Georgia K–6 mathematics standards

Identify, sort, classify, analyze, and compare two- dimensional shapes and three-dimensional figures, in different sizes and orientations, using informal language to describe their similarities, differences, number of sides and vertices, and other attributes.

Describe the relative location of an object using positional words.

Use basic shapes to represent specific shapes found in the environment by creating models and drawings.

Use two or more basic shapes to form larger shapes.

Directly compare, describe, and order common objects, using measurable attributes (length, height, width, or weight) and describe the difference.

Classify and sort up to ten objects into categories by an attribute; count the number of objects in each category and sort the categories by count.

Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to solve problems relevant to everyday life.

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

Count up to 20 objects in a variety of structured arrangements and up to 10 objects in a scattered arrangement.

When counting objects, explain that the last number counted represents the total quantity in a set (cardinality), regardless of the arrangement and order.

Given a number from 1-20, identify the number that is one more or one less.

Identify pennies, nickels, and dimes and know their name and value.

Count forward to 100 by tens and ones and backward from 20 by ones.

Count forward beginning from any number within 100 and count backward from any number within 20.

Describe numbers from 11 to 19 by composing (putting together) and decomposing (breaking apart) the numbers into ten ones and some more ones.

Identify written numerals 0- 20 and represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).

Compare two sets of up to 10 objects and identify whether the number of objects in one group is more or less than the other group, using the words “greater than,” “less than,” or “the same as”.

Compose (put together) and decompose (break apart) numbers up to 10 using objects and drawings.

Represent addition and subtraction within 10 from a given authentic situation using a variety of representations and strategies.

Use a variety of strategies to solve addition and subtraction problems within 10.

Fluently add and subtract within 5 using a variety of strategies to solve practical, mathematical problems.

Create, extend, and describe repeating patterns with numbers and shapes, and explain the rationale for the pattern.

Describe patterns involving the passage of time using words and phrases related to actual events.

Identify common two-dimensional shapes and three-dimensional figures, sort and classify them by their attributes and build and draw shapes that possess defining attributes.

Compose two-dimensional shapes (rectangles, squares, triangles, half-circles, and quarter-circles) and three-dimensional figures (cubes, rectangular prisms, cones, and cylinders) to create a shape formed of two or more common shapes and compose new shapes from the composite shape.

Partition circles and rectangles into two and four equal shares.

Estimate, measure, and record lengths of objects using non-standard units, and compare and order up to three objects using the recorded measurements. Describe the objects compared.

Tell and write time in hours and half-hours using analog and digital clocks, and measure elapsed time to the hour on the hour using a predetermined number line.

Identify the value of quarters and compare the values of pennies, nickels, dimes, and quarters.

Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to compare and order whole numbers.

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

Count within 120, forward and backward, starting at any number. In this range, read and write numerals and represent a number of objects with a written numeral.

Explain that the two digits of a 2-digit number represent the amounts of tens and ones.

Compare and order whole numbers up to 100 using concrete models, drawings, and the symbols >, =, and <.

Use a variety of strategies to solve addition and subtraction problems within 20.

Use pictures, drawings, and equations to develop strategies for addition and subtraction within 20 by exploring strings of related problems.

Recognize the inverse relationship between subtraction and addition within 20 and use this inverse relationship to solve authentic problems.

Fluently add and subtract within 10 using a variety of strategies.

Use the meaning of the equal sign to determine whether equations involving addition and subtraction are true or false.

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

Apply properties of operations as strategies to solve addition and subtraction problem situations within 20.

Use a variety of strategies to solve applicable, mathematical addition and subtraction problems with one- and two-digit whole numbers.

Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.

Add and subtract multiples of 10 within 100.

Investigate, create, and make predictions about repeating patterns with a core of up to 3 elements resulting from repeating an operation, as a series of shapes, or a number string.

Identify, describe, and create growing, shrinking, and repeating patterns based on the repeated addition or subtraction of 1s, 2s, 5s, and 10s.

Describe, compare and sort 2-D shapes including polygons, triangles, quadrilaterals, pentagons, hexagons, and 3-D shapes including rectangular prisms and cones, given a set of attributes.

Identify at least one line of symmetry in everyday objects to describe each object as a whole.

Partition circles and rectangles into two, three, or four equal shares. Identify and describe equal-sized parts of the whole using fractional names (“halves,” “thirds,” “fourths”, “half of,” “third of,” “quarter of,” etc.).

Recognize that equal shares of identical wholes may be different shapes within the same whole.

Construct simple measuring instruments using unit models. Compare unit models to rulers.

Estimate and measure the length of an object or distance to the nearest whole unit using appropriate units and standard measuring tools.

Measure to determine how much longer one object is than another and express the length difference in terms of a standard-length unit.

Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to solve problems relevant to everyday life.

Represent whole-number sums and differences within a standard unit of measurement on a number line diagram.

Tell and write time from analog and digital clocks to the nearest five minutes, and estimate and measure elapsed time using a timeline, to the hour or half hour on the hour or half hour.

Find the value of a group of coins and determine combinations of coins that equal a given amount that is less than one hundred cents, and solve problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately.

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

Explain the value of a three-digit number using hundreds, tens, and ones in a variety of ways.

Count forward and backward by ones from any number within 1000. Count forward by fives from multiples of 5 within 1000. Count forward and backward by 10s and 100s from any number within 1000. Count forward by 25s from 0.

Represent, compare, and order whole numbers to 1000 with an emphasis on place value and equality. Use >, =, and < symbols to record the results of comparisons.

Fluently add and subtract within 20 using a variety of mental, part-whole strategies.

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

Solve problems involving the addition and subtraction of two-digit numbers using part-whole strategies.

Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

Determine whether a group (up to 20) has an odd or even number of objects. Write an equation to express an even number as a sum of two equal addends.

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.

Identify, describe, and create a numerical pattern resulting from repeating an operation such as addition and subtraction.

Identify, describe, and create growing patterns and shrinking patterns involving addition and subtraction up to 20.

Identify perpendicular line segments, parallel line segments, and right angles, identify these in polygons, and solve problems involving parallel line segments, perpendicular line segments, and right angles.

Classify, compare, and contrast polygons, with a focus on quadrilaterals, based on properties. Analyze specific 3-dimensional figures to identify and describe quadrilaterals as faces of these figures.

Identify lines of symmetry in polygons.

Investigate area by covering the space of rectangles presented in realistic situations using multiple copies of the same unit, with no gaps or overlaps, and determine the total area (total number of units that covered the space).

Determine the area of rectangles (or shapes composed of rectangles) presented in relevant problems by tiling and counting.

Discover and explain how area can be found by multiplying the dimensions of a rectangle.

Determine the perimeter of a polygon and explain that the perimeter represents the distance around a polygon. Solve problems involving perimeters of polygons.

Investigate and describe how rectangles with the same perimeter can have different areas or how rectangles with the same area can have different perimeters.

Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to solve problems relevant to everyday life.

Tell and write time to the nearest minute and estimate time to the nearest fifteen minutes (quarter hour) from the analysis of an analog clock.

Solve meaningful problems involving elapsed time, including intervals of time to the hour, half hour, and quarter hour where the times presented are only on the hour, half hour, or quarter hour within a.m. or p.m. only.

Use rulers to measure lengths in halves and fourths (quarters) of an inch and a whole inch.

Estimate and measure liquid volumes, lengths and masses of objects using customary units. Solve problems involving mass, length, and volume given in the same unit, and reason about the relative sizes of measurement units within the customary system.

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

Read and write multi-digit whole numbers up to 10,000 to the thousands using base-ten numerals and expanded form.

Use place value reasoning to compare multi-digit numbers up to 10,000, using >, =, and < symbols to record the results of comparisons.

Use place value understanding to round whole numbers within up to 1000 to the nearest 10 or 100.

Describe a unit fraction and explain how multiple copies of a unit fraction form a non-unit fraction. Use parts of a whole, parts of a set, points on a number line, distances on a number line and area models.

Compare two unit fractions by flexibly using a variety of tools and strategies.

Represent fractions, including fractions greater than one, in multiple ways.

Recognize and generate simple equivalent fractions.

Fluently add and subtract within 1000 to solve problems.

Apply part-whole strategies, properties of operations and place value understanding, to solve problems involving addition and subtraction within 10,000. Represent these problems using equations with a letter standing for the unknown quantity. Justify solutions.

Describe, extend, and create numeric patterns related to multiplication. Make predictions related to the patterns.

Represent single digit multiplication and division facts using a variety of strategies. Explain the relationship between multiplication and division.

Apply properties of operations (i.e., commutative property, associative property, distributive property) to multiply and divide within 100.

Use the meaning of the equal sign to determine whether expressions involving addition, subtraction, and multiplication are equivalent.

Use place value reasoning and properties of operations to multiply one-digit whole numbers by multiples of 10, in the range 10-90.

Solve practical, relevant problems involving multiplication and division within 100 using part-whole strategies, visual representations, and/or concrete models.

Use multiplication and division to solve problems involving whole numbers to 100. Represent these problems using equations with a letter standing for the unknown quantity. Justify solutions.

Recognize angles as geometric shapes formed when two rays share a common endpoint. Draw right, acute, and obtuse angles based on the relationship of the angle measure to 90 degrees.

Measure angles in reference to a circle with the center at the common endpoint of two rays. Determine an angle’s measure in relation to the 360 degrees in a circle through division or as a missing factor problem.

