South Carolina K–6 mathematics standards

Sort pictures or objects into at least two categories. Count to determine how many are in each category. Limit to 20 pictures or objects.

Answer questions about data organized in a t-chart, object graph, or picture graph.

Identify a penny, nickel, dime, and quarter.

Directly compare two objects using words including shorter, longer, taller, lighter, and heavier.

Identify and describe the attributes of triangles, squares, rectangles, circles, cubes, and spheres to include everyday situations.

Describe relative positions of objects by appropriately using terms including below, above, beside, between, inside, outside, in front of, or behind.

Read, write, and represent the numerals 0 to 20 and represent the written numeral with concrete models.

Compose and decompose numbers from 11 to 19 into tens and ones by using concrete objects, pictorial models, or drawings to demonstrate understanding that the teen numbers are composed of one set of ten ones and a few more ones.

Count forward by ones and tens to 100 and backward from 10 by ones.

Subitize a quantity of up to 10 objects in an organized arrangement without counting, explaining how one grouped the objects within the set to determine the total quantity.

Given a group of up to 20 objects, count the number of objects in that group and represent the number of objects with a written numeral. State the number of objects in a rearrangement of that group without recounting.

Given a number from 0 to 20, count out that many objects.

Compare up to 10 objects in one set to another set of up to 10 objects using the phrases more than, fewer than, or the same as.

Add and subtract number combinations within 5.

Create a sum of 10 using objects and drawings when given one of two addends 0–9, to include real-world situations.

Compose and decompose numbers up to 10 in different ways. Record using objects or drawings.

Solve add-to/joining, take-from/separating, part-part-whole (total unknown), part-partwhole (both addends unknown) real-world situations to find sums and differences within 10.

Describe, extend, and create (to the next term) simple repeating patterns in the form of AB, AAB, ABB, and ABC.

Use critical thinking skills to reason both abstractly and quantitatively.

Demonstrate a deep and flexible conceptual understanding of mathematical ideas, operations, and relationships while making real-world connections.

Make sense of problems and persevere in solving them strategically.

Explain ideas using precise and contextually appropriate mathematical language, tools, and models.

Identify and apply regularity in repeated reasoning to make generalizations.

Sort pictures or objects into at least three categories (not to exceed 10 items in each category).

Create a survey question and collect data with up to three categories. Create charts and graphs with a single unit scale to display the data. Use the graph to draw conclusions. Limit to one-step add-to, take-from, and part-part-whole questions.

Order three objects by length from shortest to longest and longest to shortest using direct comparison.

Use nonstandard physical objects to estimate and then measure the length of an item as the number of same size units of length with no gaps or overlaps.

Use analog and digital clocks to tell and record time to the hour and half hour.

Identify and write the values of a coin or a bill using a ¢ symbol for coin values or $ symbol for bills. Limit to penny, nickel, dime, quarter, one-dollar bill, five-dollar bill, and ten-dollar bill.Count a collection of like coins to determine the total value of the set. Limit to pennies, nickels, and dimes with values not to exceed a dollar.

Count a collection of like coins to determine the total value of the set. Limit to pennies, nickels, and dimes with values not to exceed a dollar.

Sort a mixed set of polygons and describe the reasoning used while sorting the polygons.

Identify and describe the attributes of two-dimensional shapes and three-dimensional shapes. Limit to triangle, square, rectangle, rhombus, hexagon, circle, cone, cube, cylinder, square pyramid, and sphere.

Identify and describe a given shape in everyday situations to include two-dimensional shapes and three-dimensional shapes. Limit to triangle, square, rectangle, rhombus, hexagon, circle, cone, cube, cylinder, square pyramid, and sphere.

Classify shapes as two-dimensional/flat or three-dimensional/solid and explain the reasoning using formal mathematical language. Limit to triangle, square, rectangle, rhombus, hexagon, circle, cone, cube, cylinder, square pyramid, and sphere.

Analyze and compare a pair of two-dimensional shapes or a pair of three-dimensional shapes of assorted sizes and orientations using formal mathematical language. Limit to triangle, square, rectangle, rhombus, hexagon, circle, cone, cube, cylinder, square pyramid, and sphere.

Read, write, and represent numbers to 100 using concrete models, drawings, standard form, base ten language, and equations in expanded form.

Represent and explain that whole numbers 1 through 99 are organized into groups of tens and ones, and a digit has a different value depending on its placement.

