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Skills available for Virginia fourth-grade math standards

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Virginia Standards of Learning (2023): Grade 4 Virginia Standards of Learning (2023): Grade 4
Virginia Curriculum Framework Virginia Curriculum Framework
Virginia Standards of Learning (2016) Virginia Standards of Learning (2016)

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4.NS Number and Number Sense

4.NS.1 The student will use place value understanding to read, write, and identify the place and value of each digit in a nine-digit whole number.
- 4.NS.1.a Read nine-digit whole numbers, presented in standard form, and represent the same number in written form.
  - Spell word names for numbers up to one million (4-A.7)
  - Writing numbers up to one billion in words: convert digits to words (4)
- 4.NS.1.b Write nine-digit whole numbers in standard form when the numbers are presented orally or in written form.
  - Writing numbers up to one billion: convert words to digits (4)
- 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.
4.NS.2 The student will demonstrate an understanding of the base 10 system to compare and order whole numbers up to seven digits.
- 4.NS.2.a Compare two whole numbers up to seven digits each, using words (greater than, less than, equal to, or not equal to) and/or using symbols (>, <, =, ≠).
  - Compare numbers in tables (4-B.3)
  - Compare numbers up to millions (4)
- 4.NS.2.b Order up to four whole numbers up to seven digits each, from least to greatest or greatest to least.
  - Order numbers up to one million (4-B.4)
4.NS.3 The student will use mathematical reasoning and justification to represent, compare, and order fractions (proper, improper, and mixed numbers with denominators 12 or less), with and without models.
- 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. 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. Justify comparisons orally, in writing, or with a model.
- 4.NS.3.c Use benchmarks 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 =. 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.
4.NS.4 The student will use mathematical reasoning and justification to represent, compare, and order decimals through thousandths, with and without models.
- 4.NS.4.a Investigate and describe the ten-to-one place value relationship for decimals through thousandths, using concrete models.
  - Relationship between decimal place values (4)
- 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.
  - Understanding decimals expressed in words (4-Y.5)
  - Convert decimals between standard and expanded form (4)
- 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.
  - Relate decimals and money (4-Y.3)
  - Place values in decimal numbers up to thousandths (4)
- 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. Justify comparisons with a model, orally, and in writing.
4.NS.5 The student will reason about the relationship between fractions and decimals (limited to halves, fourths, fifths, tenths, and hundredths) to identify and represent equivalencies.
- 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.
  - Model decimals and fractions (4-X.1)
  - Graph fractions as decimals on number lines (4-X.3)
- 4.NS.5.c Write the decimal and fraction equivalent for a given model.

4.CE Computation and Estimation

4.CE.1 The student will estimate, represent, solve, and justify solutions to single-step and multistep problems, including those in context, using addition and subtraction with whole numbers.
- 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 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.
  - Rounding: up to thousands place (4)
  - Estimate sums and differences: round to hundreds or thousands (4)
- 4.CE.1.c Apply strategies 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 The student will estimate, represent, solve, and justify solutions to single-step and multistep problems, including those in context, using multiplication with whole numbers, and single-step problems, including those in context, using division with whole numbers; and recall with automaticity the multiplication facts through 12 × 12 and the corresponding division facts.
- 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.
  - Multi-step word problems: identify reasonable answers (4-N.9)
- 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.
  - Balance addition equations (4)
  - Balance subtraction equations (4)
- 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.
  - Multiplication and division sentences up to 12: true or false? (4)
- 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.
  - Greatest common factors: up to three numbers (4)
- 4.CE.2.g Apply strategies and algorithms, including the standard algorithm, to estimate and determine the product of two whole numbers when given: a two-digit factor and a one-digit factor; a three-digit factor and a one-digit factor; or 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 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.
  - Divide 2-digit and 3-digit numbers by 1-digit numbers: pick the better estimate (4)
- 4.CE.2.k Interpret the quotient and remainder when solving a contextual problem.
4.CE.3 The student will estimate, represent, solve, and justify solutions to single-step problems, including those in context, using addition and subtraction of fractions (proper, improper, and mixed numbers with like denominators of 2, 3, 4, 5, 6, 8, 10, and 12), with and without models; and solve single-step contextual problems involving multiplication of a whole number (12 or less) and a unit fraction, with models.
- 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 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, with models.
  - Multiply unit fractions by whole numbers: word problems (4-V.6)
- 4.CE.3.d Apply the inverse property of multiplication in models.
4.CE.4 The student will estimate, represent, solve, and justify solutions to single-step and multistep problems, including those in context, using addition and subtraction of decimals through the thousandths, with and without models.
- 4.CE.4.a Apply strategies and algorithms, including the standard algorithm, to estimate and determine the sum or difference of two decimals through the thousandths, with and without models, in which: decimals do not exceed the thousandths; and 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.

