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100</li></ul>

Generate a number or shape pattern that follows a given rule, identifying apparent features of the pattern that are not explicit in the rule itself.

Collect and interpret data from observations, surveys, and experiments; represent data using frequency tables and scaled bar graphs.

Use a line plot to display a data set of measurements in fractions of a unit, solving problems involving addition and subtraction of fractions with like denominators using data presented in line plots.

Identify angles as geometric shapes that are formed where two rays share a common endpoint, understanding that angles are measured with reference to a circle so that an angle that turns through a 1/360 of a circle is called a "one-degree angle" and an angle that turns through n one-degree angles is said to have an angle measure of n degree.

Measure angles in whole-number degrees, using a protractor, drawing angles of specified measure.

Solve real-word problems finding unknown angle measures, using addition and subtraction when an angle is decomposed into non-overlapping parts.

Identify and draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines, identifying these in quadrilaterals and triangles.

Classify two-dimensional figures based on the presence or absence of parallel lines, perpendicular lines, or angles of a specified size, involving quadrilaterals and triangles.<ul><li>Shapes include: quadrilaterals (trapezoid, parallelogram, rectangle, square, rhombus) and triangles (right, acute, obtuse)</li></ul>

Identify and/or draw lines of symmetry for a two-dimensional figure.

Apply the area and perimeter formulas for rectangles and figures composed of two or more rectangles in real-world situations.

Convert measurements of length, weight/mass, and liquid volume within the same system of measurement, metric and customary, expressing measurements from a larger unit in terms of a smaller unit.

Solve real-world problems involving time intervals that may cross the hour.

Solve real-world problems involving addition and subtraction of money, including the ability to make change.

Solve real-world problems involving distances, liquid volume, and masses of objects, including problems that require expressing measurements given in a larger unit in terms of a smaller unit.

Recognize that a digit in a given place represents ten times what it represents in the place to its right.

Read and write whole numbers up to 1,000,000 using base ten numerals, word form, and a variety of expanded forms.

Use place value understanding to round five-digit and six-digit whole numbers to any place.

Compare two five-digit whole numbers and six-digit whole numbers, using symbols (<, =, >) to record the results of comparisons.

Compare two fractions with different numerators and different denominators using symbols (<, =, >) to record the results of comparisons (e.g., by creating common denominators or numerators or by comparing to a benchmark of 0, ½, 1).

Compare two decimals to the hundredths place, using symbols (<, =, >) to record the results of comparisons.

Decompose fractions, including fractions greater than one and mixed numbers, into unit fractions, using concrete models, drawings, and/or the number line.<ul><li>Fractions include denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.</li></ul>

Explain why a fraction a/b is equivalent to a fraction (n·a)/(n·b), using visual fraction models, generating equivalent fractions using the principle a/b = (n·a)/(n·b).<ul><li>Fractions include denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.</li></ul>

Add two fractions with denominators of 10 and 100 by expressing the denominator of 10 as an equivalent fraction with a denominator of 100.

Apply decimal notation for fractions with denominators 10 or 100.

Use computational fluency to multiply multi-digit whole numbers by using strategies and algorithms, including the standard algorithm, with mastery by the end of fifth grade.

Calculate whole number quotients of whole numbers with up to four-digit dividends and two-digit divisors using strategies based on place value, properties of operations, divisibility rules, and the relationship between multiplication and division.

Add and subtract decimals to the hundredths using concrete models or drawings and strategies based on place value, properties of operations, or the relationship between addition and subtraction.

Multiply and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, or the relationship between multiplication and division.

Add and subtract fractions with like and unlike denominators by using equivalent fractions [a/b = (n·a)/(n·b)] to create common denominators; include real-world problems.<ul><li>Fractions include: mixed numbers</li></ul>

Interpret and solve fractions as division problems, (a/b = a÷b), where a and b are natural numbers.

Use visual models and equations to multiply whole numbers by fractions and fractions by fractions, including mixed numbers and fractions greater than one.

Apply previous understanding of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

Solve and create real-world problems involving multiplication of fractions and mixed numbers.

Solve real-world problems involving the division of natural numbers leading to answers in the form of fractions or mixed numbers using visual models and equations.

Solve real-world problems involving the division of unit fractions by whole numbers and whole numbers by unit fractions, using visual fraction models and equations.

Evaluate numerical expressions with parentheses or brackets and exponents with the base of ten, using the Order of Operations.

Write simple expressions that record calculations with numbers, interpreting numerical expressions without evaluating them.

Generate two numerical patterns given two rules, identifying the relationship between the corresponding terms by graphing the terms in the first quadrant of the coordinate grid.

Collect and interpret data from observations, surveys, and experiments; represent data using frequency tables, scaled bar graphs, and scaled line graphs.

Use a line plot to display a data set of measurements in fractions of a unit solving problems involving all four operations with fractions (excluding division of a fraction by fraction) using data presented in line plots.

Classify two-dimensional figures in a hierarchy based on properties with the focus on quadrilaterals and triangles when teaching hierarchies.<ul><li>Shapes to include: quadrilaterals (trapezoid, parallelogram, rectangle, square, rhombus, kite) and triangles (right, acute, obtuse, scalene, isosceles, equilateral)</li></ul>

Find the area of a rectangle with fractional and/or mixed number side lengths by using models and multiplying the fractional side lengths showing that both strategies produce the same area.