Compose and decompose whole numbers from 1 through 99 in more than one way using tens and ones. Explain and demonstrate each composition or decomposition with the use of concrete models, drawings, and/or equations.

Apply place value reasoning to identify the number that is one more and one less, ten more, and ten less than a given number with up to two digits.

Count by ones forward or backward starting at any number up to 120 making accurate decade transitions.

Skip count by fives and tens from any multiple of five to 100, identifying place value patterns in the sequence.

Compare representations of two numbers up to 100 using the phrases is greater than, is less than, or is equal to (the same value as).

Partition in multiple ways squares, rectangles, and circles into two or four equal-sized parts. Name the pieces as halves and fourths.

Determine and explain if an equation within 10 is true using a variety of equation formats.

Compose and decompose numbers less than or equal to 20 in more than one way. Record each composition or decomposition as an equation.

Solve add-to, take-from, and part-part-whole real-world situations to find sums and differences within 20. Situations include result or change unknown, both addends unknown, and total or one part unknown.

Add and subtract number combinations flexibly and accurately within 10.

Apply and explain the Commutative Property of Addition to find the sum (through 20) of two addends and explain that the value does not change when the order of the two numbers changes.

Determine an unknown number in addition and subtraction equations within 10.

Find the sum of a two-digit number and a one-digit number or a two-digit number and a multiple of 10 (1–99) using concrete models, drawings, and strategies that reflect place value understanding, the inverse relationship of addition and subtraction, and the properties of the operations to justify the sum.

Find the difference between two numbers that are multiples of 10, both in the range 10–90, and write the corresponding equation. Explain the reasoning used.

Create, describe, and extend (to the next term) a growing shape pattern.

Create, describe, and extend (to three terms within a sequence) repeating patterns using AB, AAB, ABB, and ABC type patterns.

Create a survey question and collect data with up to four categories. Create tally charts, picture graphs, dot plots, and bar graphs with a single-unit scale to read the graph, answer questions, and draw conclusions. Limit to one-step add-to, take-from, part-part-whole, and comparison questions.

Select and use appropriate tools to estimate and measure length of an object or distance to the nearest customary unit. Limit to inches, feet, and yards.

Use analog and digital clocks to tell and record time in five-minute intervals, identifying AM and PM.

Determine the value of mixed sets of coins or bills in mathematical and realworld situations and record the value using a ¢ or $ symbol. Limit to pennies, nickels, dimes, and quarters up to a dollar; one-dollar bills, five-dollar bills, tendollar bills, and twenty-dollar bills up to $100, and add-to or take-from problem types.

Identify and describe a given shape in everyday situations to include twodimensional shapes and threedimensional shapes. Limit to triangle, quadrilateral, pentagon, hexagon, octagon, circle, cone, cube, cylinder, rectangular prism, square pyramid, and sphere.

Classify shapes as polygons or nonpolygons and defend that determination based on their attributes.

Classify two-dimensional shapes as triangles or quadrilaterals and justify each classification.

Read, write, and represent numbers up to 999 using concrete models, drawings, standard form, base ten language, and equations in expanded form.

Represent and explain that whole numbers 1 through 999 are organized into groups of hundreds, tens, and ones, and a digit has a different value depending on its placement.

Compose and decompose whole numbers from 1 through 999 in more than one way using hundreds, tens, and ones. Explain and demonstrate each composition or decomposition with the use of concrete models, drawings, and equations.

Apply place value reasoning to identify the number that is 10 more, 10 less, 100 more, and 100 less than a given three digit number through 999.

Count forward and backward by ones, tens, and hundreds from any number within 999 and identify patterns in the sequence.

Compare representations of whole numbers up to 999 and write a comparison statement using words and symbols. Limit to is equal to (=), is less than (<), and/or is greater than (>).

When given a two-digit number, identify which multiple of 10 the number is closest to.

Partition in multiple ways squares, rectangles, and circles into two or four equal sized parts, and describe the parts using the words halves, fourths, a half of, and a fourth of (not quarters).

Explain that when partitioning a square, rectangle, or circle into two or four equal parts, the parts become smaller as the number of parts increases.

Use a strategy to accurately find sums and differences of two-digit numbers within 100 and justify the sum or difference.

Determine and explain if an equation (within 20) is true using a variety of equation formats.

Solve one-step add-to, take-from, part-part-whole, and additive comparison real-world situations through 99 with the unknown in any position.