Explore, investigate, and draw points, lines, line segments, rays, angles (right, acute, obtuse), perpendicular lines, parallel lines, and lines of symmetry. Identify these in two-dimensional figures.

Classify, compare, and contrast polygons based on lines of symmetry, the presence or absence of parallel or perpendicular line segments, or the presence or absence of angles of a specified size and based on side lengths.

Solve problems involving area and perimeter of composite rectangles involving whole numbers with known side lengths.

Use the four operations to solve problems involving elapsed time to the nearest minute, intervals of time, metric measurements of liquid volumes, lengths, distances, and masses of objects, including problems involving fractions with like denominators, and also problems that require expressing measurements given in a larger unit in terms of a smaller unit, and expressing a smaller unit in terms of a larger unit based on the idea of equivalence.

Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to solve problems relevant to everyday life.

Create dot plots to display a distribution of numerical (quantitative) measurement data.

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

Read and write multi-digit whole numbers to the hundred-thousands place using base-ten numerals and expanded form.

Recognize and show that a digit in one place has a value ten times greater than what it represents in the place to its right and extend this understanding to determine the value of a digit when it is shifted to the left or right, based on the relationship between multiplication and division.

Use place value reasoning to represent, compare, and order multi-digit numbers, using >, =, and < symbols to record the results of comparisons.

Use place value understanding to round multi-digit whole numbers.

Fluently add and subtract multi-digit numbers to solve practical, mathematical problems using place value understanding, properties of operations, and relationships between operations.

Interpret, model, and solve problems involving multiplicative comparison.

Solve relevant problems involving multiplication of a number with up to four digits by a 1-digit whole number or involving multiplication of two two-digit numbers using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Solve authentic division problems involving up to 4-digit dividends and 1- digit divisors (including whole number quotients with remainders) using strategies based on place-value understanding, properties of operations, and the relationships between operations.

Solve multi-step problems using addition, subtraction, multiplication, and division involving whole numbers. Use mental computation and estimation strategies to justify the reasonableness of solutions.

Using concrete materials, drawings, and number lines, demonstrate and explain the relationship between equivalent fractions, including fractions greater than one, and explain the identity property of multiplication as it relates to equivalent fractions. Generate equivalent fractions using these relationships.

Compare two fractions with the same numerator or the same denominator by reasoning about their size and recognize that comparisons are valid only when the two fractions refer to the same whole.

Compare two fractions with different numerators and/or different denominators by flexibly using a variety of tools and strategies and recognize that comparisons are valid only when the two fractions refer to the same whole.

Represent whole numbers and fractions as the sum of unit fractions.

Represent a fraction as a sum of fractions with the same denominator in more than one way, recording with an equation.

Add and subtract fractions and mixed numbers with like denominators using a variety of tools.

Demonstrate and explain the concept of equivalent fractions with denominators of 10 and 100, using concrete materials and visual models. Add two fractions with denominators of 10 and 100.

Represent, read, and write fractions with denominators of 10 or 100 using decimal notation, and decimal numbers to the hundredths place as fractions, using concrete materials and drawings.

Compare two decimal numbers to the hundredths place by reasoning about their size. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions.

Generate both number and shape patterns that follow a provided rule.

Use input-output rules, tables, and charts to represent and describe patterns, find relationships, and solve problems.

Find factor pairs in the range 1–100 and find multiples of single-digit numbers up to 100.

Identify composite numbers and prime numbers and explain the relationship with the factor pairs.

Classify, compare, and contrast polygons based on properties.

Determine, through exploration and investigation, that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.

Investigate volume of right rectangular prisms by packing them with unit cubes without gaps or overlaps. Then, determine the total volume to solve problems.

Discover and explain how the volume of a right rectangular prism can be found by multiplying the area of the base times the height to solve authentic, mathematical problems.

Explore realistic problems involving different units of measurement, including distance, mass, weight, volume, and time.

Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to solve problems relevant to everyday life

Convert among units within the metric system and then apply these conversions to solve multistep, practical problems.

Convert among units within relative sizes of measurement units within the customary measurement system.

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

Explain that in a multi-digit number, a digit in one 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 placement of digits when multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10, up to 10^3.

Fluently multiply multi-digit (up to 3- digit by 2-digit) whole numbers to solve authentic problems.

Fluently divide multi-digit whole numbers (up to 4-digit dividends and 2-digit divisors no greater than 25) to solve practical problems.

Explain the meaning of a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.

Compare and order up to three fractions with different numerators and/or different denominators by flexibly using a variety of tools and strategies.

Model and solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators.

Model and solve problems involving multiplication of a fraction and a whole number.

