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.
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.)
Solve multi-step word problem posed with whole numbers and having whole number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using situation equations and/or solution equations with a letter or symbol standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
Find all factor pairs for a whole number in the range 1 to 100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1 to 100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1 to 100 is prime or composite.
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. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.
| Standard | Definition | Code |
|---|---|---|
| Interpret a multiplication equation as a comparison | 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.OA.1 |
| Multiply or divide to solve word problems involving multiplicative comparison | 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.OA.2 |
| Solve multi-step word problem posed with whole numbers and having whole number… | Solve multi-step word problem posed with whole numbers and having whole number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using situation equations and/or solution equations with a letter or symbol standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | 4.OA.3 |
| Find all factor pairs for a whole number in the range 1 to 100 | Find all factor pairs for a whole number in the range 1 to 100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1 to 100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1 to 100 is prime or composite. | 4.OA.4 |
| Generate a number or shape pattern that follows a given rule | 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. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. | 4.OA.5 |
Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.
Read and write multi-digit whole numbers using base-ten numerals, number names, expanded form, and unit form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, <, =, and ≠ symbols to record the results of comparisons.
Use place value understanding to round multi-digit whole numbers to any place.
Fluently (efficiently, accurately, and flexibly) add and subtract multi-digit whole numbers using an efficient algorithm (including, but not limited to: traditional, partial-sums, etc.), based on place value understanding and the properties of operations.
Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit 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.
Find whole-number quotients and remainders with up to four-digit dividends and one-digit 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.
| Standard | Definition | Code |
|---|---|---|
| Recognize that in a multi-digit whole number, a digit in one place represents… | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | 4.NBT.1 |
| Read and write multi-digit whole numbers using base-ten numerals, number names… | Read and write multi-digit whole numbers using base-ten numerals, number names, expanded form, and unit form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, <, =, and ≠ symbols to record the results of comparisons. | 4.NBT.2 |
| Use place value understanding to round multi-digit whole numbers to any place | Use place value understanding to round multi-digit whole numbers to any place. | 4.NBT.3 |
| Fluently (efficiently, accurately | Fluently (efficiently, accurately, and flexibly) add and subtract multi-digit whole numbers using an efficient algorithm (including, but not limited to: traditional, partial-sums, etc.), based on place value understanding and the properties of operations. | 4.NBT.4 |
| Multiply a whole number of up to four digits by a one-digit whole number | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit 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.NBT.5 |
| Find whole-number quotients and remainders with up to four-digit dividends and… | Find whole-number quotients and remainders with up to four-digit dividends and one-digit 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.NBT.6 |
Make a data display (line plot, bar graph, pictograph) to show a set of measurements in fractions of a unit (½, ¼, 1/8, 1/16). Solve problems involving addition and subtraction of fractions by using information presented in the data display.
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 two-column table.
Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and 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 the area and perimeter formulas for rectangles in real world and mathematical problems explaining and justifying the appropriate unit of measure.
| Standard | Definition | Code |
|---|---|---|
| Make a data display | Make a data display (line plot, bar graph, pictograph) to show a set of measurements in fractions of a unit (½, ¼, 1/8, 1/16). Solve problems involving addition and subtraction of fractions by using information presented in the data display. | 4.MD.4 |
| Know relative sizes of measurement units within one system of units including… | 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 two-column table. | 4.MD.1 |
| Use the four operations to solve word problems involving distances, intervals… | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and 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. | 4.MD.2 |
| Apply the area and perimeter formulas for rectangles in real world and… | Apply the area and perimeter formulas for rectangles in real world and mathematical problems explaining and justifying the appropriate unit of measure. | 4.MD.3 |
Draw points, lines, line segments, rays, angles (right, acute, obtuse, straight, reflex), and perpendicular and parallel lines. Identify these in two-dimensional figures.
Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles (right, acute, obtuse, straight, reflex). Recognize and categorize triangles based on angles (acute, obtuse, equiangular, and right) and/or sides (scalene, isosceles, and equilateral).
Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.
| Standard | Definition | Code |
|---|---|---|
| Draw points, lines, line segments, rays, angles | Draw points, lines, line segments, rays, angles (right, acute, obtuse, straight, reflex), and perpendicular and parallel lines. Identify these in two-dimensional figures. | 4.G.1 |
| Classify two-dimensional figures based on the presence or absence of parallel… | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles (right, acute, obtuse, straight, reflex). Recognize and categorize triangles based on angles (acute, obtuse, equiangular, and right) and/or sides (scalene, isosceles, and equilateral). | 4.G.2 |
| Recognize a line of symmetry for a two-dimensional figure as a line across the… | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | 4.G.3 |
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, (e.g. by creating common numerators or denominators, or by comparing to a benchmark fraction such as ½.) Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with relational symbols >, <, =, or ≠, and justify the conclusions, (e.g. by using visual fraction models.).
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.
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.
Add and subtract mixed numbers with like denominators, e.g. by replacing each mixed number with an equivalent fraction (simplest form is not an expectation), and/or by using properties of operations 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, e.g. by using visual fraction models and equations to represent the problem.
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.
Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.
Solve word problems involving multiplication of a fraction by a whole number.
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.
Use decimal notation for fractions with denominators 10 or 100.
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 relational symbols >, < =, or ≠, and justify the conclusions, (e.g. by using a visual model.).
| Standard | Definition | Code |
|---|---|---|
| Explain why a fraction a/b is equivalent to a fraction | 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.NF.1 |
| Compare two fractions with different numerators and different denominators | Compare two fractions with different numerators and different denominators, (e.g. by creating common numerators or denominators, or by comparing to a benchmark fraction such as ½.) Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with relational symbols >, <, =, or ≠, and justify the conclusions, (e.g. by using visual fraction models.). | 4.NF.2 |
| Understand a fraction a/b with a > 1 as a sum of fractions 1/b | Understand a fraction a/b with a > 1 as a sum of fractions 1/b. | 4.NF.3 |
| Understand addition and subtraction of fractions as joining and separating… | Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. | 4.NF.3.a |
| Decompose a fraction into a sum of fractions with the same denominator in more… | 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.NF.3.b |
| Add and subtract mixed numbers with like denominators, e.g | Add and subtract mixed numbers with like denominators, e.g. by replacing each mixed number with an equivalent fraction (simplest form is not an expectation), and/or by using properties of operations and the relationship between addition and subtraction. | 4.NF.3.c |
| Solve word problems involving addition and subtraction of fractions referring… | 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.NF.3.d |
| Apply and extend previous understandings of multiplication to multiply a… | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | 4.NF.4 |
| Understand a fraction a/b as a multiple of 1/b | Understand a fraction a/b as a multiple of 1/b. | 4.NF.4.a |
| Understand a multiple of a/b as a multiple of 1/b | 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.4.b |
| Solve word problems involving multiplication of a fraction by a whole number | Solve word problems involving multiplication of a fraction by a whole number. | 4.NF.4.c |
| Express a fraction with denominator 10 as an equivalent fraction with… | 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.5 |
| Use decimal notation for fractions with denominators 10 or 100 | Use decimal notation for fractions with denominators 10 or 100. | 4.NF.6 |
| Compare two decimals to hundredths by reasoning about their size | 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 relational symbols >, < =, or ≠, and justify the conclusions, (e.g. by using a visual model.). | 4.NF.7 |