Illinois Priority Learning Standards: Grade 4
Skills available for Illinois fourth-grade math standards
Section
Print skill plan
4.NBT
Number and Operations in Base Ten
4.NBT.A Generalize place value understanding for multi-digit whole numbers.
4.NBT.A.1 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. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
4.NBT.A.1 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. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
4.NBT.A.2 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 to record the results of comparisons.
Base-ten numerals
Number names
Expanded form
Comparison
4.NBT.A.2 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 to record the results of comparisons.
Base-ten numerals
Number names
Expanded form
Comparison
4.NBT.A.3 Use place value understanding to round multi-digit whole numbers to any place.
Rounding
Estimate sums
Estimate differences
Estimate products
Estimate quotients
Mixed operations
4.NBT.A.3 Use place value understanding to round multi-digit whole numbers to any place.
Rounding
Estimate sums
Estimate differences
Estimate products
Estimate quotients
Mixed operations
4.NBT.B Use place value understanding and properties of operations to perform multi-digit arithmetic.
4.NBT.B.4-1 Fluently add multi-digit whole numbers using the standard algorithm.
4.NBT.B.4-1 Fluently add multi-digit whole numbers using the standard algorithm.
4.NBT.B.4-2 Fluently subtract multi-digit whole numbers using the standard algorithm.
4.NBT.B.4-2 Fluently subtract multi-digit whole numbers using the standard algorithm.
4.NBT.B.5-1 Multiply a whole number of up to four digits by a one-digit whole number using strategies based on place value and the properties of operations.
Multiplication facts
Multiply 1-digit numbers using models
Multiply 1-digit numbers
4.NBT.B.5-1 Multiply a whole number of up to four digits by a one-digit whole number using strategies based on place value and the properties of operations.
Multiplication facts
Multiply 1-digit numbers using models
Multiply 1-digit numbers
4.NBT.B.5-2 Multiply two two-digit numbers, using strategies based on place value and the properties of operations.
Multiply 2-digit numbers using models
Multiply 2-digit numbers
Properties of multiplication
4.NBT.B.5-2 Multiply two two-digit numbers, using strategies based on place value and the properties of operations.
Multiply 2-digit numbers using models
Multiply 2-digit numbers
Properties of multiplication
4.NBT.B.6-1 Find whole-number quotients and remainders with three-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.
4.NBT.B.6-1 Find whole-number quotients and remainders with three-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.
4.NBT.B.6-2 Find whole-number quotients and remainders with 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.
Divide larger numbers
Properties of division
4.NBT.B.6-2 Find whole-number quotients and remainders with 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.
Divide larger numbers
Properties of division
4.NBT.Int.1 Perform computations by applying conceptual understanding of place value, rather than by applying multi-digit algorithms.
Addition and subtraction
Multiplication
Division
4.NBT.Int.1 Perform computations by applying conceptual understanding of place value, rather than by applying multi-digit algorithms.
Addition and subtraction
Multiplication
Division
4.Int.2 Solve one-step word problems involving multiplying two two-digit numbers.
4.Int.2 Solve one-step word problems involving multiplying two two-digit numbers.
4.Int.3 Solve one-step word problems involving multiplying a four-digit number by a one-digit number.
4.Int.3 Solve one-step word problems involving multiplying a four-digit number by a one-digit number.
4.Int.4 Solve one-step word problems involving dividing a four-digit number by a one-digit number.
4.Int.4 Solve one-step word problems involving dividing a four-digit number by a one-digit number.
4.Int.7 Solve one-step word problems involving adding or subtracting two four-digit numbers.
4.Int.7 Solve one-step word problems involving adding or subtracting two four-digit numbers.
4.NF
Number and Operations—Fractions
4.NF.A Extend understanding of fraction equivalence and ordering.
4.NF.A.1-2 Use the principle a/b = (n×a)/(n×b) to recognize and generate equivalent fractions.
4.NF.A.1-2 Use the principle a/b = (n×a)/(n×b) to recognize and generate equivalent fractions.
4.NF.A.2-1 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or by comparing to a benchmark fraction such as 1/2. Record the results of comparisons with symbols >, =, or <.