For any number from 0 to 99, find the number that makes 100 when added to the given number.

Add and subtract number combinations flexibly and accurately within 20.

Apply the Associative Property of Addition to find the sum (through 20) of three addends and explain that the value can be found using various grouping strategies.

Determine the unknown number in addition and subtraction equations within 20, with the unknown in any position.

Sort a collection of 20 or fewer objects into two groups to determine if the number of objects is even or odd.

Find the total number of objects arranged in equal groups or in a rectangular array and write an addition equation to express the total as a sum (up to 25) of equal addends.

Describe, extend, and create a growing shape pattern with up to three terms within a sequence.

Create, describe, and extend an appropriate one-step rule for number patterns using addition and subtraction within 100.

Collect and organize categorical and numerical data based on observations, surveys, experiments, and investigations with whole number values using tables, scaled picture graphs, scaled bar graphs, or dot plots. Use titles and labels. Limit scales to multiples of 1, 2, 5, and 10.

Solve one-step, real-world situations using whole number data represented in tables, scaled picture graphs, scaled bar graphs, or dot plots. Limit scales to multiples of 1, 2, 5, and 10.

Identify the possible outcomes of a simple event.

Determine the area of squares and rectangles presented in relevant problems by covering the space with square units and counting the total number of units needed.

Determine the perimeter of regular and irregular triangles and quadrilaterals with known side lengths.

Determine if a real-world situation is an example of the need for finding the area or the perimeter of a figure.

Determine the value of any collection of coins, not to exceed $5. Write the amount in the form of dollars and cents using the decimal notation. Limit to penny, nickel, dime, and quarter.

Use analog and digital clocks to tell and record time to 1-minute intervals, identifying AM and PM.

Solve problems involving addition and subtraction of time intervals to determine elapsed time to the nearest half hour.

Estimate and measure length/distance to the nearest half inch and nearest whole centimeter.

Determine which unit of liquid volume is most appropriate to measure in real-world situations. Limit to fluid ounces, cups, pints, quarts, gallons, milliliters, and liters.

Describe and draw right, acute, obtuse, and straight angles. Identify these angle types in two-dimensional figures including triangles and quadrilaterals.

Identify, describe, and draw points, lines, line segments, rays, intersecting lines, perpendicular lines, and parallel lines. Identify these in two-dimensional figures.

Read, write, and represent whole numbers through the thousands period (0 to 999,999) on a number line and in standard, base ten language, word, and equations in expanded form.

Compose and decompose 4-digit whole numbers in multiple ways using thousands, hundreds, tens, and ones.

Compare two whole numbers up to 999,999 based on the place value of the digits using the symbols for is equal to (=), is less than (<), or is greater than (>).

Round whole numbers from 0 to 1,000 to the nearest 10 or 100.

Identify unit fractions as the quantity formed by one part when a whole is partitioned into 2, 3, 4, 6, or 8 equal-sized parts. Express each part as a unit fraction of the whole.

Represent fractions from 0 to 1 using concrete, set, area, and linear models, and write them in standard form and word form. Limit denominators to 2, 3, 4, 6, and 8.

Express whole numbers as fractions and identify fractions that are equivalent to whole numbers. Limit denominators to 1, 2, 3, 4, 6, and 8.

Compose fractions between the whole numbers 0 and 5 using unit fractions. Record the composition as a mixed number or fraction greater than 1. Limit denominators to 2, 3, 4, 6, and 8.

Recognize two fractions are equivalent based on the same size whole. Limit denominators to 2, 3, 4, 6, and 8, and fractions should be limited to fractions between 0 and 1.

Compare two fractions with the same numerator or same denominator based on the same size whole by reasoning about their size. Use the symbols for is equal to (=), is less than (<), or is greater than (>). Limit denominators to 2, 3, 4, 6, and 8, and fractions should be limited to fractions between 0 and 1.

Use a strategy to compute sums and differences up to 1,000.

Multiply whole numbers (factors 0–10) and divide whole numbers (divisors 1–10) using a model and write a corresponding equation.

Multiply two whole numbers from 0 to 10 and divide using related facts flexibly and accurately.

Determine the unknown whole number in a multiplication or division real-world situation relating three whole numbers when the unknown is a missing factor, product, dividend, divisor, or quotient.

Solve one- and two-step real-world situations using addition and subtraction up to 1,000.

