Grade 4 Mathematics Indiana Academic Standards Crosswalk

Grade 4 Mathematics Indiana Academic Standards Crosswalk 2014 2015 The Process Standards demonstrate the ways in which students should develop conceptual understanding of mathematical content and the ways in which students should synthesize and apply mathematical skills. These process standards should be embedded in and taught with all content standards. See pages 8 and 9 for more information. Number Sense INCC 4.NBT.2: (partial alignment) Read and write multi-digit whole numbers using base-ten numerals, number names, 4.NS.1: Read and write whole numbers up to 1,000,000. expanded form. Compare two multi-digit numbers based on Use words, models, standard form and expanded form to meanings of the digits in each place, using >, =, and < represent and show equivalent forms of whole numbers up symbols to record the results of comparisons. to 1,000,000. IAS 4.1.1: Read and write whole numbers up to 1,000,000. IAS 4.1.2: Identify and write whole numbers up to 1,000,000, given a place-value model. 4.NS.2: Compare two whole numbers up to 1,000,000 using >, =, and < symbols. 4.NS.3: Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers. Name and write mixed numbers using objects or pictures. Name and write mixed numbers as improper fractions using objects or pictures. 4.NS.4: 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. [In grade 4, limit denominators of fractions to 2, 3, 4, 5, 6, 8, 10, 25, 100.] INCC 4.NBT.2: (partial alignment) Read and write multi-digit whole numbers using base-ten numerals, number names, 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. IAS 4.1.4: Order and compare whole numbers using symbols for less than (<), equal to (=), and greater than (>). IAS 4.1.5: Rename and rewrite whole numbers as fractions IAS 4.1.6: Name and write mixed numbers, using objects or pictures. IAS 4.1.7: Name and write mixed numbers as improper fractions, using objects or pictures. INCC 4.NF.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. INCC 4.NF.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.NS.2 is limited to comparing two numbers as opposed to ordering a set of numbers. Note that 4.NC.3 continues to expect the use of objects and pictures as support when renaming mixed numbers as fractions and vice versa. Indianapolis Public Schools Curriculum and Instruction Page 1 of 10

Number Sense 4.NS.5: Compare two fractions with different numerators INCC 4.NF.2: Compare two fractions with different and different denominators (e.g., by creating common numerators and different denominators, e.g., by creating denominators or numerators, or by comparing to a common denominators or numerators, or by comparing to a benchmark, such as 0, 1/2, and 1). Recognize comparisons benchmark fraction such as 1/2. Recognize that comparisons 4.NS.5 includes the whole numbers 0 and 1 as are valid only when the two fractions refer to the same are valid only when the two fractions refer to the same benchmarks. whole. Record the results of comparisons with symbols >, =, whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions (e.g., by using a visual or <, and justify the conclusions, e.g., by using a visual fraction model). fraction model. 4.NS.6: Write tenths and hundredths in decimal and fraction notations. Use words, models, standard form and expanded form to represent decimal numbers to hundredths. Know the fraction and decimal equivalents for halves and fourths (e.g., 1/2 = 0.5 = 0.50, 7/4 = 1 3/4 = 1.75). 4.NS.7: Compare two decimals to hundredths by reasoning about their size based on the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions (e.g., by using a visual model). 4.NS.8: Find all factor pairs for a whole number in the range 1 100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1 100 is a multiple of a given one-digit number. 4.NS.9: Use place value understanding to round multi-digit whole numbers to any given place value. INCC 4.NF.6: Use decimal notation for fractions with denominators 10 or 100. IAS 4.1.8: Write tenths and hundredths in decimal and fraction notations. Know the fraction and decimal equivalents for halves and fourths (e.g., ½ = 0.5 = 0.50, 7/4 = 1¾ = 1.75) INCC 4.NF.7: Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when 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. INCC 4.OA.4: Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. INCC 4.NBT.3: Use place value understanding to round multidigit whole numbers to any place. IAS 4.1.3: Round whole numbers up to 10,000 to the nearest ten, hundred, and thousand. 4.NS.6 requires the use of words, models and expanded form in addition to standard form. 4.NS.8 does not include the concept of prime and composite numbers, which has moved to 6 th grade. Indianapolis Public Schools Curriculum and Instruction Page 2 of 10