Models
Benchmark fractions
Compare fractions
4.NF.A.2-1 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or by comparing to a benchmark fraction such as 1/2. Record the results of comparisons with symbols >, =, or <.
Models
Benchmark fractions
Compare fractions
4.NF.B Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.B.3a: Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
Area models
Strip models
Number lines
Equations
4.NF.B.3a: Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
Area models
Strip models
Number lines
Equations
4.NF.B.3b-1: Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Examples: 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
4.NF.B.3b-1: Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Examples: 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
4.NF.B.3c: 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.NF.B.3c: 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.NF.B.3d: 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.B.3d: 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.B.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
4.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
4.NF.B.4a: Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).
4.NF.B.4a: Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).
4.NF.B.4b-1: Understand a multiple of a/b as a multiple of 1/b. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5).
4.NF.B.4b-1: Understand a multiple of a/b as a multiple of 1/b. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5).
4.NF.B.4b-2: Use the understanding that a multiple of a/b is a multiple of 1/b to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6/5. (In general, n × (a/b) = (n×a)/b.)
Multiply with models
Multiply without models
4.NF.B.4b-2: Use the understanding that a multiple of a/b is a multiple of 1/b to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6/5. (In general, n × (a/b) = (n×a)/b.)
Multiply with models
Multiply without models
4.NF.B.4c: 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. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?
4.NF.B.4c: 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. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?
4.NF.C Understand decimal notation for fractions, and compare decimal fractions.
4.NF.C.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. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
4.NF.C.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. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.
4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.
4.NF.C.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.NF.C.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.NF.A.Int.1 Apply conceptual understanding of fraction equivalence and ordering to solve simple word problems requiring fraction comparison. Content Scope: 4.NF.A
4.NF.A.Int.1 Apply conceptual understanding of fraction equivalence and ordering to solve simple word problems requiring fraction comparison. Content Scope: 4.NF.A
4.NF.Int.1 Solve one-step word problems requiring integration of knowledge and skills articulated in 4.NF. Content Scope: 4.NF
4.NF.Int.1 Solve one-step word problems requiring integration of knowledge and skills articulated in 4.NF. Content Scope: 4.NF
4.NF.Int.2 Solve one-step addition word problems. Content Scope: 4.NF.5, 4.NF.6
4.NF.Int.2 Solve one-step addition word problems. Content Scope: 4.NF.5, 4.NF.6
4.OA
Operations and Algebraic Thinking
4.OA.A Use the four operations with whole numbers to solve problems.
4.OA.A.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.
4.OA.A.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.
4.OA.A.1-2 Represent verbal statements of multiplicative comparisons as multiplication equations.
4.OA.A.1-2 Represent verbal statements of multiplicative comparisons as multiplication equations.
4.OA.A.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.OA.A.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.OA.A.3-1 Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations.
Multi-step problems
Variable equations
Identify reasonable answers
4.OA.A.3-1 Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations.
Multi-step problems
Variable equations
Identify reasonable answers
4.OA.A.3-2 Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, in which remainders must be interpreted.
4.OA.A.3-2 Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, in which remainders must be interpreted.
4.OA.B Gain familiarity with factors and multiples.
4.OA.B.4-1 Find all factor pairs for a whole number in the range 1-100.
4.OA.B.4-1 Find all factor pairs for a whole number in the range 1-100.
4.OA.B.4-2 Recognize that a whole number is a multiple of each of its factors.
4.OA.B.4-2 Recognize that a whole number is a multiple of each of its factors.
4.OA.B.4-3 Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number.
4.OA.B.4-3 Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number.
4.OA.B.4-4 Determine whether a given whole number in the range 1-100 is prime or composite.
4.OA.B.4-4 Determine whether a given whole number in the range 1-100 is prime or composite.
4.OA.C Generate and analyze patterns.
4.OA.C.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. 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.
Make patterns
Identify features of patterns
Analyze patterns
4.OA.C.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. 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.
Make patterns
Identify features of patterns
Analyze patterns
4.Int.2 Solve one-step word problems involving multiplying two two-digit numbers
4.Int.2 Solve one-step word problems involving multiplying two two-digit numbers
4.Int.3 Solve one-step word problems involving multiplying a four-digit number by a one-digit number.
4.Int.3 Solve one-step word problems involving multiplying a four-digit number by a one-digit number.
