Oklahoma K–6 mathematics standards

Sort and group up to 10 objects into a set based upon characteristics such as color, size, and shape. Explain verbally what the objects have in common.

Recognize, duplicate, complete, and extend repeating, increasing, and decreasing patterns in a variety of contexts (i.e., shape, color, size, objects, sounds, movement).

Collect and organize information about objects and events in the environment.

Use categorical data to create real-object graphs and pictographs.

Draw conclusions from real-object graphs and pictographs.

Recognize squares, circles, triangles, and rectangles.

Sort two-dimensional objects using characteristics such as shape and size.

Identify attributes of two-dimensional shapes using informal and formal geometric language interchangeably, such as the number of corners/vertices and the number of sides/edges.

Use smaller two-dimensional shapes to fill in the outline of a larger two-dimensional shape.

Compose larger, undefined shapes and structures using three-dimensional objects.

Use basic shapes and spatial reasoning to represent objects in the real world.

Use words to compare objects according to length, size, weight, position, and location.

Order up to 6 objects using measurable attributes, such as length and weight.

Identify more than one shared attribute between objects, and sort objects into sets.

Compare the number of objects needed to fill two different containers.

Develop an awareness of simple time concepts within daily life, using age-appropriate vocabulary (e.g., yesterday, today, tomorrow, morning, afternoon, night).

Count aloud forward in sequence to 100 by 1s and 10s.

Recognize that a number can be used to represent how many objects are in a set up to 10.

Use ordinal numbers to represent the position of an object in a sequence up to 10.

Recognize without counting (subitize) the quantity of a small group of objects in organized and random arrangements up to 10.

Count forward, with and without objects, from any given number up to 20.

Read, write, discuss, and represent whole numbers from 0 to at least 20. Representations may include numerals, pictures, real-object and pictographs, spoken words, and manipulatives.

Find a number that is 1 more or 1 less than a given number up to 10.

Compare and order whole numbers from 0 to 10 with and without objects, using the vocabulary "more than," "less than," or "equal to."

Compose and decompose numbers up to 10 using objects and pictures.

Distribute a set of objects into at least two smaller equal sets.

Identify pennies, nickels, dimes, and quarters by name.

Identify, create, complete, and extend repeating, increasing, and decreasing patterns in a variety of contexts (e.g., quantity, numbers, or shapes).

Collect, sort, and organize data in up to three categories using representations (e.g., tally marks, tables, Venn diagrams).

Use data to create pictographs and bar graphs that demonstrate one-to-one correspondence.

Draw conclusions from pictographs and bar graphs.

Identify regular and irregular trapezoids and hexagons by pointing to the shape when given the name.

Compose larger, defined shapes using smaller two-dimensional shapes.

Compose structures with three-dimensional shapes.

Recognize three-dimensional shapes such as cubes, cones, cylinders, pyramids, and spheres.

Use nonstandard and standard measuring tools to measure the length of objects.

Illustrate that the length of an object is the number of same-size units of length that, when laid end-to-end with no gaps or overlaps, reach from one end of the object to the other.

Measure the same object/distance with units of two different lengths, and describe how and why the measurements differ.

Describe a length to the nearest whole unit using a number with standard and nonstandard units.

Use standard and nonstandard tools to identify volume/capacity. Compare and sort containers that hold more, less, or the same amount.

Tell time to the hour and half-hour (analog and digital).

Describe and measure calendar time by days, weeks, months, and years.

Recognize numbers to 20 without counting (subitize) the quantity of structured arrangements.

Use concrete representations to describe whole numbers between 10 and 100 in terms of tens and ones. Know that 10 is equivalent to 10 ones and 100 is equivalent to 10 tens.

Read, write, discuss, and represent whole numbers up to 100. Representations may include numerals, words, addition and subtraction, pictures, tally marks, number lines, and manipulatives.

Count forward, with objects, from any given number up to 100 by 1s, 2s, 5s and 10s.

