
4Grade 4 Standards
Top Mathematicians

Number and Operations in Base Ten

4.NBT.1.1
Recognize that in a multidigit whole number, a digit in one place represents ten times what it represents in the place to its right.

4.NBT.1.2
Read and write multidigit whole numbers using baseten numerals, number names, and expanded form. Compare two multidigit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.


4.8020

4.8120

4.8315

4.8425

4.8520

4.8615

4.8720

4.8820

4.8915


4.NBT.1.3
Use place value understanding to round multidigit whole numbers to any place.


4.9015

4.9115

4.9220

4.9320

4.9420

4.9520

4.9620

4.9720

4.9820

4.9920

4.10020


4.NBT.2.4
Fluently add and subtract multidigit whole numbers using the standard algorithm.


4.10125

4.10220

4.10320

4.10420

4.1055

4.10615

4.10720


4.NBT.2.5
Multiply a whole number of up to four digits by a onedigit whole number, and multiply two twodigit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.


4.10820

4.10920

4.1105

4.11120

4.11215

4.11315

4.11415

4.11510

4.1165

4.11710

4.11815


4.NBT.2.6
Find wholenumber quotients and remainders with up to fourdigit dividends and onedigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.


4.11915

4.12020

4.12120

4.12220


4.NBT.1.1

Number and Operations  Fractions

4.NF.1.1
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.


4.4410

4.4520

4.4715

4.4815

4.4910

4.5020

4.5120

4.5220


4.NF.1.2
Compare two fractions with different numerators and different denominators, e.g., 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 <, and justify the conclusions, e.g., by using a visual fraction model.

4.NF.2.3a
Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.


4.5520

4.5615

4.5720

4.5820

4.5920


4.NF.2.3b
Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model.


4.5820

4.5920


4.NF.2.3c
Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.


4.6020

4.6120


4.NF.2.3d
Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.


4.6215

4.6320

4.6420

4.655


4.NF.2.4a
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b.

4.NF.2.4b
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.

4.NF.2.4c
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem.

4.NF.3.5
Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.

4.NF.3.6
Use decimal notation for fractions with denominators 10 or 100.

4.NF.3.7
Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.


4.4520

4.7415

4.7515

4.7615

4.7720


4.NF.1.1

Operations and Algebraic Thinking

4.OA.1.1
Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.


4.11215

4.11315

4.11415

4.12315


4.OA.1.2
Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.


4.2120

4.12420

4.12520

4.12615

4.12720

4.12820

4.12920

4.13020

4.13120

4.13220

4.13320

4.13420

4.13520

4.1365

4.1375

4.1385


4.OA.1.3
Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, 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.


4.9015

4.9115

4.13520

4.13920

4.14020

4.14120

4.14220

4.14320

4.14420

4.14520

4.1465

4.1475


4.OA.1.a
Determine whether an equation is true or false by using comparative relational thinking.


4.8720

4.8820

4.8915


4.OA.1.b
Determine the unknown whole number in an equation relating four whole numbers using comparative relational thinking.


4.OA.2.4a
Find all factor pairs for a whole number in the range 1100.


4.14820


4.OA.2.4b
Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1100 is a multiple of a given onedigit number.

4.OA.2.4c
Determine whether a given whole number in the range 1100 is prime or composite.


4.15010


4.OA.3.5
Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.


4.2620

4.15120

4.15220

4.15315

4.15410

4.1555

4.15615

4.15715

4.15820

4.15915


4.OA.1.1

Measurement and Data

4.MD.1.1
Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a twocolumn table.


4.75

4.85

4.95

4.105

4.115

4.125

4.135

4.145

4.155


4.MD.1.2
Use the four operations to solve word problems involving distances, intervals of time, and money, including problems involving simple fractions or decimals. Represent fractional quantities of distance and intervals of time using linear models.


4.155

4.1615

4.1710

4.1810

4.195

4.2015

4.2120

4.2220

4.2320

4.2420

4.255

4.2620

4.2815


4.MD.1.3
Apply the area and perimeter formulas for rectangles in real world and mathematical problems.


4.2815

4.2915

4.3015

4.3115

4.3215

4.3315

4.345


4.MD.2.4
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots.


4.355

4.365

4.375

4.385

4.395


4.MD.3.5a
Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a "onedegree angle," and can be used to measure angles.

4.MD.3.5b
Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle that turns through n onedegree angles is said to have an angle measure of n degrees.


4.405

4.4115

4.425


4.MD.3.6
Measure angles in wholenumber degrees using a protractor. Sketch angles of specified measure.


4.4115

4.4310


4.MD.3.7
Recognize angle measure as additive. When an angle is decomposed into nonoverlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.


4.425


4.MD.1.1

Geometry

4.G.1.1
Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures.

4.G.1.2
Classify twodimensional 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.


4.45

4.55


4.G.1.3
Recognize a line of symmetry for a twodimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify linesymmetric figures and draw lines of symmetry.


4.65


4.G.1.1