Virginia flagVirginia: Grade 4 Math Standards

126 standards · 6 domains

COMPUTATION AND ESTIMATION

  • 4.CE.1.a Determine and justify whether an estimate or an exact answer is appropriate when solving contextual problems involving addition and subtraction with whole numbers. Refine estimates by adjusting the final amount, using terms such as closer to, between, and a little more than.
  • 4.CE.1.b Apply strategies (e.g., rounding to the nearest 100 or 1,000, using compatible numbers, other number relationships) to estimate a solution for single-step or multistep addition or subtraction problems with whole numbers, where addends or minuends do not exceed 10,000.
  • 4.CE.1.c Apply strategies (e.g., place value, properties of addition, other number relationships) and algorithms, including the standard algorithm, to determine the sum or difference of two whole numbers, where addends and minuends do not exceed 10,000.
  • 4.CE.1.d Estimate, represent, solve, and justify solutions to single-step and multistep contextual problems involving addition and subtraction with whole numbers where addends and minuends do not exceed 1,000,000.
  • 4.CE.2.a Determine and justify whether an estimate or an exact answer is appropriate when solving contextual problems involving multiplication and division of whole numbers. Refine estimates by adjusting the final amount, using terms such as closer to, between, and a little more than.
  • 4.CE.2.b Recall with automaticity the multiplication facts through 12 × 12 and the corresponding division facts.
  • 4.CE.2.c Create an equation using addition, subtraction, multiplication, and division to represent the relationship between equivalent mathematical expressions (e.g., 4 × 3 = 2 × 6; 10 + 8 = 36 ÷ 2; 12 × 4 = 60 –12).
  • 4.CE.2.d Identify and use the appropriate symbol to distinguish between expressions that are equal and expressions that are not equal, using addition, subtraction, multiplication, and division (e.g., 4 × 12 = 8 × 6 and 64 ÷ 8 ≠ 8 × 8).
  • 4.CE.2.e Determine all factor pairs for a whole number 1 to 100, using concrete, pictorial, and numerical representations.
  • 4.CE.2.f Determine common factors and the greatest common factor of no more than three numbers.
  • 4.CE.2.g.i a two-digit factor and a one-digit factor;
  • 4.CE.2.g.ii a three-digit factor and a one-digit factor; or
  • 4.CE.2.g.iii a two-digit factor and a two-digit factor.
  • 4.CE.2.h Estimate, represent, solve, and justify solutions to single-step and multistep contextual problems that involve multiplication with whole numbers.
  • 4.CE.2.i Apply strategies (e.g., rounding, compatible numbers, place value) and algorithms, including the standard algorithm, to estimate and determine the quotient of two whole numbers, given a one-digit divisor and a two- or three-digit dividend, with and without remainders.
  • 4.CE.2.j Estimate, represent, solve, and justify solutions to single-step contextual problems involving division with whole numbers.
  • 4.CE.2.k Interpret the quotient and remainder when solving a contextual problem.
  • 4.CE.3.a Estimate and determine the sum or difference of two fractions (proper or improper) and/or mixed numbers, having like denominators limited to 2, 3, 4, 5, 6, 8, 10, and 12 (e.g., 3/8 + 3/8, 2 1/5 + 4/5, 7/4 – 5/4) and simplify the resulting fraction. Addition and subtraction with fractions may include regrouping.
  • 4.CE.3.b Estimate, represent, solve, and justify solutions to single-step contextual problems using addition and subtraction with fractions (proper or improper) and/or mixed numbers, having like denominators limited to 2, 3, 4, 5, 6, 8, 10, and 12, and simplify the resulting fraction. Addition and subtraction with fractions may include regrouping.
  • 4.CE.3.c Solve single-step contextual problems involving multiplication of a whole number, limited to 12 or less, and a unit fraction (e.g., 6 × 1/3, 1/5 × 8, 2 × 1/10), with models.
  • 4.CE.3.d Apply the inverse property of multiplication in models (e.g., use a visual fraction model to represent 4/4 or 1 as the product of 4 × 1/4).
  • 4.CE.4.a.i decimals do not exceed the thousandths; and
  • 4.CE.4.a.ii addends, subtrahends, and minuends are limited to four digits.
  • 4.CE.4.b Estimate, represent, solve, and justify solutions to single-step and multistep contextual problems using addition and subtraction of decimals through the thousandths.