Count forward, without objects, by multiples of 1s, 2s, 5s, and 10s, up to 100.

Find a number that is 10 more or 10 less than a given number up to 100.

Compare and order whole numbers from 0 to 100.

Use knowledge of number relationships to locate the position of a given whole number, up to 20, on an open number line.

Use words such as "more than," "less than," and "equal to" to describe the relative value of numbers.

Represent and solve problems using addition and subtraction with sums and minuends of up to 10.

Determine if equations involving addition and subtraction are true.

Demonstrate fluency with basic facts of addition and subtraction with sums and minuends of up to 10.

Partition a regular polygon using physical models and recognize when those parts are equal.

Partition (fair share) sets of objects into two and three equal groups.

Identify pennies, nickels, dimes, and quarters by name and value.

Write a number with the cent symbol to describe the value of a coin.

Determine the value of a collection of pennies, nickels, or dimes up to one dollar, counting by 1s, 5s, and 10s.

Represent, create, describe, complete, and extend increasing and decreasing patterns with quantity and numbers in a variety of contexts.

Represent and describe repeating patterns involving shapes in a variety of contexts.

Use objects and number lines to represent number sentences.

Generate models and situations to represent number sentences and vice versa.

Apply the commutative property, identity property, and number sense to find values for unknowns that make addition and subtraction number sentences true or false.

Explain that the length of a bar in a bar graph and the number of objects in a pictograph represents the number of data points for a given category.

Organize a collection of data with up to four categories using pictographs and bar graphs in intervals of 1s, 2s, 5s or 10s.

Write and solve one-step word problems involving addition or subtraction using data represented within pictographs and bar graphs with intervals of one.

Draw conclusions and make predictions from information in a pictograph and bar graph.

Recognize regular and irregular trapezoids and hexagons.

Describe, compare, and classify two-dimensional figures according to their geometric attributes.

Compose and decompose two-dimensional shapes using triangles, squares, hexagons, trapezoids, and rhombi.

Sort three-dimensional shapes based on attributes such as number of faces, vertices, and edges.

Recognize right angles and classify angles as smaller or larger than a right angle.

Explain the relationship between the size of the unit of measurement and the number of units needed to measure the length of an object.

Explain the relationship between length and the numbers on a ruler by using a ruler to measure lengths to the nearest whole unit.

Explore how varying shapes and styles of containers can have the same capacity.

Distinguish between a.m. and p.m.

Read and write time to the quarter hour on an analog and digital clock.

Read, write, discuss, and represent whole numbers up to 1,000. Representations should include, but are not limited to, numerals, words, pictures, tally marks, number lines, and manipulatives.

Use knowledge of number relationships to locate the position of a given whole number, up to 100, on an open number line.

Use place value to describe whole numbers between 10 and 1,000 in terms of hundreds, tens, and ones, including written, standard, and expanded forms. Know that 10 is equivalent to 10 ones and 100 is equivalent to 10 tens.

Find 10 more or 10 less than a given three-digit number. Find 100 more or 100 less than a given three-digit number.

Use objects to determine whether a number is even or odd.

Use place value understanding to round numbers to the nearest ten and nearest hundred (up to 1,000). Recognize when to round in real-world situations.

Use place value to compare and order whole numbers up to 1,000 using comparative language, numbers, and symbols (e.g., 425 > 276, 73 < 107, page 351 comes after page 350, 753 is between 700 and 800).

Use the relationship between addition and subtraction to generate basic facts with sums and minuends of up to 20.

Demonstrate fluency with basic facts of addition and subtraction with sums and minuends of up to 20.

Estimate sums and differences up to 100.

Use strategies and algorithms based on knowledge of place value and equality to add and subtract two-digit numbers.

Solve addition and subtraction problems involving whole numbers up to two digits.

Use concrete models and structured arrangements, such as repeated addition, arrays, and ten frames to develop an understanding of multiplication.