Identify, create, and extend numerical patterns to determine the next three terms in an addition or subtraction sequence.

Recognize that a whole number is a multiple of each of its factors 1–10.

Collect and organize numerical and categorical data based on observations, investigations, surveys, and experiments using tables, scaled bar graphs, or dot plots. Use titles and labels. Scales to include whole numbers, halves, and fourths.

Solve one-step, real-world situations using whole number and fractional data represented in tables, scaled picture graphs, scaled bar graphs, or dot plots. Limit to like denominators of 2, 3, 4, 5, 6, 8, and 10.

Determine the possible outcomes of a simple event and record the probability as certain, possible, or impossible.

Apply perimeter formulas for rectangles to solve real-world situations including finding the perimeter, given the side lengths, and finding an unknown side length.

Apply area formulas for rectangles to solve real-world situations. Use square units to label area measurements.

Calculate the value of a collection of coins and bills in real-world situations to determine whether there is enough money to make a purchase. Justify based on comparison of money amounts.

Solve real-world situations involving addition and subtraction of time intervals within 60 minutes to find elapsed time, start time, or end time.

Measure length to the nearest quarter inch.

Measure weight in customary units and metric units to the nearest whole unit. Limit to ounces, pounds, grams, and kilograms.

Convert customary units of length, weight, and liquid volume from a larger unit to a smaller unit, given direct comparisons of the two measurements and/or the unit equivalencies within a single system of measurement. Limit to inches, feet, yards, ounces, pounds, fluid ounces, cups, pints, quarts, and gallons when given unit equivalencies.

Classify triangles according to side length (isosceles, equilateral, scalene) and angle measure (acute, obtuse, right, equiangular).

Classify quadrilaterals in a hierarchy based on their shared attributes.

Read and write whole numbers through the millions period (0 to 999,999,999) in word, standard, and equations in expanded form.

Estimate sums, differences, products, and quotients of multi-digit whole numbers, using rounding and place value to determine the reasonableness of real-world problem solutions. Write an equation for the estimate.

Order whole numbers within 999,999 (no more than 3) in ascending or descending order and record the comparison(s) using symbols for is less than (<) and/or is greater than (>).Represent and compare fractions in multiple ways using part-whole relationships

Represent fractions with denominators of 10 and 100 in words, models, and decimal notations.

Compare decimal numbers to the hundredths using the benchmarks 0, 0.5, and 1.0, concrete area, and linear models. Use the symbols for is equal to (=), is less than (<), and/or is greater than (>).

Generate equivalent fractions, including fractions greater than 1, using multiple representations. Limit fractions to denominators of 2, 3, 4, 5, 6, 8, 10, 12, 20, 25, 50, and 100.

Represent the composition and decomposition of fractions with the same denominator, including mixed numbers and fractions greater than 1, using multiple representations. Limit fractions to denominators of 2, 3, 4, 5, 6, 8, 10, 12, 20, 25, 50, and 100.

Explain and demonstrate how a mixed number is equivalent to a fraction greater than 1 and how a fraction greater than 1 is equivalent to a mixed number. Limit fractions to denominators of 2, 3, 4, 5, 6, 8, 10, 12, 20, 25, 50, and 100.

Compare fractions and mixed numbers with like and unlike denominators applying benchmark fractions such as 0, 1 2 , and 1 using the symbols for is equal to (=), is less than (<), or is greater than (>). Limit fractions to denominators of 2, 3, 4, 5, 6, 8, 10, 12, 20, 25, 50, and 100.

Use a strategy to accurately compute sums and differences of whole numbers up to 100,000 and justify the sum or difference.

Compute the product of a one-digit whole number times a multiple of 10 (from 10 to 90) and 100 (from 100 to 900) based on place value and properties of operations.

Decompose numbers by the value of each digit to multiply whole numbers up to four digits by a one-digit number and two 2- digit whole numbers.

Use a strategy to divide up to a four-digit dividend by a one-digit divisor, with and without remainders. Justify the calculation.

Use a strategy to accurately compute sums and differences of fractions with like denominators and justify the reasonableness of the answer. Limit denominators to 2, 3, 4, 5, 6, 8, 10, 12, 25, and 100.

Use fraction and decimal equivalencies to add and subtract tenths and hundredths, to include mixed numbers and fractions greater than 1.

Represent and compute the product of a whole number times a unit fraction. Limit denominators to 2, 3, 4, 5, 6, 8, 10, 12, 25, and 100.

