Alabama K–6 mathematics standards

Categorize data on Venn diagrams, pictographs, and "yes-no" charts using real objects, symbolic representations, or pictorial representations.

Count forward orally from 0 to 100 by ones and by tens. Count backward orally from 10 to 0 by ones.

Count to 100 by ones beginning with any given number between 0 and 99.

Represent 0 to 20 using concrete objects when given a written numeral from 0 to 20 (with 0 representing a count of no objects).

Say the number names in consecutive order when counting objects.

Indicate that the last number name said tells the number of objects counted in a set.

Indicate that the number of objects in a set is the same regardless of their arrangement or the order in which they were counted.

Explain that each successive number name refers to a quantity that is one larger.

Count using no more than 20 concrete objects arranged in a line, a rectangular array, or a circle.

Count using no more than 10 concrete objects in a scattered configuration.

Draw the number of objects that matches a given numeral from 0 to 20.

Orally identify whether the number of objects in one group is <em>greater/more than, less/fewer than,</em> or <em>equal/the same</em> as the number of objects in another group, in groups containing up to 10 objects, by using matching, counting, or other strategies.

Compare two numbers between 0 and 10 presented as written numerals (without using inequality symbols).

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

Correctly name shapes regardless of their orientations or overall sizes.

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, parts (number of sides and vertices or "corners"), and other attributes.

Model shapes in the world by building them from sticks, clay balls, or other components and by drawing them.

Use simple shapes to compose larger shapes.

Identify and describe measurable attributes (length, weight, height) of a single object using vocabulary such as <em>long/short, heavy/light, or tall/short</em>.

Directly compare two objects with a measurable attribute in common to see which object has "more of" or "less of" the attribute and describe the difference.

Represent addition and subtraction up to 10 with concrete objects, fingers, pennies, mental images, drawings, claps or other sounds, acting out situations, verbal explanations, expressions, or equations.

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

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

For any number from 0 to 10, find the number that makes 10 when added to the given number, by using concrete objects or drawings, and record the answer with a drawing or equation.

Fluently add and subtract within 5.

Duplicate and extend simple patterns using concrete objects.

Compose and decompose numbers from 11 to 19 by using concrete objects or drawings to demonstrate understanding that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.

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.

Ask and answer questions about the total number of data points in organized data.

Summarize data on Venn diagrams, pictographs, and "yes-no" charts using real objects, symbolic representations, or pictorial representations.

Determine "how many" in each category using up to three categories of data.

Determine "how many more" or "how many less" are in one category than in another using data organized into two or three categories.

Distinguish between defining attributes and non-defining attributes.

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

Describe "the whole" as two of or four of the shares of circles and rectangles partitioned into two or four equal shares.

Explain that decomposing into more equal shares creates smaller shares of circles and rectangles.

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

Determine the length of an object using non-standard units with no gaps or overlaps, expressing the length of the object with a whole number.

Tell and write time to the hours and half hours using analog and digital clocks.

Identify pennies and dimes by name and value.

Count forward and backward by ones, starting at any number less than 120.

Read numerals from 0 to 120.

Write numerals from 0 to 120.

Represent a number of objects from 0 to 120 with a written numeral.

Identify a bundle of ten ones as a "ten."

Identify the numbers from 11 to 19 as composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.

Identify the numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 as one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

Compare pairs of two-digit numbers based on the values of the tens and ones digits, recording the results of comparisons with the symbols >, =, and < and orally with the words "is greater than," "is equal to," and "is less than."

Add a two-digit number and a one-digit number.

Add a two-digit number and a multiple of 10.

Demonstrate that in adding two-digit numbers, tens are added to tens, ones are added to ones, and sometimes it is necessary to compose a ten.

Relate the strategy for adding a two-digit number and a one-digit number to a written method and explain the reasoning used.

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

Subtract multiples of 10 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Relate the strategy to a written method and explain the reasoning used.

Add to with change unknown to solve word problems within 20.

Take from with change unknown to solve word problems within 20.

Put together/take apart with addend unknown to solve word problems within 20.