Computation INCC 4.NBT.4: Fluently add and subtract multi-digit whole 4.C.1: Add and subtract multi-digit whole numbers fluently numbers using the standard algorithm. using a standard algorithmic approach. IAS 4.2.1: Understand and use standard algorithms for addition and subtraction. 4.C.2: 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. Describe the strategy and explain the reasoning. 4.C.3: 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. Describe the strategy and explain the reasoning. 4.C.4: Multiply fluently within 100. 4.C.5: Add and subtract fractions with common denominators. Decompose a fraction into a sum of fractions with common denominators. Understand addition and subtraction of fractions as combining and separating parts referring to the same whole. INCC 4.NBT.5: 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. IAS 4.2.5: Use a standard algorithm to multiply numbers up to 100 by numbers up to 10, using relevant properties of the number system. INCC 4.NBT.6: 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. IAS 4.2.6: Use a standard algorithm to divide numbers up to 100 by numbers up to 10 without remainders, using relevant properties of the number system. IAS 4.2.4: Demonstrate mastery of the multiplication tables for numbers between 1 and 10 and of the corresponding division facts. INCC 4.NF.3ab: Understand a fraction a/b with a > 1 as a sum of fractions 1/b. a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. 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.C.2 does not specify which kinds of representations should be used within your instruction. 4.C.3 does not specify which kinds of representations should be used within your instruction. 4.C.4 does not include division facts. 4.C.5 does not require justifying the results of decomposition with a visual model. Indianapolis Public Schools Curriculum and Instruction Page 3 of 10

Computation Algebraic Thinking 4.C.6: Add and subtract mixed numbers with common INCC 4.NF.3c: Add and subtract mixed numbers with like denominators (e.g. by replacing each mixed number with denominators, e.g., by replacing each mixed number with an an equivalent fraction and/or by using properties of equivalent fraction, and/or by using properties of operations operations and the relationship between addition and and the relationship between addition and subtraction. subtraction). 4.C.7: Show how the order in which two numbers are multiplied (commutative property) and how numbers are grouped in multiplication (associative property) will not change the product. Use these properties to show that numbers can by multiplied in any order. Understand and use the distributive property. 4.AT.1: Solve real-world problems involving addition and subtraction of multi-digit whole numbers (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). 4.AT.2: Recognize and apply the relationships between addition and multiplication, between subtraction and division, and the inverse relationship between multiplication and division to solve real-world and other mathematical problems. 4.AT.3: 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.AT.4: Solve real-world problems with whole numbers 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. [In grade 4, division problems should not include a remainder.] No corresponding Indiana Common Core Standard or IAS Indicator INCC 4.OA.3: (partial alignment) 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. IAS 4.3.6: Recognize and apply the relationships between addition and multiplication, between subtraction and division, and the inverse relationship between multiplication and division to solve problems. INCC 4.OA.1: Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 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. INCC 4.OA.2: (partial alignment) 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.AT.4 states that division word problems should not include remainders. Indianapolis Public Schools Curriculum and Instruction Page 4 of 10

Algebraic Thinking Geometry 4.AT.5: Solve real-world problems involving addition and INCC 4.NF.3d: Solve word problems involving addition and subtraction of fractions referring to the same whole and subtraction of fractions referring to the same whole and having common denominators (e.g., by using visual having like denominators, e.g., by using visual fraction models fraction models and equations to represent the problem). and equations to represent the problem. INCC 4.OA.5: (partial alignment) 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.AT.6: Understand that an equation, such as y = 3x + 5, is a rule to describe a relationship between two variables and can be used to find a second number when a first number is given. Generate a number pattern that follows a given rule. 4.G.1: Identify, describe, and draw parallelograms, rhombuses, and trapezoids using appropriate tools (e.g., ruler, straightedge and technology). 4.G.2: Recognize and draw lines of symmetry in twodimensional figures. Identify figures that have lines of symmetry. 4.G.3: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint. IAS 4.3.4: Understand that an equation such as y = 3x + 5 is a rule for finding a second number when a first number is given. IAS 4.3.1: Use letters, boxes, or other symbols to represent any number in simple expressions, equations, or inequalities (i.e., demonstrate an understanding of and the use of the concept of a variable. IAS 4.3.4: Continue number patterns using multiplication and division. IAS 4.3.5: Continue number patterns using multiplication and division. IAS 4.4.3: Identify, describe, and draw parallelograms, rhombuses, and trapezoids, using appropriate mathematical tools and technology. INCC 4.G.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 line-symmetric figures and draw lines of symmetry. IAS 4.4.5 Identify and draw lines of symmetry in polygons. INCC 4.MD.5: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. 4.AT.6 does not require instruction on shape patterns. Indianapolis Public Schools Curriculum and Instruction Page 5 of 10