Identify the parts of a set and area that represent fractions for halves, thirds, and fourths.

Construct equal-sized portions through fair sharing (length, set, and area models for halves, thirds, and fourths).

Determine the value of a collection of coins up to one dollar using the cent symbol.

Use a combination of coins to represent a given amount of money up to one dollar.

Create, describe, and extend patterns involving addition, subtraction, or multiplication to solve problems in a variety of contexts.

Describe the rule (limited to a single operation) for a pattern from an input/output table or function machine involving addition, subtraction, or multiplication.

Explore and develop visual representations of increasing and decreasing geometric patterns and construct the next steps.

Use number sense with the properties of addition, subtraction, and multiplication, to find unknowns (represented by symbols) in one-step equations. Generate real-world situations to represent number sentences.

Identify, represent, and apply the number properties (commutative, identity, and associative properties of addition and multiplication) using models and manipulatives to solve problems.

Collect and organize a data set with multiple categories using a frequency table, line plot, pictograph, or bar graph with scaled intervals.

Solve one- and two-step problems using categorical data represented with a frequency table, pictograph, or bar graph with scaled intervals.

Sort three-dimensional shapes based on attributes.

Build a three-dimensional figure using unit cubes when shown a picture of a three-dimensional shape.

Classify angles within a polygon as acute, right, obtuse, and straight.

Find the perimeter of a polygon, given whole number lengths of the sides, using a variety of models.

Analyze why length and width are multiplied to find the area of a rectangle by decomposing the rectangle into one unit by one unit squares and viewing these as rows and columns to determine the area.

Count cubes systematically to identify the number of cubes needed to pack the whole or half of a three-dimensional structure.

Find the area of two-dimensional figures by counting the total number of same-size unit squares that fill the shape without gaps or overlaps

Choose an appropriate measurement instrument and measure the length of objects to the nearest whole centimeter or whole meter.

Choose an appropriate measurement instrument and measure the length of objects to the nearest whole yard, whole foot, or half inch.

Use an analog thermometer to determine temperature to the nearest degree in Fahrenheit and Celsius.

Read and write time to the nearest five-minute interval (analog and digital).

Determine the solutions to problems involving addition and subtraction of time in intervals of five minutes, up to one hour, using pictorial models, number line diagrams, or other tools.

Read, write, discuss, and represent whole numbers up to 100,000. Representations should include but are not limited to numerals, words, pictures, number lines, and manipulatives (e.g., 350 = 3 hundreds, 5 tens = 35 tens = 3 hundreds, 4 tens, 10 ones).

Use place value to describe whole numbers between 1,000 and 100,000 in terms of ten thousands, thousands, hundreds, tens and ones, including written, standard, and expanded forms.

Applying knowledge of place values, use mental strategies (no written computations) to find 100 more or 100 less than a given number, 1,000 more or 1,000 less than a given number, and 10,000 more or 10,000 less than a given number, up to a five-digit number.

Use place value to compare and order whole numbers, up to 100,000, using comparative language, numbers, and symbols.

Use place value understanding to round numbers to the nearest thousand, ten-thousand and hundred thousand.

Represent multiplication facts by modeling a variety of approaches (e.g., manipulatives, repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line, skip counting).

Demonstrate fluency with multiplication facts using factors up to 10.

Use strategies and algorithms based on knowledge of place value and equality to fluently add and subtract up to five-digit numbers (answer not to exceed 100,000).

Recognize when to round numbers and apply understanding to estimate sums and differences to the nearest ten thousand, thousand, hundred, and ten.

Use addition and subtraction to solve problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction and the context of the problem to assess the reasonableness of results.

Represent division facts and divisibility by modeling a variety of approaches (e.g., repeated subtraction, equal sharing, forming equal groups) to show the relationship between multiplication and division.

Apply the relationship between multiplication and division to represent and solve problems.