4.Int.4 Solve one-step word problems involving dividing a four-digit number by a one-digit number.
4.Int.4 Solve one-step word problems involving dividing a four-digit number by a one-digit number.
4.MD
Measurement and Data
4.MD.A.2-2 Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
4.MD.A.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 two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36).
Customary units
Metric units
Time
4.MD.A.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 two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36).
Customary units
Metric units
Time
4.MD.A.2-1 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, in 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.
Measurement
Time
4.MD.A.2-1 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, in 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.
Measurement
Time
4.MD.A.2-2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, in problems involving simple fractions. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
4.MD.A.2-2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, in problems involving simple fractions. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
4.MD.A.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.
Perimeter
Area
Area and perimeter
4.MD.A.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.
Perimeter
Area
Area and perimeter
4.MD.B Represent and interpret data.
4.MD.B.4-1 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8).
4.MD.B.4-1 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8).
4.MD.B.4-2 Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.
4.MD.B.4-2 Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.
4.MD.C Geometric measurement: understand concepts of angle and measure angles.
4.MD.C.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
4.MD.C.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
4.MD.C.5a: 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 "one-degree angle," and can be used to measure angles.
4.MD.C.5a: 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 "one-degree angle," and can be used to measure angles.
4.MD.C.5b: An angle that turns through n one-degree angles is said to have an angle measure of n degrees.
4.MD.C.5b: An angle that turns through n one-degree angles is said to have an angle measure of n degrees.
4.MD.C.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
4.MD.C.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
4.MD.C.7 Recognize angle measure as additive. When an angle is decomposed into non-overlapping 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.MD.C.7 Recognize angle measure as additive. When an angle is decomposed into non-overlapping 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.Int.3 Solve one-step word problems involving multiplying a four-digit number by a one-digit number.
4.Int.3 Solve one-step word problems involving multiplying a four-digit number by a one-digit number.
4.Int.4 Solve one-step word problems involving dividing a four-digit number by a one-digit number.
4.Int.4 Solve one-step word problems involving dividing a four-digit number by a one-digit number.
4.Int.7 Solve one-step word problems involving adding or subtracting two four-digit numbers.
4.Int.7 Solve one-step word problems involving adding or subtracting two four-digit numbers.
4.G
Geometry
4.G.A Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
4.G.A.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
Parallel, perpendicular, and intersecting lines
Points, lines, and angles
Two-dimensional figures
4.G.A.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
Parallel, perpendicular, and intersecting lines
Points, lines, and angles
Two-dimensional figures
4.G.A.2 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.
Triangles
Quadrilaterals
4.G.A.2 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.
Triangles
Quadrilaterals
4.G.A.3 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.A.3 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.C
Reasoning
4.C.1-1 Base explanations/reasoning on the properties of operations. Content Scope: Knowledge and skills articulated in 4.NBT.5
Multiplication strategies
Properties of multiplication
4.C.1-1 Base explanations/reasoning on the properties of operations. Content Scope: Knowledge and skills articulated in 4.NBT.5
Multiplication strategies
Properties of multiplication
4.C.1-2 Base explanations/reasoning on the properties of operations. Content Scope: Knowledge and skills articulated in 4.NBT.6
4.C.1-2 Base explanations/reasoning on the properties of operations. Content Scope: Knowledge and skills articulated in 4.NBT.6
4.C.2 Base explanations/reasoning on the relationship between multiplication and division. Content Scope: Knowledge and skills articulated in 4.NBT.6
