Wyoming K–6 mathematics standards

Count to 100 by ones and by tens.

Count to 100 by ones and by tens.

Count backwards by ones from 20.

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).

Write numbers from 0 to 20.

Represent a number of objects with a written numeral 0-20 [with 0 (zero) representing a count of no objects].

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

Use one-to-one correspondence when counting objects.

Understand that the last number name said, tells the number of objects counted regardless of their arrangement.

Understand that each successive number name refers to a quantity that is one more, and each previous number name refers to a quantity that is one less.

Solve word problems using objects and drawings to find sums up to 10 and differences within 10.

Decompose numbers less than or equal to 10 in more than one way.

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.

Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. (Limit category counts to be less than or equal to 10.)

Correctly name shapes regardless of their orientations or overall size.

Analyze and compare two- and three-dimensional shapes, using informal language to describe their similarities, differences, and attributes.

Use simple shapes to compose squares, rectangles, and hexagons.

Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, by using objects, drawings, or equations with a symbol for the unknown number to represent the problem.

Add and subtract within 20, demonstrating fluency in addition and subtraction within 10. Use strategies such as counting on; making ten using the relationship between addition and subtraction.

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

Extend the number sequences to 120. In this range:

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

Read numerals.

Write numerals.

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. Understand the following as special cases:

10 can be thought of as a bundle of ten ones — called a “ten”.

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

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

Add within 100, using concrete models or drawings and strategies based on place value:

Including adding a two-digit number and a one-digit number.

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

Understand that in adding two-digit numbers, adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

Relate the strategy to a written method and explain the reasoning used.

Work with time and money

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

Identify U.S. coins by value (pennies, nickels, dimes, quarters).

Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); for a wide variety of shapes; build and draw shapes to possess defining attributes.

Partition circles and rectangles into two and four equal shares and:

Describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of.

Describe the whole as two of, or four of the shares.

Recognize that decomposing into more equal shares creates smaller shares.

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, with unknowns in all positions, by using drawings and equations with a symbol for the unknown number to represent the problem.

Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know automatically all sums of two one-digit numbers based on strategies.

Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; and demonstrate that cases: a. 100 can be thought of as a bundle of ten tens — called a “hundred.” b. 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).

100 can be thought of as a bundle of ten tens — called a “hundred.”

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).

Three-digit numbers can be decomposed in multiple ways (e.g. 524 can be decomposed as 5 hundreds, 2 tens and 4 ones or 4 hundreds, 12 tens, and 4 ones, etc.)

Compare pairs of three-digit numbers based on meanings of the hundreds, tens, and ones digits, using the words "is greater than," "is equal to," "is less than," and with the symbols >, =, and < to record the results of comparisons.

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

Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of addition, and/or the relationship between addition and subtraction:

Relate the strategy to a written method and explain the reasoning used.

Understand that in adding or subtracting three-digit numbers, add or subtract hundreds and hundreds, tens and tens, ones and ones.

Understand that sometimes it is necessary to compose or decompose tens or hundreds.

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

Tell and write time from analog and digital clocks in five minute increments using a.m. and p.m.

Solve word problems up to $10 involving dollar bills, quarters, dimes, nickels, and pennies, using $ (dollars) and ¢ (cents) symbols appropriately.

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., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

Describing the shares using the words halves, thirds, half of, a third of, etc.

Describing the whole as two halves, three thirds, four fourths.

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

Fluently multiply and divide with factors 1 - 10 using mental strategies. By the end of Grade 3, know automatically all products of one-digit factors based on strategies.

Solve two-step word problems (limited to the whole number system) using the four basic operations. Students should apply the Order of Operations when there are no parentheses to specify a particular order.

Represent these problems using equations with a symbol standing for the unknown quantity.

Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

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

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 and represent fractions on a number line diagram.

Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.

Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

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

Understand two fractions as equivalent if they are the same size, or the same point on a number line.

Recognize and generate simple equivalent fractions. Explain why the fractions are equivalent.