Use various strategies (e.g., base ten blocks, area models, arrays, repeated addition, algorithms) based on knowledge of place value, equality, and properties of addition and multiplication to multiply a two-digit factor by a one-digit factor.

Read and write fractions with words and symbols using appropriate terminology (i.e., numerator and denominator).

Model fractions using length, set, and area for halves, thirds, fourths, sixths, and eighths.

Apply understanding of unit fractions and use this understanding to compose and decompose fractions related to the same whole.

Use models and number lines to order and compare fractions that are related to the same whole.

Use addition and subtraction to determine the value of a collection of coins up to one dollar using the cent symbol and in monetary transactions.

Add and subtract a collection of bills up to twenty dollars using whole dollars in monetary transactions.

Create an input/output chart or table to represent or extend a numerical pattern.

Describe the single operation rule for a pattern from an input/output table or function machine involving any operation of a whole number.

Construct models to show growth patterns involving geometric shapes and define the single operation rule of the pattern.

Use the relationships between multiplication and division with the properties of multiplication to solve problems and find values for variables that make number sentences true.

Solve for a variable in an equation involving addition, subtraction, multiplication, or division with whole numbers. Analyze models to represent number sentences and vice versa.

Determine the unknown addend or factor in equivalent and non-equivalent expressions (e.g., 5 + 6 = 4 + __, 3 ∙ 8 < 3 ∙ __).

Create and organize data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units.

Organize data sets to create tables, bar graphs, timelines, and Venn diagrams. The data may include benchmark fractions or decimals (¼, 1/3, ½, 2/3, ¾, 0.25, 0.50, 0.75).

Solve one- and two-step problems by analyzing data in whole number, decimal, or fraction form in a frequency table and line plot.

Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various models.

Describe, classify, and construct quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms, and kites. Recognize quadrilaterals in various models.

Given two three-dimensional shapes, identify each shape. Compare and contrast their similarities and differences based on their attributes.

Measure angles in geometric figures and real-world objects with a protractor or angle ruler.

Find the area of polygons by determining if they can be decomposed into rectangles.

Develop the concept that the volume of rectangular prisms with whole-number edge lengths can be found by counting the total number of same-sized unit cubes that fill a shape without gaps or overlaps. Use a variety of tools and create models to determine the volume using appropriate measurements (e.g., cm³).

Choose an appropriate instrument to measure the length of an object to the nearest whole centimeter or quarter inch.

Recognize and use the relationship between inches, feet, and yards to measure and compare objects.

Recognize and use the relationship between millimeters, centimeters, and meters to measure and compare objects.

Determine and justify the best use of customary and metric measurements in a variety of situations (liquid volumes, mass vs. weight, temperatures above 0 (zero) degrees, and length).

Determine elapsed time.

Convert one measure of time to another including seconds to minutes, minutes to hours, hours to days, and vice versa, using various models.

Read, write, discuss, and represent whole numbers up to 1,000,000. Representations may include numerals, words, pictures, number lines, and manipulatives.

Use place value to describe whole numbers between 1,000 and 1,000,000 in terms of millions, hundred thousands, ten thousands, thousands, hundreds, tens, and ones with written, standard, and expanded forms.

Applying knowledge of place value, use mental strategies (no written computations) to multiply or divide a number by 10, 100 and 1,000.

Use place value to compare and order whole numbers up to 1,000,000, using comparative language, numbers, and symbols.

Demonstrate fluency with multiplication and division facts with factors up to 12.

Multiply 3-digit by 1-digit and 2-digit by 2-digit whole numbers, using various strategies, including but not limited to standard algorithms.

Estimate products of 3-digit by 1-digit and 2-digit by 2-digit whole number factors using a variety of strategies (e.g., rounding, front end estimation, adjusting, compatible numbers) to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns.

Apply and analyze models to solve multi-step problems requiring the use of addition, subtraction, and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results.

Use strategies and algorithms (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties) based on knowledge of place value, equality, and properties of operations to divide a 3-digit dividend by a 1-digit whole number divisor, with and without remainders.

