Delaware K–6 mathematics standards

Count to 100 by ones and by tens.

Count forward beginning from a given number within the known sequence (instead of having to begin at 1).

Write numbers from 0 to 20. Represent a number of objects with a written numeral 0–20 (with 0 representing a count of no objects).

Understand the relationship between numbers and quantities; connect counting to cardinality.

Count to answer "how many?" questions about as many as 20 things arranged in a line, array, or circle, or as many as 10 things in a scattered configuration.

Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group.

Compare two numbers between 1 and 10 presented as written numerals.

Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.

Solve addition and subtraction word problems, and add and subtract within 10, using objects or drawings to represent the problem.

Decompose numbers less than or equal to 10 into pairs in more than one way, and record each decomposition by a drawing or equation.

For any number from 1 to 9, find the number that makes 10 when added to the given number.

Fluently add and subtract within 5.

Compose and decompose numbers from 11 to 19 into ten ones and some further ones to understand that these numbers are composed of ten ones and one, two, three, … nine ones.

Describe measurable attributes of objects, such as length or weight; describe several measurable attributes of a single object.

Directly compare two objects with a measurable attribute in common, to see which object has "more of"/"less of" the attribute.

Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.

Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.

Correctly name shapes regardless of their orientations or overall size.

Identify shapes as two-dimensional (lying in a plane, "flat") or three-dimensional ("solid").

Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, and parts.

Model shapes in the world by building shapes from components and drawing shapes.

Compose simple shapes to form larger shapes.

Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing.

Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20.

Apply properties of operations as strategies to add and subtract (commutative and associative properties).

Understand subtraction as an unknown-addend problem.

Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

Add and subtract within 20, demonstrating fluency for addition and subtraction within 10.

Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.

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

Count to 120, starting at any number less than 120. Read and write numerals and represent a number of objects with a written numeral.

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

Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results with the symbols >, =, and <.

Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10.

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

Subtract multiples of 10 in the range 10–90 from multiples of 10 in the range 10–90 (positive or zero differences).

Order three objects by length; compare the lengths of two objects indirectly by using a third object.

Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object end to end.

Tell and write time in hours and half-hours using analog and digital clocks.

Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points.

Distinguish between defining attributes versus non-defining attributes; build and draw shapes to possess defining attributes.

Compose two-dimensional shapes or three-dimensional shapes to create a composite shape, and compose new shapes from the composite shape.

Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters.

Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing.

Fluently add and subtract within 20 using mental strategies. Know from memory all sums of two one-digit numbers.

Determine whether a group of objects (up to 20) has an odd or even number of members.

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.

Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones.

Count within 1000; skip-count by 5s, 10s, and 100s.

Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.

Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols.

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

Add up to four two-digit numbers using strategies based on place value and properties of operations.

Add and subtract within 1000, using concrete models or drawings and strategies based on place value.

Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.

Explain why addition and subtraction strategies work, using place value and the properties of operations.

Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.

Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate.

Estimate lengths using units of inches, feet, centimeters, and meters.

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

Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units.

Represent whole numbers as lengths from 0 on a number line diagram, and represent whole-number sums and differences within 100 on a number line.

Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.

Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately.

Generate measurement data by measuring lengths of several objects, and show the measurements by making a line plot.

Draw a picture graph and a bar graph to represent a data set with up to four categories; solve simple put-together, take-apart, and compare problems using the information.

Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces; identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.

Partition circles and rectangles into two, three, or four equal shares; describe the shares using the words halves, thirds, half of, a third of, etc.

Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each.

Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares.

Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities.

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

Apply properties of operations as strategies to multiply and divide (commutative, associative, and distributive properties).

Understand division as an unknown-factor problem.

Fluently multiply and divide within 100. By the end of Grade 3, know from memory all products of two one-digit numbers.

Solve two-step word problems using the four operations; represent these problems using equations with a letter standing for the unknown quantity.

Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.

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

Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

Multiply one-digit whole numbers by multiples of 10 in the range 10–90 using strategies based on place value and properties of operations.

Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

Understand a fraction as a number on the number line; represent fractions on a number line diagram.

Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

Tell and write time to the nearest minute and measure time intervals in minutes; solve word problems involving addition and subtraction of time intervals.

Measure and estimate liquid volumes and masses of objects using standard units of grams, kilograms, and liters; solve one-step problems involving these quantities.

Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories; solve one- and two-step "how many more" and "how many less" problems.

Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch; show the data by making a line plot.

Recognize area as an attribute of plane figures and understand concepts of area measurement.

Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).

Relate area to the operations of multiplication and addition.

Solve real-world and mathematical problems involving perimeters of polygons, including finding an unknown side length.