4.C.2 Base explanations/reasoning on the relationship between multiplication and division. Content Scope: Knowledge and skills articulated in 4.NBT.6
4.C.3 Reason about the place value system itself. Content Scope: Knowledge and skills articulated in 4.NBT.A
Place value
Expanded form
Compare numbers
Round numbers
4.C.3 Reason about the place value system itself. Content Scope: Knowledge and skills articulated in 4.NBT.A
Place value
Expanded form
Compare numbers
Round numbers
4.C.4-1 Base arithmetic explanations/reasoning on concrete referents such as diagrams (whether provided in the prompt or constructed by the student in her response), connecting the diagrams to a written (symbolic) method. Content Scope: Knowledge and skills articulated in 4.NF.A
Find equivalent fractions
Compare fractions
4.C.4-1 Base arithmetic explanations/reasoning on concrete referents such as diagrams (whether provided in the prompt or constructed by the student in her response), connecting the diagrams to a written (symbolic) method. Content Scope: Knowledge and skills articulated in 4.NF.A
Find equivalent fractions
Compare fractions
4.C.4-2 Base arithmetic explanations/reasoning on concrete referents such as diagrams (whether provided in the prompt or constructed by the student in her response), connecting the diagrams to a written (symbolic) method. Content Scope: Knowledge and skills articulated in 4.NF.3a, 4.NF.3b
Add and subtract fractions
Decompose fractions
4.C.4-2 Base arithmetic explanations/reasoning on concrete referents such as diagrams (whether provided in the prompt or constructed by the student in her response), connecting the diagrams to a written (symbolic) method. Content Scope: Knowledge and skills articulated in 4.NF.3a, 4.NF.3b
Add and subtract fractions
Decompose fractions
4.C.4-3 Base arithmetic explanations/reasoning on concrete referents such as diagrams (whether provided in the prompt or constructed by the student in her response), connecting the diagrams to a written (symbolic) method. Content Scope: Knowledge and skills articulated in 4.NF.4a
4.C.4-3 Base arithmetic explanations/reasoning on concrete referents such as diagrams (whether provided in the prompt or constructed by the student in her response), connecting the diagrams to a written (symbolic) method. Content Scope: Knowledge and skills articulated in 4.NF.4a
4.C.4-4 Base arithmetic explanations/reasoning on concrete referents such as diagrams (whether provided in the prompt or constructed by the student in her response), connecting the diagrams to a written (symbolic) method. Content Scope: Knowledge and skills articulated in 4.NF.4b
4.C.4-4 Base arithmetic explanations/reasoning on concrete referents such as diagrams (whether provided in the prompt or constructed by the student in her response), connecting the diagrams to a written (symbolic) method. Content Scope: Knowledge and skills articulated in 4.NF.4b
4.C.4-5 Base arithmetic explanations/reasoning on concrete referents such as diagrams (whether provided in the prompt or constructed by the student in her response), connecting the diagrams to a written (symbolic) method. Content Scope: Knowledge and skills articulated in 4.NF.C
Represent decimals and fractions
Compare decimals and fractions
4.C.4-5 Base arithmetic explanations/reasoning on concrete referents such as diagrams (whether provided in the prompt or constructed by the student in her response), connecting the diagrams to a written (symbolic) method. Content Scope: Knowledge and skills articulated in 4.NF.C
Represent decimals and fractions
Compare decimals and fractions
4.C.5-1 - 4.C.5-6 Distinguish correct explanation/reasoning from that which is flawed, and — if there is a flaw in the argument — present corrected reasoning. (For example, some flawed 'student' reasoning is presented and the task is to correct and improve it.) Content Scope: Knowledge and skills articulated in 4.OA.3, 4.NF.1, 4.NF.2, 4.NF.B, 4.NF.C, 3.OA.B, 3.NF, 3.MD.C
4.C.5-1 - 4.C.5-6 Distinguish correct explanation/reasoning from that which is flawed, and — if there is a flaw in the argument — present corrected reasoning. (For example, some flawed 'student' reasoning is presented and the task is to correct and improve it.) Content Scope: Knowledge and skills articulated in 4.OA.3, 4.NF.1, 4.NF.2, 4.NF.B, 4.NF.C, 3.OA.B, 3.NF, 3.MD.C
4.C.6-1 Present solutions to multi-step problems in the form of valid chains of reasoning, using symbols such as equals signs appropriately (for example, rubrics award less than full credit for the presence of nonsense statements such as 1 + 4 = 5 + 7 = 12, even if the final answer is correct), or identify or describe errors in solutions to multi-step problems and present corrected solutions. Content Scope: Knowledge and skills articulated in 4.OA.3