4.MG Measurement and Geometry

4.MG.1 The student will reason mathematically to solve problems, including those in context, that involve length, weight/mass, and liquid volume using U.S. Customary and metric units.
- 4.MG.1.a Determine an appropriate unit of measure to use when measuring:
  - 4.MG.1.a.i length in both U.S. Customary (inch, foot, yard, mile) and metric units (millimeter, centimeter, meter);
    - Which customary unit of length is appropriate? (4)
    - Which metric unit of length is appropriate? (4)
  - 4.MG.1.a.ii weight/mass in both U.S. Customary (ounce, pound) and metric units (gram, kilogram); and
    - Which customary unit of weight is appropriate? (4)
    - Which metric unit of mass is appropriate? (4)
  - 4.MG.1.a.iii liquid volume in both U.S. Customary (cup, pint, quart, gallon) and metric units (milliliter, liter).
    - Which metric unit of volume is appropriate? (4)
    - Which customary unit of volume is appropriate: cups or gallons? (4)
- 4.MG.1.b Estimate and measure:
  - 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
    - Which customary unit of weight is appropriate? (4)
    - Which metric unit of mass is appropriate? (4)
  - 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 Given the equivalent measure of one unit, solve problems, including those in context, by determining the equivalent measures within the U.S. Customary system for:
  - 4.MG.1.d.i length (inches and feet, feet and yards, inches and yards);
    - Compare and convert customary units of length (4)
  - 4.MG.1.d.ii weight/mass (ounces and pounds); and
    - Compare and convert customary units of weight: ounces and pounds (4)
  - 4.MG.1.d.iii liquid volume (cups, pints, quarts, and gallons).
    - Compare and convert customary units of volume: cups, pints, quarts, gallons (4)
4.MG.2 The student will solve single-step and multistep contextual problems involving elapsed time (limited to hours and minutes within a 12-hour period).
- 4.MG.2.a Solve single-step and multistep contextual problems involving elapsed time in hours and minutes, within a 12-hour period (within a.m., within p.m., and across a.m. and p.m.) when given:
  - 4.MG.2.a.i the starting time and the ending time, determine the amount of time that has elapsed in hours and minutes;
    - Elapsed time (4-DD.4)
    - Elapsed time: word problems (4-DD.5)
  - 4.MG.2.a.ii the starting time and amount of elapsed time in hours and minutes, determine the ending time; or
    - Find end times: word problems (4)
  - 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 The student will use multiple representations to develop and use formulas to solve problems, including those in context, involving area and perimeter limited to rectangles and squares (in both U.S. Customary and metric units).
- 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.
  - Find the perimeter of rectangles using formulas (4-HH.3)
  - Find the area of rectangles using formulas (4-II.2)
- 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.
  - Find the perimeter of rectangles using formulas (4-HH.3)
  - Find the area of rectangles using formulas (4-II.2)
- 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 The student will identify, describe, and draw points, rays, line segments, angles, and lines, including intersecting, parallel, and perpendicular lines.
- 4.MG.4.a Identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices.
  - Identify points, lines, segments, and rays (4)
- 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.
  - Parallel sides in quadrilaterals (4-MM.1)
  - Sides in polygons (4)
- 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 The student will classify and describe quadrilaterals (parallelograms, rectangles, squares, rhombi, and/or trapezoids) using specific properties and attributes.
- 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.
  - Sides and angles of quadrilaterals (4-MM.2)
- 4.MG.5.c Identify and describe parallel, intersecting, perpendicular, and congruent sides in quadrilaterals.
  - Parallel sides in quadrilaterals (4-MM.1)
- 4.MG.5.d Compare, contrast, and classify quadrilaterals (parallelograms, rectangles, squares, rhombi, and/or trapezoids) based on the following properties and attributes: parallel sides; perpendicular sides; congruence of sides; and 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.
  - Pick all the names for a quadrilateral (4-MM.8)
- 4.MG.5.f Use symbolic notation to name line segments and angles in quadrilaterals.
4.MG.6 The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces), with and without models.
- 4.MG.6.a Identify concrete models and pictorial representations of solid figures (cube, rectangular prism, square pyramid, sphere, cone, and cylinder).
  - Identify three-dimensional figures (4)
- 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).
  - Properties of three-dimensional figures (4)
- 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).
  - Count vertices, edges, and faces of cubes and rectangular prisms (4)