Measure volumes by counting unit cubes using cubic cm (cm³), cubic in (in³), cubic ft (ft³), and improvised units (u³).

Solve real-world and mathematical problems involving the volume of rectangular prisms with whole number side lengths by applying the formulas (V = l·w·h or V = B·h) and the properties of operations.

Solve real-world problems by calculating volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts.

Convert among different-sized standard measurement units within the same system, including both the metric and customary systems, and solve multi-step, real-world problems using conversions.

Graph points with whole number coordinates on a coordinate plane in the first quadrant, explaining how the coordinates relate to the horizontal and vertical axes to describe the location of points in the plane.

Represent real-world and mathematical problems by graphing points in the first quadrant on a coordinate plane, interpreting coordinate values of points in the context of the situation.

Recognize that, in a multi-digit number, a digit in a given place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

Explain patterns in the number of zeros and/or the decimal point when multiplying or dividing a number by a power of 10, using whole-number exponents to denote powers of 10.

Read and write decimals to thousandths, using base-ten numerals, word form, and a variety of expanded forms.

Apply place value understanding to round decimals to any place up to the thousandths.

Compare two decimals to thousandths based on the value of the digits in each place, using symbols (<, =, >) to record the results of comparisons.

Use visual models to explain the product of multiplying a whole number by a fraction greater than and less than one.

Read and write expressions in real-world or mathematical problems in which letters stand for numbers.

Use mathematical terms to identify parts of an expression, including the names of operations, terms, factors, coefficients, variables, and constants.

Write and evaluate expressions for given values of variables, using order of operations, including expressions with whole number exponents.

Generate equivalent expressions by applying the associative, commutative, distributive, and identity properties.

Identify when two expressions are equivalent by using properties of operations including like terms.

Use substitution to determine if a given value in a specified set makes an equation or inequality true.<ul><li>Include the following inequality symbols: <,>,≤,≥,≠</li></ul>

Write and solve one-step equations in real-world and mathematical problems, involving positive rational numbers and zero.

Write, solve, and graph one-step inequalities in real-world and mathematical problems.

Find the area of triangles, quadrilaterals, and polygons by composing or decomposing to solve real-world and mathematical problems.

Apply the formulas V = lwh and V = Bh to find the volume of right rectangular prisms with fractional edge lengths to solve real-world and mathematical problems, including solving for an unknown dimension.

Construct nets of a rectangular prism, rectangular pyramid, triangular prism, and triangular pyramid, using the nets to find the surface area of these prisms.

Find and graph pairs of rational numbers in all four quadrants of the coordinate plane in real-world and mathematical problems.

Draw polygons in the coordinate plane when given coordinates for the vertices.

Use coordinates to calculate vertical and horizontal distances between points with the same x-coordinate or the same y-coordinate to solve real-world and mathematical problems.

Convert measurements within and between the metric and customary measurement systems to solve real-world and mathematical problems.

Explain positive and negative integers as being opposite values or directions and the meaning of 0 in a real-world context.

Find and plot rational numbers on horizontal and vertical number lines in real-world and mathematical problems.

Compare rational numbers, using inequalities (<,>,≤,≥,≠) and order on a number line.

Interpret the absolute value of numbers for positive or negative quantities in a real-world context.

Convert between fractions, decimals, and percents in real-world and mathematical problems.

Interpret and represent quotients of fractions.<ul><li>Fractions include all forms of fractions.</li></ul>

Solve problems involving the division of fractions in real-world and mathematical problems.<ul><li>Fractions include all forms of fractions.</li></ul>

Divide multi-digit numbers fluently in real-world and mathematical problems.

Use any standard algorithm to fluently add and subtract multi-digit decimals and fractions in real-world and mathematical problems.

Use any standard algorithm to fluently multiply and divide multi-digit decimals and fractions in real-world and mathematical problems.

Solve real-world and mathematical problems with the greatest common factor of two whole numbers less than or equal to 100.

Solve real-world and mathematical problems with the least common multiple of two whole numbers less than or equal to 12.

Use the distributive property and the greatest common factor to rewrite the sum of two whole numbers, 1 through 100.

Use precise ratio language and notation to describe a ratio as a relationship between two quantities.

Calculate unit rates to include unit pricing and constant speed.

Give examples of unit rates as a ratio that compares two quantities with different units of measure, limited to non-complex fractions.

Create various representations to compare ratios and find missing values to solve real-world and mathematical problems.

Find a percent of a quantity as a rate per 100 and solve problems involving finding the whole when given a part and the percent.

Identify the difference between statistical and non-statistical questions and write simple statistical questions that allow variable responses.

Calculate and interpret any measure of center (mean, median, and mode) of a numerical data set.

Determine which measure of center (mean or median) is more appropriate to describe the center of data and justify the choice.

Describe how the mean or median is affected by outliers of a numerical data set.

Calculate and interpret the measure of variation [range and interquartile range (IQR)] of a numerical data set.

Determine which measure of variation (range or interquartile range) is more appropriate to describe the shape; justify the choice.

Represent numerical data on a number line, histogram, and box plot.

Calculate the relative frequency of an interval of data values when given a histogram.

Interpret a box plot to answer statistical questions about a data set.