Represent and rename equivalent fractions using fraction models (e.g., parts of a set, area models, fraction strips, number lines).

Use benchmark fractions (0, ¼. 1/3, ½, 2/3, ¾, 1) to locate additional fractions with denominators up to twelfths on a number line.

Use models to order and compare whole numbers and fractions less than and greater than one, using comparative language and symbols.

Decompose a fraction into a sum of fractions with the same denominator in more than one way, using concrete and pictorial models and recording results with numerical representations (e.g., ¾ = ¼ + ¼ + ¼ and ¾ = 2/4 + ¼).

Use models to add and subtract fractions with like denominators.

Represent tenths and hundredths with concrete and pictorial models, making connections between fractions and decimals.

Read and write decimals in standard, word, and expanded form up to at least the hundredths place in a variety of contexts, including money.

Compare and order decimals and whole numbers using place value and various models including but not limited to grids, number lines, and base 10 blocks.

Compare and order benchmark fractions (0, ¼, 1/3, ½, 2/3, ¾, 1) and decimals (0, 0.25, 0.50, 0.75, 1.00) in a variety of representations.

Select the fewest number of coins for a given amount of money up to one dollar.

Given a total cost (dollars and coins up to twenty dollars) and amount paid (dollars and coins up to twenty dollars), find the change required in a variety of ways.

Use tables and rules with up to two operations to describe patterns of change and make predictions and generalizations about various mathematical situations.

Use a rule or table to represent ordered pairs of whole numbers and graph these ordered pairs on a coordinate plane, identifying the origin and axes in relation to the coordinates.

Generate equivalent numerical expressions and solve problems using number sense involving whole numbers by applying the commutative property, associative property, distributive property, and order of operations (excluding exponents).

Determine whether an equation or inequality involving a variable is true or false for a given value of the variable.

Evaluate expressions involving variables when values for the variables are given.

Find the measures of central tendency (i.e., mean, median, mode) and range of a set of data. Understand that the mean is a "leveling out" or central balance point of the data.

Create and analyze line and double-bar graphs with increments of whole numbers, fractions, and decimals.

Describe, identify, classify, and construct triangles (equilateral, right, scalene, isosceles) by their attributes using various mathematical models.

Describe, identify, and classify three-dimensional figures (cubes, rectangular prisms, and pyramids) and their attributes (number of edges, faces, vertices, shapes of faces), given various mathematical models.

Recognize and draw a net for a three-dimensional figure (cube, rectangular prism, pyramid).

Determine the volume of rectangular prisms by the number of unit cubes (n) used to construct the shape and by the product of the dimensions of the prism a · b · c = n. Understand rectangular prisms of different dimensions (p, q, and r) can have the same volume if a · b · c = p · q · r = n

Estimate the perimeter of polygons and create arguments for reasonable perimeter values of shapes that may include curves.

Measure and compare angles according to size using various tools.

Measure the length of an object to the nearest whole centimeter or up to 1/16 inch using an appropriate instrument.

Apply the relationship between inches, feet, and yards to measure, convert, and compare objects to solve problems.

Apply the relationship between millimeters, centimeters, and meters to measure, convert, and compare objects to solve problems.

Estimate lengths and geometric measurements to the nearest whole unit, using benchmarks in customary and metric measurement systems.

Represent decimal fractions (e.g., 1/10, 1/100) using a variety of models (e.g., 10 by 10 grids, base-ten blocks, meter stick) and show the rational number relationships among fractions, decimals and whole numbers.

Read, write, and represent decimals using place value to describe decimal numbers including fractional numbers as small as thousandths and whole numbers up to seven digits.

Compare and order decimals and fractions, including mixed numbers and fractions less than one, and locate on a number line.

Recognize and generate equivalent terminating decimals, fractions, mixed numbers, and fractions in various models.

Estimate solutions to division problems to assess the reasonableness of results.