DATA MODELING

  • 4.DS.7.a Explain why determining the reliability of big data sources is a key skill that data scientists use to build data trust across an organization.
  • 4.DS.7.b Describe the difference between reliability of a data source compared to statistical reliability and validity in research analysis. Assess processing source data for reliability based on validity, completeness, and uniqueness.
  • 4.DS.8.a Explain the pros and cons of collecting data versus acquiring it from existing sources.
  • 4.DS.8.b.i wrangle the data (sort, select, filter, and replace);
  • 4.DS.8.b.ii clean the data;
  • 4.DS.8.b.iii format and enrich the data; and
  • 4.DS.8.b.iv combine and store the data.
  • 4.DS.8.c Read data from different sources for preparation and analysis.
  • 4.DS.8.d Identify important parameters about a big data set based on the context of data collected/acquired.
  • 4.DS.8.e.i making data more easily understood by a wider audience; and
  • 4.DS.8.e.ii connecting data with existing contextual data.
  • 4.DS.9.a Identify factors that contribute to the overall behavior of a data set (e.g., true values, bias, and noise).
  • 4.DS.9.b Fit models based on the behavior of the data, (e.g., models of univariate and bivariate data), in order to make predictions.
  • 4.DS.9.c Distinguish between linear and nonlinear associations between variables using visualizations.
  • 4.DS.9.d Identify models that are overly complex and therefore fitting to random noise which decreases their predictive accuracy.
  • 4.DS.9.e Use regression techniques to perform selection of optimal features.
  • 4.DS.9.f Recognize the potential implications of removing features.
  • 4.DS.9.g Select the optimal model for a data set from among a large collection of models, using technological tools.
  • 4.DS.10.a Apply descriptive statistics to explain measures of central tendency and measures of variability/dispersion to describe center and spread in visualizations of distributions.
  • 4.DS.10.b.i a heat map, which uses color to show changes and magnitude of a third variable to a two-dimensional plot; and
  • 4.DS.10.b.ii a bubble chart, which is a multivariate graph that is both a scatterplot and a proportional area chart. Typically, each plotted point then represents a third variable by the area of its circle.
  • 4.DS.10.c Interpret various emerging visualizations by describing patterns, trends, and relationships between and among the variables.
  • 4.DS.11.a Calculate the theoretical probability of random events and compare them to the observed frequencies.
  • 4.DS.11.b Describe the normal curve determined by the mean and standard deviation of a univariate data set.
  • 4.DS.11.c Fit nonlinear models to data sets and use these models to predict unobserved data values.
  • 4.DS.11.d Select pairs of variables that identify meaningful clusters of data.
  • 4.DS.11.e.i Normal;
  • 4.DS.11.e.ii Binomial; and
  • 4.DS.11.e.iii Poisson.