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

Compare two fractions with the same numerator or the same denominator, by reasoning about their size, Recognize that valid comparisons rely on the two fractions referring to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions.

Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Use the data to create a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters.

Relate area to the operations of multiplication and addition.

Find the area of a rectangle with whole-number side lengths (dimensions) by multiplying them. Show that this area is the same as when counting unit squares.

Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.

Use area models to represent the distributive property in mathematical reasoning. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c.

Use attributes of quadrilaterals to classify rhombuses, rectangles, and squares. Understand that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

Solve multi-step word problems posed with whole numbers, including problems in which remainders must be interpreted.

Represent these problems using equations with a letter standing for the unknown quantity.

Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols.

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

Use strategies based on place value and the properties of multiplication to:

Multiply a whole number of up to four digits by a one-digit whole number.

Multiply a pair of two-digit numbers.

Use appropriate models to explain the calculation, such as by using equations, rectangular arrays, and/or area models.

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

Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. 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 such as 1/2.

Recognize that comparisons are valid only when the two fractions refer to the same whole.

Record the results of comparisons with symbols >, =, or <.

Justify the conclusions by using a visual fraction model.

Understand a fraction a/b with a > 1 as a sum of unit fractions (1/b).

Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions by using a visual fraction model.

Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction, and/or by using properties of addition and the relationship between addition and subtraction.

Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators.

Compare and order decimal numbers to hundredths and justify by using concrete and visual models. Record the results of comparisons with the words "is greater than," "is equal to," "is less than," and with the symbols >, =, and <.

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

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

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 as a category, and identify right triangles.

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

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

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 explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole number exponents to denote powers of 10.

Add, subtract, multiply, and divide decimals to hundredths 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.

Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by 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.

Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers by using visual fraction models or equations to represent the problem.

Solve real world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem.

Extend the concept of division to divide unit fractions and whole numbers by using visual fraction models and equations.

Interpret division of a unit fraction by a non-zero whole number and compute the quotient.

Interpret division of a whole number by a unit fraction and compute the quotient.

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

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

Find the volume of a right rectangular prism with whole number dimensions by multiplying them. Show that this volume is the same as when counting unit cubes.

Find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems given the formulas V =(l)(w)(h) and V = (B)(h) for rectangular prisms.

Plot and interpret points in the first quadrant of the coordinate plane to represent real-world and mathematical situations.

Use ratio and rate reasoning to solve real-world and mathematical problems.

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

Understand that a percentage is a rate per 100 and use this to solve problems involving wholes, parts, and percentages.

Use ratio reasoning to convert measurement units; convert units appropriately when multiplying or dividing quantities.

Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem.

Add, subtract, multiply, and divide manageable multi-digit decimals using efficient and generalizable procedures including, but not limited to the standard algorithm for each operation.

Understand ordering and absolute value of rational numbers.

Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.

Write, interpret, and explain statements of order for rational numbers in real-world contexts.

Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.

Distinguish comparisons of absolute value from statements about order.

Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Find distances between points with the same first coordinate or the same second coordinate; relate absolute value and distance.

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

Write expressions that record operations with numbers and with letters standing for numbers.

Identify parts of an expression using mathematical terms (sum, difference, term, product, factor, quotient, coefficient, constant).

Use Order of Operations to evaluate algebraic expressions at using positive rational numbers and whole-number exponents. Include expressions that arise from formulas in real-world problems.

Apply the properties of operations to generate equivalent expressions.

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

Write and solve real-world and mathematical problems in the form of one-step, linear equations involving 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. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

Find area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures in the context of solving real-world and mathematical problems.

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

Summarize numerical data sets in relation to their real-world context.

Report the sample size.

Describe the context of the data under investigation, including how it was measured and its units of measurement.

Find quantitative measures of center (median, mode and mean) and variability (range and interquartile range). Describe any overall pattern (including outliers, clusters, and distribution), with reference to the context in which the data was gathered.

Justify the choice of measures of center (median, mode, or mean) based on the shape of the data distribution and the context in which the data was gathered.