Divide multi-digit numbers, by one- and two-digit divisors, based on knowledge of place value, including but not limited to standard algorithms.

Recognize that remainders can be represented in a variety of ways, including a whole number, fraction, or decimal. Determine the most meaningful form of a remainder based on the context of the problem.

Construct models to solve multi-digit whole number problems requiring addition, subtraction, multiplication, and division using various representations, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results.

Estimate sums and differences of fractions with like and unlike denominators, mixed numbers, and decimals to assess the reasonableness of the results.

Illustrate addition and subtraction of fractions with like and unlike denominators, mixed numbers, and decimals using a variety of mathematical models (e.g., fraction strips, area models, number lines, fraction rods).

Add and subtract fractions with like and unlike denominators, mixed numbers, and decimals, involving money, measurement, geometry, and data. Use various models and efficient strategies, including but not limited to standard algorithms.

Apply mental math and knowledge of place value (no written computations) to find 0.1 more or 0.1 less than a number, 0.01 more or 0.01 less than a number, and 0.001 more or 0.001 less than a number.

Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs.

Represent relationships between two varying positive quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.

Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.

Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to model and solve mathematical problems.

Model mathematical situations using expressions, equations and inequalities involving variables and rational numbers.

Use number sense and properties of operations and equality to model and solve mathematical problems involving equations in the form x + p = q and px = q, where p and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.

Interpret the mean, median, and mode for a set of data.

Explain and justify which measure of center (mean, median, or mode) would provide the most descriptive information for a given set of data.

Represent possible outcomes using a probability continuum from impossible to certain.

Determine the sample space for a given experiment and determine which members of the sample space are related to certain events. Sample space may be determined by the use of tree diagrams, tables or pictorial representations.

Demonstrate simple experiments in which the probabilities are known and compare the resulting relative frequencies with the known probabilities, recognizing that there may be differences between the two results.

Predict, describe, and apply translations (slides), reflections (flips), and rotations (turns) to a two-dimensional figure.

Recognize that translations, reflections, and rotations preserve congruence and use them to show that two figures are congruent.

Identify and describe the line(s) of symmetry in two-dimensional shapes.

Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithms and finding unknown measures.

Develop and use formulas to determine the area of triangles and find unknown measures.

Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes.

Solve problems using the relationships between the angles (vertical, complementary, and supplementary) formed by intersecting lines.

Develop and use the fact that the sum of the interior angles of a triangle is 180̊ to determine missing angle measures in a triangle.

Estimate weights and capacities using benchmarks in customary and metric measurement systems with appropriate units.

Solve problems that require the conversion of lengths within the same measurement systems using appropriate units.

Use manipulatives and models (e.g., number lines) to determine positive and negative numbers and their contexts, identify opposites, and explain the meaning of 0 (zero) in a variety of situations.

Compare and order positive rational numbers, represented in various forms, or integers using the symbols "<", ">", and "=".

Explain that a percent represents parts "out of 100" and ratios "to 100."

Determine equivalencies among fractions, mixed numbers, decimals, and percents.

Estimate solutions for integer addition and subtraction of problems in order to assess the reasonableness of results.

Illustrate addition and subtraction of integers using a variety of representations.

Add and subtract integers in a variety of situations; use efficient and generalizable procedures including but not limited to standard algorithms.

Identify and represent patterns with whole-number exponents and perfect squares. Evaluate powers with whole-number bases and exponents.

Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents.

Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.

Identify and use ratios to compare and relate quantities in multiple ways. Recognize that multiplicative comparison and additive comparison are different.

Determine the unit rate for ratios.

Apply the relationship between ratios, equivalent fractions, unit rates, and percents to solve problems in various contexts.

Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers, and use the estimates to assess the reasonableness of results in the context of the problem.

Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.

Multiply and divide fractions and decimals using efficient and generalizable procedures.

Use mathematical modeling to solve and interpret problems including money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.