MEASUREMENT AND GEOMETRY

  • 4.MG.1.a.i length in both U.S. Customary (inch, foot, yard, mile) and metric units (millimeter, centimeter, meter);
  • 4.MG.1.a.ii weight/mass in both U.S. Customary (ounce, pound) and metric units (gram, kilogram); and
  • 4.MG.1.a.iii liquid volume in both U.S. Customary (cup, pint, quart, gallon) and metric units (milliliter, liter).
  • 4.MG.1.b.i length of an object to the nearest U.S. Customary unit (1/2 inch, 1/4 inch, 1/8 inch, foot, yard) and nearest metric unit (millimeter, centimeter, or meter);
  • 4.MG.1.b.ii weight/mass of an object to the nearest U.S. Customary unit (ounce, pound) and nearest metric unit (gram, kilogram); and
  • 4.MG.1.b.iii liquid volume to the nearest U.S. Customary unit (cup, pint, quart, gallon) and nearest metric unit (milliliter, liter).
  • 4.MG.1.c Compare estimates of length, weight/mass, or liquid volume with the actual measurements.
  • 4.MG.1.d.i length (inches and feet, feet and yards, inches and yards);
  • 4.MG.1.d.ii weight/mass (ounces and pounds); and
  • 4.MG.1.d.iii liquid volume (cups, pints, quarts, and gallons).
  • 4.MG.2.a.i the starting time and the ending time, determine the amount of time that has elapsed in hours and minutes;
  • 4.MG.2.a.ii the starting time and amount of elapsed time in hours and minutes, determine the ending time; or
  • 4.MG.2.a.iii the ending time and the amount of elapsed time in hours and minutes, determine the starting time.
  • 4.MG.3.a Use concrete materials and pictorial models to develop a formula for the area and perimeter of a rectangle (including a square).
  • 4.MG.3.b Determine the area and perimeter of a rectangle when given the measure of two adjacent sides (in whole number units), with and without models.
  • 4.MG.3.c Determine the area and perimeter of a square when given the measure of one side (in whole number units), with and without models.
  • 4.MG.3.d Use concrete materials and pictorial models to explore the relationship between area and perimeter of rectangles.
  • 4.MG.3.e Identify and represent rectangles with the same perimeter and different areas or with the same area and different perimeters.
  • 4.MG.3.f Solve contextual problems involving area and perimeter of rectangles and squares.
  • 4.MG.4.a Identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices.
  • 4.MG.4.b Describe endpoints and vertices in relation to lines, line segments, rays, and angles.
  • 4.MG.4.c Draw representations of points, line segments, rays, angles, and lines, using a ruler or straightedge.
  • 4.MG.4.d Identify parallel, perpendicular, and intersecting lines and line segments in plane and solid figures, including those in context.
  • 4.MG.4.e Use symbolic notation to name points, lines, line segments, rays, angles, and to describe parallel and perpendicular lines.
  • 4.MG.5.a Develop definitions for parallelograms, rectangles, squares, rhombi, and trapezoids through the exploration of properties and attributes.
  • 4.MG.5.b Identify and describe points, line segments, angles, and vertices in quadrilaterals.
  • 4.MG.5.c Identify and describe parallel, intersecting, perpendicular, and congruent sides in quadrilaterals.
  • 4.MG.5.d.i parallel sides;
  • 4.MG.5.d.ii perpendicular sides;
  • 4.MG.5.d.iii congruence of sides; and
  • 4.MG.5.d.iv number of right angles.
  • 4.MG.5.e Denote properties of quadrilaterals and identify parallel sides, congruent sides, and right angles by using geometric markings.
  • 4.MG.5.f Use symbolic notation to name line segments and angles in quadrilaterals.
  • 4.MG.6.a Identify concrete models and pictorial representations of solid figures (cube, rectangular prism, square pyramid, sphere, cone, and cylinder).
  • 4.MG.6.b Identify and describe solid figures (cube, rectangular prism, square pyramid, and sphere) according to their characteristics (number of angles, vertices, edges, and by the number and shape of faces).
  • 4.MG.6.c Compare and contrast plane and solid figures (limited to circles, squares, triangles, rectangles, spheres, cubes, square pyramids, and rectangular prisms) according to their characteristics (number of sides, angles, vertices, edges, and the number and shape of faces).