4.C.6-1 Present solutions to multi-step problems in the form of valid chains of reasoning, using symbols such as equals signs appropriately (for example, rubrics award less than full credit for the presence of nonsense statements such as 1 + 4 = 5 + 7 = 12, even if the final answer is correct), or identify or describe errors in solutions to multi-step problems and present corrected solutions. Content Scope: Knowledge and skills articulated in 4.OA.3
4.C.6-2 Present solutions to multi-step problems in the form of valid chains of reasoning, using symbols such as equals signs appropriately (for example, rubrics award less than full credit for the presence of nonsense statements such as 1 + 4 = 5 + 7 = 12, even if the final answer is correct), or identify or describe errors in solutions to multi-step problems and present corrected solutions. Content Scope: Knowledge and skills articulated in 4.NF.3c
4.C.6-2 Present solutions to multi-step problems in the form of valid chains of reasoning, using symbols such as equals signs appropriately (for example, rubrics award less than full credit for the presence of nonsense statements such as 1 + 4 = 5 + 7 = 12, even if the final answer is correct), or identify or describe errors in solutions to multi-step problems and present corrected solutions. Content Scope: Knowledge and skills articulated in 4.NF.3c
4.C.6-3 Present solutions to multi-step problems in the form of valid chains of reasoning, using symbols such as equals signs appropriately (for example, rubrics award less than full credit for the presence of nonsense statements such as 1 + 4 = 5 + 7 = 12, even if the final answer is correct), or identify or describe errors in solutions to multi-step problems and present corrected solutions. Content Scope: Knowledge and skills articulated in 4.NF.3d, 4.NF.4c
4.C.6-3 Present solutions to multi-step problems in the form of valid chains of reasoning, using symbols such as equals signs appropriately (for example, rubrics award less than full credit for the presence of nonsense statements such as 1 + 4 = 5 + 7 = 12, even if the final answer is correct), or identify or describe errors in solutions to multi-step problems and present corrected solutions. Content Scope: Knowledge and skills articulated in 4.NF.3d, 4.NF.4c
4.C.7-1 Base explanations/reasoning on a number line diagram (whether provided in the prompt or constructed by the student in her response) Content Scope: Knowledge and skills articulated in 4.NF.1
4.C.7-1 Base explanations/reasoning on a number line diagram (whether provided in the prompt or constructed by the student in her response) Content Scope: Knowledge and skills articulated in 4.NF.1
4.C.7-2 Base explanations/reasoning on a number line diagram (whether provided in the prompt or constructed by the student in her response) Content Scope: Knowledge and skills articulated in 4.NF.2
4.C.7-2 Base explanations/reasoning on a number line diagram (whether provided in the prompt or constructed by the student in her response) Content Scope: Knowledge and skills articulated in 4.NF.2
4.C.7-3 Base explanations/reasoning on a number line diagram (whether provided in the prompt or constructed by the student in her response) Content Scope: Knowledge and skills articulated in 4.NF.3a
4.C.7-3 Base explanations/reasoning on a number line diagram (whether provided in the prompt or constructed by the student in her response) Content Scope: Knowledge and skills articulated in 4.NF.3a
4.C.7-4 Base explanations/reasoning on a number line diagram (whether provided in the prompt or constructed by the student in her response) Content Scope: Knowledge and skills articulated in 4.NF.4a, 4.NF.4b
4.C.7-4 Base explanations/reasoning on a number line diagram (whether provided in the prompt or constructed by the student in her response) Content Scope: Knowledge and skills articulated in 4.NF.4a, 4.NF.4b
4.D
Modeling
4.D.1 Solve multi-step contextual word problems with degree of difficulty appropriate to Grade 4, requiring application of knowledge and skills articulated in Type I, Sub-Claim A Evidence Statements.
4.D.1 Solve multi-step contextual word problems with degree of difficulty appropriate to Grade 4, requiring application of knowledge and skills articulated in Type I, Sub-Claim A Evidence Statements.
4.D.2 Solve multi-step contextual problems with degree of difficulty appropriate to Grade 4, requiring application of knowledge and skills articulated in 3.OA.A, 3.OA.8, 3.NBT, and/or 3.MD
Addition and subtraction
Area and perimeter
Time
4.D.2 Solve multi-step contextual problems with degree of difficulty appropriate to Grade 4, requiring application of knowledge and skills articulated in 3.OA.A, 3.OA.8, 3.NBT, and/or 3.MD
Addition and subtraction
Area and perimeter
Time