4.PS Probability and Statistics

4.PS.1 The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on line graphs.
- 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.
- 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.
  - Create line graphs (4-BB.6)
- 4.PS.1.d Analyze data represented in line graphs and communicate results orally and in writing:
  - 4.PS.1.d.i describe the characteristics of the data represented in a line graph and the data as a whole;
  - 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;
    - Interpret line graphs (4-BB.7)
  - 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.
    - Interpret line graphs (4-BB.7)
4.PS.2 The student will model and determine the probability of an outcome of a simple event.
- 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.
  - Understanding probability (4)
- 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.
- 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.
  - Find probability (4)
- 4.PS.2.d Determine the likelihood of an event occurring and relate it to its whole number or fractional representation.
- 4.PS.2.e Create a model or contextual problem to represent a given probability.

4.PFA Patterns, Functions, and Algebra

4.PFA.1 The student will identify, describe, extend, and create increasing and decreasing patterns (limited to addition, subtraction, and multiplication of whole numbers), including those in context, using various representations.
- 4.PFA.1.a Identify, describe, extend, and create increasing and decreasing patterns using various representations.
- 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).
  - Use a rule to complete a number pattern (4-O.1)
  - Use a rule to complete an input/output table (4-O.13)
- 4.PFA.1.d Solve contextual problems that involve identifying, describing, and extending increasing and decreasing patterns using single-operation input and output rules.
  - Number patterns: word problems (4-O.7)

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4.NS Number and Number Sense

4.NS.1 The student will use place value understanding to read, write, and identify the place and value of each digit in a nine-digit whole number.

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.

4.NS.2 The student will demonstrate an understanding of the base 10 system to compare and order whole numbers up to seven digits.

4.NS.2.a Compare two whole numbers up to seven digits each, using words (greater than, less than, equal to, or 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 The student will use mathematical reasoning and justification to represent, compare, and order fractions (proper, improper, and mixed numbers with denominators 12 or less), with and without models.

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. 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. Justify comparisons orally, in writing, or with a model.

4.NS.3.c Use benchmarks 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 =. 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.

4.NS.4 The student will use mathematical reasoning and justification to represent, compare, and order decimals through thousandths, with and without models.

4.NS.4.a Investigate and describe the ten-to-one place value relationship for decimals through thousandths, using concrete models.

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.

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. Justify comparisons with a model, orally, and in writing.

4.NS.5 The student will reason about the relationship between fractions and decimals (limited to halves, fourths, fifths, tenths, and hundredths) to identify and represent equivalencies.

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.

4.CE Computation and Estimation

4.CE.1 The student will estimate, represent, solve, and justify solutions to single-step and multistep problems, including those in context, using addition and subtraction with whole numbers.

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 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 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.

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.

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 Apply strategies and algorithms, including the standard algorithm, to estimate and determine the product of two whole numbers when given: a two-digit factor and a one-digit factor; a three-digit factor and a one-digit factor; or 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 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 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, with models.

4.CE.3.d Apply the inverse property of multiplication in models.

4.CE.4 The student will estimate, represent, solve, and justify solutions to single-step and multistep problems, including those in context, using addition and subtraction of decimals through the thousandths, with and without models.

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.

4.MG Measurement and Geometry

4.MG.1 The student will reason mathematically to solve problems, including those in context, that involve length, weight/mass, and liquid volume using U.S. Customary and metric units.

4.MG.1.a Determine an appropriate unit of measure to use when measuring:

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 Estimate and measure:

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 Given the equivalent measure of one unit, solve problems, including those in context, by determining the equivalent measures within the U.S. Customary system for:

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 The student will solve single-step and multistep contextual problems involving elapsed time (limited to hours and minutes within a 12-hour period).

4.MG.2.a Solve single-step and multistep contextual problems involving elapsed time in hours and minutes, within a 12-hour period (within a.m., within p.m., and across a.m. and p.m.) when given:

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 The student will use multiple representations to develop and use formulas to solve problems, including those in context, involving area and perimeter limited to rectangles and squares (in both U.S. Customary and metric units).

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 The student will identify, describe, and draw points, rays, line segments, angles, and lines, including intersecting, parallel, and perpendicular lines.

4.MG.4.a Identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices.

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);