Explain why multiplying a whole number by a fraction greater than one results in a product greater than the whole number, and why multiplying a whole number by a fraction less than one results in a product less than the whole number and multiplying a whole number by a fraction equal to one results in a product equal to the whole number.

Model and solve problems involving division of a unit fraction by a whole number and a whole number by a unit fraction.

Read and write decimal numbers to the thousandths place using base-ten numerals written in standard form and expanded form.

Represent, compare, and order decimal numbers to the thousandths place based on the meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Use place value understanding to round decimal numbers to the hundredths place.

Solve problems involving addition and subtraction of decimal numbers to the hundredths place using a variety of strategies.

Write, interpret, and evaluate simple numerical expressions involving whole numbers with or without grouping symbols to represent actual situations.

Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms by completing a table.

Represent problems by plotting ordered pairs and explain coordinate values of points in the first quadrant of the coordinate plane.

Explore area as a measurable attribute of triangles, quadrilaterals, and other polygons conceptually by composing or decomposing into rectangles, triangles, and other shapes. Find the area of these geometric figures to solve problems.

Given the net of three-dimensional figures with rectangular and triangular faces, determine the surface area of these figures.

Calculate the volume of right rectangular prisms with fractional edge lengths by applying the formula, V = (area of base) x (height).

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

Fluently add and subtract any combination of fractions to solve problems.

Multiply and divide any combination of whole numbers, fractions, and mixed numbers using a student-selected strategy. Interpret products and quotients of fractions and solve word problems.

Perform operations with multi-digit decimal numbers fluently using models and student-selected strategies

Describe and interpret the center of the distribution by the equal share value (mean).

Summarize categorical and quantitative (numerical) data sets in relation to the context: display the distributions of quantitative (numerical) data in plots on a number line, including dot plots, histograms, and box plots and display the distribution of categorical data using bar graphs.

Interpret numerical data to answer a statistical investigative question created. Describe the distribution of a quantitative (numerical) variable collected, including its center, variability, and overall shape.

Design simple experiments and collect data. Use data gathered from realistic scenarios and simulations to determine quantitative measures of center (median and/or mean) and variability (interquartile range and range). Use these quantities to draw conclusions about the data, compare different numerical data sets, and make predictions.

Relate the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

Describe the impact that inserting or deleting a data point has on the mean and the median of a data set. Create data displays using a dot plot or box plot to examine this impact.

Identify and compare integers and explain the meaning of zero based on multiple authentic situations.

Order and plot integers on a number line and use distance from zero to discover the connection between integers and their opposites.

Recognize and explain that opposite signs of integers indicate locations on opposite sides of zero on the number line; recognize and explain that the opposite of the opposite of a number is the number itself.

Write, interpret, and explain statements of order for rational numbers in authentic, mathematical situations. Compare rational numbers, including integers, using equality and inequality symbols.

Explain the absolute value of a rational number as its distance from zero on the number line; interpret absolute value as distance for a positive or negative quantity in a relevant situation.

Distinguish comparisons of absolute value from statements about order.

Explain the concept of a ratio, represent ratios, and use ratio language to describe a relationship between two quantities.

Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

Solve problems involving proportions using a variety of student-selected strategies.

Describe the concept of rates and unit rate in the context of a ratio relationship.

Solve unit rate problems including those involving unit pricing and constant speed.

Calculate a percent of a quantity as a rate per 100 and solve everyday problems given a percent.

Use ratios to convert within measurement systems (customary and metric) to solve authentic problems that exist in everyday life.

Write and evaluate numerical expressions involving rational bases and whole-number exponents.

Determine greatest common factors and least common multiples using a variety of strategies to make sense of applicable problems.

Write and read expressions that represent operations with numbers and variables in realistic situations.

Evaluate expressions when given values for the variables, including expressions that arise in everyday situations.

Apply the properties of operations to identify and generate equivalent expressions.

Solve one-step equations and inequalities involving variables when values for the variables are given. Determine whether an equation and inequality involving a variable is true or false for a given value of the variable.

Write one-step equations and inequalities to represent and solve problems; explain that a variable can represent an unknown number or any number in a specified set.

Solve problems by writing and solving equations of the form x + p = q, px = q and x/p = q for cases in which p, q and x are all nonnegative rational numbers.

Recognize and generate inequalities of the form x > c, x ≥ c, x ≤ c, or x < c to explain situations that have infinitely many solutions; represent solutions of such inequalities on a number line.

Locate and position rational numbers on a horizontal or vertical number line; find and position pairs of integers and other rational numbers on a coordinate plane.

Show and explain that signs of numbers in ordered pairs indicate locations in quadrants of the coordinate plane and determine how two ordered pairs may differ based only on the signs.

Solve problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same x-coordinate or the same y-coordinate.

Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same x-coordinate or the same y-coordinate.