NUMBER AND NUMBER SENSE

  • 4.NS.1.a Read nine-digit whole numbers, presented in standard form, and represent the same number in written form.
  • 4.NS.1.b Write nine-digit whole numbers in standard form when the numbers are presented orally or in written form.
  • 4.NS.1.c Apply patterns within the base 10 system to determine and communicate, orally and in written form, the place and value of each digit in a nine-digit whole number (e.g., in 568,165,724, the 8 represents 8 millions and its value is 8,000,000).
  • 4.NS.2.a Compare two whole numbers up to seven digits each, using words (greater than, less than, equal to, not equal to) and/or using symbols (>, <, =, ≠).
  • 4.NS.2.b Order up to four whole numbers up to seven digits each, from least to greatest or greatest to least.
  • 4.NS.3.a Compare and order no more than four fractions (proper or improper), and/or mixed numbers, with like denominators by comparing the number of parts (numerators) using fractions with denominators of 12 or less (e.g., 1/5 < 3/5). Justify comparisons orally, in writing, or with a model.
  • 4.NS.3.b Compare and order no more than four fractions (proper or improper), and/or mixed numbers, with like numerators and unlike denominators by comparing the size of the parts using fractions with denominators of 12 or less (e.g., 3/8 < 3/5). Justify comparisons orally, in writing, or with a model.
  • 4.NS.3.c Use benchmarks (e.g., 0, 1/2, or 1) to compare and order no more than four fractions (proper or improper), and/or mixed numbers, with like and unlike denominators of 12 or less. Justify comparisons orally, in writing, or with a model.
  • 4.NS.3.d Compare two fractions (proper or improper) and/or mixed numbers using fractions with denominators of 12 or less, using the symbols >, <, and = (e.g., 2/3 > 1/7). Justify comparisons orally, in writing, or with a model.
  • 4.NS.3.e Represent equivalent fractions with denominators of 12 or less, with and without models.
  • 4.NS.3.f Compose and decompose fractions (proper and improper) and/or mixed numbers with denominators of 12 or less, in multiple ways, with and without models.
  • 4.NS.3.g Represent the division of two whole numbers as a fraction given a contextual situation and a model (e.g., 3/5 means the same as 3 divided by 5 or 3/5 represents the amount of muffin each of five children will receive when sharing three muffins equally).
  • 4.NS.4.a Investigate and describe the ten-to-one place value relationship for decimals through thousandths, using concrete models (e.g., place value mats/charts, decimal squares, base 10 blocks).
  • 4.NS.4.b Represent and identify decimals expressed through thousandths, using concrete, pictorial, and numerical representations.
  • 4.NS.4.c Read and write decimals expressed through thousandths, using concrete, pictorial, and numerical representations.
  • 4.NS.4.d Identify and communicate, both orally and in written form, the place and value of each digit in a decimal through thousandths (e.g., given 0.385, the 8 is in the hundredths place and has a value of 0.08).
  • 4.NS.4.e Compare using symbols (<, >, =) and/or words (greater than, less than, equal to) and order (least to greatest and greatest to least), a set of no more than four decimals expressed through thousandths, using multiple strategies (e.g., benchmarks, place value, number lines). Justify comparisons with a model, orally, and in writing.
  • 4.NS.5.a Represent fractions (proper or improper) and/or mixed numbers as decimals through hundredths, using multiple representations, limited to halves, fourths, fifths, tenths, and hundredths.
  • 4.NS.5.b Identify and model equivalent relationships between fractions (proper or improper) and/or mixed numbers and decimals, using halves, fourths, fifths, tenths, and hundredths.
  • 4.NS.5.c Write the decimal and fraction equivalent for a given model (e.g., 1/4 = 0.25 or 0.25 = 1/4; 1.25 = 5/4 or 1 1/4; 1.02 = 102/100 or 1 2/100).

PATTERNS, FUNCTIONS, AND ALGEBRA

  • 4.PFA.1.a Identify, describe, extend, and create increasing and decreasing patterns using various representations (e.g., objects, pictures, numbers, number lines, input/output tables, and function machines).
  • 4.PFA.1.b Analyze an increasing or decreasing single-operation numerical pattern found in lists, input/output tables, or function machines and generalize the change to identify the rule, extend the pattern, or identify missing terms.
  • 4.PFA.1.c Given a rule, create increasing and decreasing patterns using numbers and input/output tables (including function machines).
  • 4.PFA.1.d Solve contextual problems that involve identifying, describing, and extending increasing and decreasing patterns using single-operation input and output rules.

PROBABILITY AND STATISTICS

  • 4.PS.1.a Formulate questions that require the collection or acquisition of data.
  • 4.PS.1.b Determine the data needed to answer a formulated question and collect or acquire existing data (limited to 10 or fewer data points) using various methods (e.g., observations, measurements, experiments).
  • 4.PS.1.c Organize and represent a data set using line graphs with a title and labeled axes with whole number increments, with and without the use of technology tools.
  • 4.PS.1.d.i describe the characteristics of the data represented in a line graph and the data as a whole (e.g., the time period when the temperature increased the most);
  • 4.PS.1.d.ii identify parts of the data that have special characteristics and explain the meaning of the greatest, the least, or the same (e.g., the highest temperature shows the warmest day);
  • 4.PS.1.d.iii make inferences about data represented in line graphs;
  • 4.PS.1.d.iv draw conclusions about the data and make predictions based on the data to answer questions; and
  • 4.PS.1.d.v solve single-step and multistep addition and subtraction problems using data from line graphs.
  • 4.PS.2.a Describe probability as the degree of likelihood of an outcome occurring using terms such as impossible, unlikely, equally likely, likely, and certain.
  • 4.PS.2.b Model and determine all possible outcomes of a given simple event where there are no more than 24 possible outcomes, using a variety of manipulatives (e.g., coins, two-sided counters, number cubes, spinners).
  • 4.PS.2.c Write the probability of a given simple event as a fraction between 0 and 1, where there are no more than 24 possible outcomes.
  • 4.PS.2.d Determine the likelihood of an event occurring and relate it to its whole number or fractional representation (e.g., impossible or zero; equally likely; certain or one).
  • 4.PS.2.e Create a model or contextual problem to represent a given probability.