Compare quantities, with difference unknown, bigger unknown, and smaller unknown while solving word problems within 20.

Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 by using concrete objects, drawings, or equations with a symbol for the unknown number to represent the problem.

Apply properties of operations as strategies to add and subtract.

Explain subtraction as an unknown-addend problem.

Relate counting to addition and subtraction.

Demonstrate fluency with addition and subtraction facts with sums or differences to 10 by counting on.

Demonstrate fluency with addition and subtraction facts with sums or differences to 10 by making ten.

Demonstrate fluency with addition and subtraction facts with sums or differences to 10 by decomposing a number leading to a ten.

Demonstrate fluency with addition and subtraction facts with sums or differences to 10 by using the relationship between addition and subtraction.

Demonstrate fluency with addition and subtraction facts with sums or differences to 10 by creating equivalent but easier or known sums.

Explain that the equal sign means "the same as." Determine whether equations involving addition and subtraction are true or false.

Solve for the unknown whole number in various positions in an addition or subtraction equation, relating three whole numbers that would make it true.

Reproduce, extend, and create patterns and sequences of numbers using a variety of materials.

Create a line plot where the horizontal scale is marked off in whole-number units to show the lengths of several measured objects.

Using information presented in a bar graph, solve simple "put-together," "take-apart," and "compare" problems.

Using Venn diagrams, pictographs, and "yes-no" charts, analyze data to predict an outcome.

Recognize and draw shapes having specified attributes.

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

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

Measure the length of an object by selecting and using standard units of measurement shown on rulers, yardsticks, meter sticks, or measuring tapes.

Measure objects with two different units, and describe how the two measurements relate to each other and the size of the unit chosen.

Estimate lengths using the following standard units of measurement: inches, feet, centimeters, and meters.

Measure to determine how much longer one object is than another, expressing the length difference of the two objects using standard units of length.

Use addition and subtraction within 100 to solve word problems involving same units of length, representing the problem with drawings (such as drawings of rulers) and/or equations with a symbol for the unknown number.

Create a number line diagram using whole numbers and use it to represent whole-number sums and differences within 100.

Express an understanding of common terms such as, but not limited to, <em>quarter past, half past, and quarter to</em>.

Identify nickels and quarters by name and value.

Find the value of a collection of quarters, dimes, nickels, and pennies.

Solve word problems by adding and subtracting within one dollar, using the $ and ¢ symbols appropriately (not including decimal notation).

Explain the following three-digit numbers as special cases: 100 can be thought of as a bundle of ten tens, called a "hundred," and the numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).

Count within 1000 by ones, fives, tens, and hundreds.

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

Compare two three-digit numbers based on the value of the hundreds, tens, and ones digits, recording the results of comparisons with the symbols >, =, and < and orally with the words "is greater than," "is equal to," and "is less than."

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

Use a variety of strategies to add up to four two-digit numbers.

Explain that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

Mentally add and subtract 10 or 100 to a given number between 100 and 900.

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

Use addition and subtraction within 100 to solve one- and two-step word problems by using drawings and equations with a symbol for the unknown number to represent the problem.

State automatically all sums of two one-digit numbers.

Write an equation to express an even number as a sum of two equal addends.

Write an equation to express the total number of objects in a rectangular array with up to 5 rows and up to 5 columns as a sum of equal addends.

Reproduce, extend, create, and describe patterns and sequences using a variety of materials.

Determine a simple probability from a context that includes a picture.

Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled graphs.

Measure lengths using rulers marked with halves and fourths of an inch to generate data and create a line plot marked off in appropriate units to display the data.

Draw examples of quadrilaterals that are and are not rhombuses, rectangles, and squares.

Solve real-world problems involving addition and subtraction of time intervals in minutes by representing the problem on a number line diagram.

Use the four operations to solve one-step word problems involving masses or volumes given in the same metric units.

Find the area of a rectangle with whole number side lengths by tiling without gaps or overlays and counting unit squares.

Count unit squares (square cm, square m, square in, square ft, and improvised or non-standard units) to determine area.