Interpret a fraction as an equal sharing division situation, where a quantity (the numerator) is divided into equal parts (the denominator) to include real-world situations.

Find all factor pairs for a whole number in the range 1–50. Determine whether the whole number is prime or composite.

Describe and extend a numerical pattern that follows a rule using function tables and real-world situations.

Solve real-world situations involving multiplicative comparison situations and write equations to represent the problem using a variable for the unknown.

Solve two-step, real-world situations using the four operations involving whole number answers. Represent the problem using an equation with a variable as the unknown in any position.

Describe data by determining the range and mode, including whole numbers, fractional data, and decimal data. Limit fractions to denominators of 2, 3, 4, 5, 6, 8, and 10, and limit decimals to decimals through the hundredths place.

Solve two-step, real-world situations using whole number and fractional data represented in tables, line graphs, scaled bar graphs, or dot plots. Limit fractions to denominators of 2, 3, 4, 5, 6, 8, 10, 12, 20, 25, 50, and 100.

Analyze categorical and numerical data in graphical displays to make predictions or draw conclusions. Limit displays to tables, bar graphs, dot plots, line graphs, and circle graphs with scales of whole numbers, halves, fourths, and eighths.

Represent the probability of a simple event as 0, a fraction, or 1. Limit fractions to denominators of 2, 3, 4, 5, 6, 8, 10, 20, and 25.

Solve problems involving area and perimeter of composite figures by decomposing with rectangles.

Estimate and measure the volume of a right rectangular prism with whole-number side lengths by filling it with unit cubes.

Given the unit equivalencies, convert within a single system of measurement from larger units to smaller units and smaller units to larger units for length, weight, liquid volume, and time. Use these conversions in solving real-world situations. Limit units to inches, feet, yards, ounces, pounds, fluid ounces, cups, pints, quarts, gallons, seconds, minutes, hours, milli-, centi-, kilo-, and.base units (grams, liters, meters)

Estimate and measure lengths to the nearest eighth of an inch or nearest millimeter.

Identify the origin, x-axis, and y-axis in the coordinate system. Write, plot, and label ordered pairs, including values in a function table, in the first quadrant of the coordinate plane.

Represent mathematical and real-world situations by graphing, labeling, and interpreting points in the first quadrant of the coordinate plane.

Read, write, and represent multi-digit numbers from 0 to 999 with decimals to the thousandths place. Use pictorial, word, standard, or expanded form with fraction or decimal notation.

Explain how the value of a digit in a multi-digit number changes if the digit moves one or more places to the left or right in the base ten system. Include decimals to the thousandths place.

Round decimal numbers up to 999 with decimals to the thousandths place to the nearest hundredth, tenth, or whole number.

Use patterns to explain the exponents when multiplying and dividing by powers of 10, not to exceed the thousandths place.

Compare fractions and mixed numbers with like and unlike denominators of 2, 3, 4, 5, 6, 8, 10, 12, 20, 25, and 100 using equivalence to create a common denominator. Use the symbols for is less than (<), is more than (>), or is equal to (=) to record the comparison.

Use a strategy to compute the product of a two- or three-digit factor times a two-digit factor to include real-world situations.

Use a strategy to compute the quotient of a multi-digit whole number dividend divided by a two-digit whole number divisor, with and without remainders, to include real-world situations. Limit the dividend to four digits.

Use a strategy to compute sums and differences of decimal numbers to the hundredths.

Use a strategy to multiply a one-digit whole number by a decimal to the hundredths and divide a decimal to the hundredths (dividend) by a one-digit whole number (divisor). Justify the calculation.

Use a strategy to compute sums and differences of fractions and mixed numbers with unlike denominators and justify the sum or difference to include real-world situations. Limit denominators to 2, 3, 4, 5, 6, 8, 10, 12, 20, 25, 50, and 100.Use a strategy to multiply a fraction by a fraction or a fraction by a whole to include real-world situations. Limit denominators to 2, 3, 4, 5, 6, 8, 10, and 12.

Use a strategy to multiply a fraction by a fraction or a fraction by a whole to include real-world situations. Limit denominators to 2, 3, 4, 5, 6, 8, 10, and 12.

Interpret and represent division of a whole number dividend by a unit fraction divisor and a unit fraction dividend by a whole number divisor and apply to real-world situations. Limit denominators to 2, 3, 4, 5, 6, 8, 10, and 12.