Understand that shapes in different categories may share attributes, and that the shared attributes can define a larger category; recognize rhombuses, rectangles, and squares as examples of quadrilaterals.

Partition shapes into parts with equal areas; express the area of each part as a unit fraction of the whole.

Interpret a multiplication equation as a comparison; represent verbal statements of multiplicative comparisons as multiplication equations.

Multiply or divide to solve word problems involving multiplicative comparison, distinguishing multiplicative comparison from additive comparison.

Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems with remainders.

Find all factor pairs for a whole number in the range 1–100; recognize that a whole number is a multiple of each of its factors; determine whether a number is prime or composite.

Generate a number or shape pattern that follows a given rule; identify apparent features of the pattern that were not explicit in the rule itself.

Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.

Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form; compare two multi-digit numbers using >, =, and < symbols.

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

Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value.

Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using place value strategies and the relationship between multiplication and division.

Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models; use this principle to recognize and generate equivalent fractions.

Compare two fractions with different numerators and different denominators by creating common denominators or numerators, or by comparing to a benchmark fraction.

Understand a fraction a/b with a > 1 as a sum of fractions 1/b; decompose a fraction into a sum of fractions with the same denominator; add and subtract mixed numbers.

Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.

Use decimal notation for fractions with denominators 10 or 100.

Compare two decimals to hundredths by reasoning about their size; record the results of comparisons with the symbols >, =, or <.

Know relative sizes of measurement units within one system of units; express measurements in a larger unit in terms of a smaller unit.

Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money.

Apply the area and perimeter formulas for rectangles in real-world and mathematical problems.

Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8); solve problems involving addition and subtraction of fractions using the data.

Recognize angles as geometric shapes formed wherever two rays share a common endpoint, and understand concepts of angle measurement.

Measure angles in whole-number degrees using a protractor; sketch angles of specified measure.

Recognize angle measure as additive; solve addition and subtraction problems to find unknown angles on a diagram.

Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines; identify these in two-dimensional figures.

Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size; recognize right triangles.

Recognize a line of symmetry for a two-dimensional figure; identify line-symmetric figures and draw lines of symmetry.

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

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

Generate two numerical patterns using two given rules; identify apparent relationships between corresponding terms and graph the ordered pairs.

Recognize 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 number of zeros of the product when multiplying a number by powers of 10, and in the placement of the decimal point; denote powers of 10 with exponents.

Read, write, and compare decimals to thousandths using base-ten numerals, number names, expanded form, and >, =, < symbols.

Use place value understanding to round decimals to any place.

Fluently multiply multi-digit whole numbers using the standard algorithm.

Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value and the relationship between operations.

Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value.

Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions with a common denominator.

Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators; estimate to assess reasonableness.

Interpret a fraction as division of the numerator by the denominator; solve word problems involving division of whole numbers leading to fraction or mixed-number answers.

Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

Interpret multiplication as scaling (resizing) by comparing the size of a product to the size of one factor.

Solve real-world problems involving multiplication of fractions and mixed numbers using visual fraction models or equations.

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

Convert among different-sized standard measurement units within a given measurement system, and use these conversions in solving multi-step, real-world problems.

Make a line plot to display a data set of measurements in fractions of a unit; use operations on fractions to solve problems involving information presented in line plots.

Recognize volume as an attribute of solid figures and understand concepts of volume measurement using unit cubes.

Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume.

Use a pair of perpendicular number lines (axes) to define a coordinate system; understand that the first number in an ordered pair indicates how far to travel along the x-axis.

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

Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.

Classify two-dimensional figures in a hierarchy based on properties.

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.

Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number lines, or equations.

Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.

Fluently divide multi-digit numbers using the standard algorithm.

Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

Find the greatest common factor of two whole numbers ≤ 100 and the least common multiple of two whole numbers ≤ 12; use the distributive property to express a sum.

Understand that positive and negative numbers are used together to describe quantities having opposite directions or values; use positive and negative numbers to represent quantities in real-world contexts.

Understand a rational number as a point on the number line; extend number line diagrams and coordinate axes to represent points with negative number coordinates.

Understand ordering and absolute value of rational numbers.

Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane.

Write and evaluate numerical expressions involving whole-number exponents.

Write, read, and evaluate expressions in which letters stand for numbers.

Apply the properties of operations to generate equivalent expressions.

Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).

Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true?

Use variables to represent numbers and write expressions when solving a real-world or mathematical problem.

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

Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem; represent solutions on number line diagrams.

Use variables to represent two quantities in a real-world problem that change in relationship to one another; analyze the relationship using graphs and tables.

Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles.

Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes; apply the formulas V = l w h and V = b h.

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 first or second coordinate.

Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures.

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary.

Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

Summarize numerical data sets in relation to their context, reporting the number of observations, measures of center, and measures of variability.