Relate area to the operations of multiplication using real-world problems, concrete materials, mathematical reasoning, and the distributive property.

Decompose rectilinear figures into smaller rectangles to find the area, using concrete materials.

Construct rectangles with the same perimeter and different areas or the same area and different perimeters.

Solve real-world problems involving perimeters of polygons, including finding the perimeter given the side lengths and finding an unknown side length of rectangles.

Identify the nearest 10 or 100 when rounding whole numbers, using place value understanding.

Use various strategies to add and subtract fluently within 1000.

Use concrete materials and pictorial models based on place value and properties of operations to find the product of a one-digit whole number by a multiple of ten (from 10 to 90).

Demonstrate that a unit fraction represents one part of an area model or length model of a whole that has been equally partitioned; explain that a numerator greater than one indicates the number of unit pieces represented by the fraction.

Represent a unit fraction (1/b) on a number line by defining the interval from 0 to 1 as the whole and partitioning it into <em>b</em> equal parts as specified by the denominator.

Represent a fraction (a/b) on a number line by marking off <em>a</em> lengths of size (1/b) from zero.

Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers.

Compare two fractions with the same numerator or with the same denominator by reasoning about their size (recognizing that fractions must refer to the same whole for the comparison to be valid). Record comparisons using < , >, or = and justify conclusions.

Illustrate the product of two whole numbers as equal groups by identifying the number of groups and the number in each group and represent as a written expression.

Illustrate and interpret the quotient of two whole numbers as the number of objects in each group or the number of groups when the whole is partitioned into equal shares.

Solve word situations using multiplication and division within 100 involving equal groups, arrays, and measurement quantities; represent the situation using models, drawings, and equations with a symbol for the unknown number.

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

Develop and apply properties of operations as strategies to multiply and divide.

Use the relationship between multiplication and division to represent division as an equation with an unknown factor.

Fluently determine all products obtained by multiplying two one-digit numbers.

State automatically all products of two one-digit numbers by the end of third grade.

Determine and justify solutions for two-step word problems using the four operations and write an equation with a letter standing for the unknown quantity. Determine reasonableness of answers using number sense, context, mental computation, and estimation strategies including rounding.

Recognize and explain arithmetic patterns using properties of operations.

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

Describe right triangles as a category, and identify right triangles.

Identify line-symmetric figures and draw lines of symmetry.

Within one system of units, express measurements of a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.

Solve measurement problems involving simple fractions or decimals.

Solve measurement problems that require expressing measurements given in a larger unit in terms of a smaller unit.

Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

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

Identify an angle as a geometric shape formed wherever two rays share a common endpoint.

Use a protractor to measure angles in whole-number degrees and sketch angles of specified measure.

Solve addition and subtraction problems on a diagram to find unknown angles in real-world or mathematical problems.

Using models and quantitative reasoning, explain that in a multi-digit whole number, a digit in any place represents ten times what it represents in the place to its right.

Read and write multi-digit whole numbers using standard form, word form, and expanded form.

Use place value understanding to compare two multi-digit numbers using >, =, and < symbols.

Round multi-digit whole numbers to any place using place value understanding.

Use place value strategies to fluently add and subtract multi-digit whole numbers and connect strategies to the standard algorithm.

Illustrate and explain the product of two factors using equations, rectangular arrays, and area models.

Illustrate and/or explain quotients using equations, rectangular arrays, and/or area models.

Apply principles of fraction equivalence to recognize and generate equivalent fractions.

Explain that comparison of two fractions is valid only when the two fractions refer to the same whole.

Decompose a fraction as a sum of unit fractions and as a sum of fractions with the same denominator in more than one way using area models, length models, and equations.

Add and subtract fractions and mixed numbers with like denominators using fraction equivalence, properties of operations, and the relationship between addition and subtraction.

Solve word problems involving addition and subtraction of fractions and mixed numbers having like denominators, using drawings, visual fraction models, and equations to represent the problem.

Model and explain how a non-unit fraction can be represented by a whole number times the unit fraction.