Determine the least common multiple (LCM) to find a common denominator. Limit denominators to 2, 3, 4, 5, 6, 8, 10, 12, 20, 25, 50, and 100.

Determine the greatest common factor (GCF) of two numbers both less than or equal to 50 to simplify a fraction into its standard form.

Identify a rule that can describe the pattern from the data of a function table and write it as an expression.

Translate a two-step real-world situation into a numerical expression using parentheses as grouping symbols and evaluate the expression.

Identify the sample size for a numerical set of data in mathematical and real-world situations.

Create box plots to represent numerical data sets in mathematical and real-world situations.

Use the shape of the graph to determine whether median or mode best describes the data set.

Calculate and interpret the median, mode, range, interquartile range in mathematical and real-world situations.

Given the probability of a random event, expressed as a number from 0 to 1, state the likelihood of the event occurring.

Find the probability of simple events in mathematical and real-world situations. Limit denominators to 2, 4, 5, 8, 10, 25, 50, and 100.

Given the probability of an event, identify and calculate the complement of that event.

Find the area of a triangle, square, rectangle, parallelogram, and trapezoid.

Create nets to represent three-dimensional shapes.

Calculate the surface area of rectangular prisms, right triangular prisms, rectangular pyramids, and right triangular pyramids using two-dimensional nets.

Find the area of composite figures by decomposing them into triangles and rectangles to solve mathematical and real-world situations.

Calculate the volume of a right rectangular prism using the formula (V = Bh) in mathematical and real-world situations.

Determine if two angles are complementary or supplementary.

Determine the measure of angles using a protractor.

Plot ordered pairs in all four quadrants and identify points on a graph by writing ordered pairs.

Graph a polygon on a coordinate plane given the coordinates of the vertices.

Convert positive rational numbers into equivalent forms among terminating decimals, fractions (including mixed numbers), and percentages. Limit fractions to denominators of 2, 4, 5, 8, 10, 20, 25, 50, 100, and 200.

Compare two positive rational numbers and write statements using the symbols for is equal to (=), is not equal to (≠), is less than (<), and/or is greater than (>) in mathematical and real-world situations. Limit fractions to denominators of 2, 4, 5, 8, 10, 20, 25, 50, 100, and 200.

Sort a set of positive rational numbers in ascending and/or descending order in mathematical and real-world situations. Limit sets to no more than 5 numbers. Limit fractions to denominators of 2, 4, 5, 8, 10, 20, 25, 50, 100, and 200.

Represent quantities with integers in realworld situations and explain the meaning of zero.

Identify and compare the opposite value and absolute value of positive and negative rational numbers.

Use tables, graphs, verbal descriptions, and equations to represent the relationship between independent and dependent variables of functions.

Identify the independent and dependent variable of a function in mathematical and real-world situations.

Identify parts of an algebraic expression using the mathematical terms sum, difference, term, variable, product, factor, quotient, coefficient, and constant.

Write and evaluate numerical expressions containing powers. Limit to positive whole number bases and positive whole number exponents.

Evaluate numerical expressions with positive whole number bases and positive whole number exponents using the Order of Operations.

Write and evaluate expressions using variables to represent quantities in mathematical and real-world situations.

Write and solve one-step equations and inequalities with one variable involving positive rational numbers in mathematical and real-world situations.

Interpret the concept of a ratio as the relationship between two quantities, including part-to-part and part-to-whole.

Explain the relationship between ratios and rates, including unit rates.

Solve ratio and rate problems in real-world situations.

Use one-step dimensional analysis to convert units within the metric or customary systems.

Represent the solutions of inequalities on a number line and explain that the solution set may contain an infinite number of solutions. Limited to the symbols for is less than (<) and is greater than (>).

Identify the multiplicative inverse of a number and multiply multiplicative inverses to find their product is equal to 1.

Identify the additive inverse of a number and add additive inverses to find their sum is equal to zero.

Apply the properties of operations to create equivalent algebraic expressions and justify the properties used. Limit properties to the Identity, Inverse, Commutative, Associative, and Distributive Properties.

Add, subtract, multiply, and divide integers in mathematical and real-world situations.

Add, subtract, multiply, and divide positive fractions, including mixed numbers in mathematical and real-world situations.

Add, subtract, multiply, and divide multidigit positive decimals, up to the thousandths place, to solve problems in mathematical and real-world situations.