Extend previous understanding of multiplication to multiply a whole number times any fraction less than one.

Solve word problems involving multiplying a whole number times a fraction using visual fraction models and equations to represent the problem.

Use fraction equivalency to add two fractions with denominators of 10 and 100.

Use models and decimal notation to represent fractions with denominators of 10 and 100.

Use visual models and reasoning to compare two decimals to hundredths (referring to the same whole), recording comparisons using symbols >, =, or <, and justifying the conclusions.

Interpret and write equations for multiplicative comparisons.

Solve word problems involving multiplicative comparison using drawings and write equations to represent the problem, using a symbol for the unknown number.

Write equations to show solutions for multi-step word problems with a letter standing for the unknown quantity.

Determine reasonableness of answers for multi-step word problems, using mental computation and estimation strategies including rounding.

Determine whether a whole number in the range 1 to 100 is a multiple of a given one-digit number.

Determine whether a whole number in the range 1 to 100 is prime or composite.

Generate and analyze a number or shape pattern that follows a given rule.

Create a line plot to display a data set of measurements in fractions of a unit (12,14,18).

Solve problems involving addition and subtraction of fractions using information presented in line plots.

Add, subtract, multiply, and divide fractions to solve problems involving information presented in line plots.

Graph points in the first quadrant of the coordinate plane, and interpret coordinate values of points to represent real-world and mathematical problems.

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

Classify quadrilaterals in a hierarchy based on properties.

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

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

Pack a solid figure without gaps or overlaps using <em>n</em> unit cubes to demonstrate volume as <em>n</em> cubic units.

Use the associative property of multiplication to find the volume of a right rectangular prism and relate it to packing the prism with unit cubes. Show that the volume can be determined by multiplying the three edge lengths or by multiplying the height by the area of the base.

Apply the formulas <em>V = l × w × h</em> and <em>V = B × h</em> for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real-world and mathematical problems.

Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the two parts, applying this technique to solve real-world problems.

Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, using whole-number exponents to denote powers of 10.

Explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10, using whole-number exponents to denote powers of 10.

Read and write decimals to thousandths using base-ten numerals, number names, and expanded form.

Compare two decimals to thousandths based on the meaning of the digits in each place, using >, =, and < to record the results of comparisons.

Use place value understanding to round decimals to thousandths.

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

Use strategies based on place value, properties of operations, and/or the relationship between multiplication and division to find whole-number quotients and remainders with up to four-digit dividends and two-digit divisors. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Use concrete models and drawings to solve problems with decimals to hundredths.

Solve problems in a real-world context with decimals to hundredths.

Model and solve real-word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally, and assess the reasonableness of answers.

Add and subtract fractions and mixed numbers with unlike denominators, using fraction equivalence to calculate a sum or difference of fractions or mixed numbers with like denominators.

Model and interpret a fraction as division of the numerator by the denominator (<em>a/b = a ÷ b</em>)

Use visual fraction models, drawings, or equations to represent word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers

Use a visual fraction model (area model, set model, or linear model) to show (a/b) × q and create a story context for this equation to interpret the product as a parts of a partition of <em>q</em> into <em>b</em> equal parts.

Use a visual fraction model (area model, set model, or linear model) to show (a/b) × (c/d) and create a story context for this equation to interpret the product.

Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths to show that the area is the same as would be found by multiplying the side lengths.

Compare the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

Explain why multiplying a given number by a fraction greater than 1 results in a product greater than the given number and relate the principle of fraction equivalence.

Explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number and relate the principle of fraction equivalence.

Model and solve real-world problems involving multiplication of fractions and mixed numbers using visual fraction models, drawings, or equations to represent the problem.

Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions and illustrate using visual fraction models, drawings, and equations to represent the problem.

Create a story context for a unit fraction divided by a whole number, and use a visual fraction model to show the quotient.

Create a story context for a whole number divided by a unit fraction, and use a visual fraction model to show the quotient.

Write, explain, and evaluate simple numerical expressions involving the four operations to solve up to two-step problems. Include expressions involving parentheses, brackets, or braces, using commutative, associative, and distributive properties.

Use data from an input/output table to identify apparent relationships between corresponding terms.

Form ordered pairs from values in an input/output table.

Graph ordered pairs from an input/output table on a coordinate plane.

Write, evaluate, and compare expressions involving whole number exponents.

Interpret a variable as an unknown value for any number in a specified set, depending on the context.

Write expressions to represent verbal statements and real-world scenarios.

Identify parts of an expression using mathematical terms such as <em>sum, term, product, factor, quotient</em>, and <em>coefficient</em>.

Evaluate expressions (which may include absolute value and whole number exponents) with respect to order of operations.

Generate equivalent algebraic expressions using the properties of operations, including inverse, identity, commutative, associative, and distributive.

Determine whether two expressions are equivalent and justify the reasoning.

Determine whether a value is a solution to an equation or inequality by using substitution to conclude whether a given value makes the equation or inequality true.

Interpret the solution of an equation in the context of the problem.

Interpret the solution of an inequality in the context of a problem.

Represent the solutions of inequalities on a number line and explain that the solution set may contain infinitely many solutions.

Use tables, graphs, and equations to represent the relationship between independent and dependent variables.

Write examples and non-examples of statistical questions, explaining that a statistical question anticipates variability in the data related to the question.

Determine which measure of center best represents a real-world data set.

Interpret the measures of center and variability in the context of a problem.

Analyze the graphical representation of data by describing the center, spread, shape (including approximately symmetric or skewed), and unusual features (including gaps, peaks, clusters, and extreme values).

Use graphical representations of real-world data to describe the context from which they were collected.

Determine missing vertices of a rectangle with the same <em>x</em>-coordinate or the same <em>y</em>-coordinate when graphed in the coordinate plane.

Use coordinates to find the length of a side between points having the same <em>x</em>-coordinate or the same <em>y</em>-coordinate.

Calculate perimeter and area of a polygon graphed in the coordinate plane (limiting to polygons in which consecutive vertices have the same <em>x</em>-coordinate or the same <em>y</em>-coordinate).

Apply the techniques of composing and decomposing polygons to find area in the context of solving real-world and mathematical problems.

Determine the surface area of three-dimensional figures by representing them with nets composed of rectangles and triangles to solve real-world and mathematical problems.

Use models (cubes or drawings) and the volume formulas (V = <em>lwh</em> and V = <em>Bh</em>) to find and compare volumes of right rectangular prisms.

Use quotients of fractions to analyze and solve problems.

Fluently divide multi-digit whole numbers using a standard algorithm to solve real-world and mathematical problems.

Add, subtract, multiply, and divide decimals using a standard algorithm.

Use the distributive property to express the sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor.

Use factors and multiples to determine prime factorization.

Use signed numbers to describe quantities that have opposite directions or values and to represent quantities in real-world contexts.

Define <em>opposites</em> as numbers located on opposite sides of 0 and the same distance from 0 on a number line.

Use rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.

Identify quadrant locations of ordered pairs on the coordinate plane based on the signs of the <em>x</em> and <em>y</em> coordinates.

Identify <em>(a,b)</em> and <em>(a,-b)</em> as reflections across the <em>x</em>-axis.

Identify <em>(a,b)</em> and <em>(-a,b)</em> as reflections across the <em>y</em>-axis.

Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane, including finding distances between points with the same first or second coordinate.

Explain the meaning of absolute value and determine the absolute value of rational numbers in real-world contexts

Compare and order rational numbers and absolute value of rational numbers with and without a number line in order to solve real-world and mathematical problems.

Use appropriate notations [<em>a/b, a to b, a:b</em>] to represent a proportional relationship between quantities and use ratio language to describe the relationship between quantities.

Use unit rates to represent and describe ratio relationships.

Use ratio and rate reasoning to solve mathematical and real-world problems (including but not limited to percent, measurement conversion, and equivalent ratios) using a variety of models, including tables of equivalent ratios, tape diagrams, double number lines, and equations.