Geometry Measurement INCC 4.G.1: Draw points, lines, line segments, rays, angles (right, acute, obtuse, straight), and perpendicular, parallel, and oblique lines. Identify these in two-dimensional figures. 4.G.4: Identify, describe, and draw rays, angles (right, IAS 4.4.1: Identify, describe, and draw rays, right angles, acute acute, obtuse), and perpendicular and parallel lines using angles, obtuse angles, and straight angles using appropriate appropriate tools (e.g., ruler, straightedge and mathematical tools and technology. technology). Identify these in two-dimensional figures. IAS 4.4.2: Identify, describe, and draw parallel, perpendicular, and oblique lines using appropriate mathematical tools and technology. 4.G.5: Classify triangles and quadrilaterals based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles (right, acute, obtuse). 4.M.1: Measure length to the nearest quarter-inch, eighthinch, and millimeter. 4.M.2: Know relative sizes of measurement units within one system of units, including km, m, cm; kg, g; lb, oz; l, ml; hr, min, sec. Express measurements in a larger unit in terms of a smaller unit within a single system of measurement. Record measurement equivalents in a twocolumn table. 4.M.3: Use the four operations (addition, subtraction, multiplication and division) to solve real-world problems involving distances, intervals of time, volumes, masses of objects, and money. Include addition and subtraction problems involving simple fractions and problems that require expressing measurements given in a larger unit in terms of a smaller unit. INCC 4.G.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. IAS 4.5.1: Measure length to the nearest quarter-inch, eighthinch and millimeter. INCC 4.MD.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. INCC 4.MD.2: 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. IAS 4.5.2: Subtract units of length that may require renaming of feet to inches or meters to centimeters. IAS 4.5.9: Add time intervals involving hours and minutes. 4.G.5 does not require recognizing right triangles as a category. 4.M.3 does not require using the four operations with decimals. It also does not suggest the type of diagram to be used in instruction. Indianapolis Public Schools Curriculum and Instruction Page 6 of 10

Measurement Data Analysis 4.M.4: Apply the area and perimeter formulas for rectangles to solve real-world problems and other mathematical problems. Recognize area as additive and find the area of complex shapes composed of rectangles by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts; apply this technique to solve real-world problems and other mathematical problems. 4.M.5: Understand that 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. Understand an angle that turns through 1/360 of a circle is called a one-degree angle, and can be used to measure other angles. Understand an angle that turns through n one-degree angles is said to have an angle measure of n degrees. 4.M.6: Measure angles in whole-number degrees using appropriate tools. Sketch angles of specified measure. 4.DA.1: Formulate questions that can be addressed with data. Use observations, surveys, and experiments to collect, represent, and interpret the data using tables (including frequency tables), line plots, and bar graphs. 4.DA.2: 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 data displayed in line plots. 4.DA.3: Interpret data displayed in a circle graph. INCC 4.MD.3: Apply the area and perimeter formulas for rectangles in real world and mathematical problems. IAS 4.5.3: Know and use formulas for finding the perimeters of rectangles and squares. IAS 4.3.2: Use and interpret formulas to answer questions about quantities and their relationship. IAS 4.5.4: Know and use formulas for finding the areas of rectangles and squares. INCC 4.MD.5ab: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: a. 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. b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees. INCC 4.MD.6: Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. IAS 4.6.3: Summarize and display the results of probability experiments in a clear and organized way. INCC 4.MD.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. IAS 4.6.2: Interpret data graphs to answer questions about a situation. No corresponding Indiana Common Core Standard or IAS Indicator 4.M.4 includes finding the area of complex shapes composed of rectangles. 4.DA.2 is specific to line plots. Indianapolis Public Schools Curriculum and Instruction Page 7 of 10

Process Standards for Mathematics The Process Standards demonstrate the ways in which students should develop conceptual understanding of mathematical content and the ways in which students should synthesize and apply mathematical skills. These process standards should be embedded in and taught with all content standards. Indianapolis Public Schools Curriculum and Instruction Page 8 of 10

Indianapolis Public Schools Curriculum and Instruction Page 9 of 10

Content that No Longer Needs to Be Taught In This Grade Level Comments INCC 4.NBT.1: Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents Now in 5 in the place to its right. th grade (5.NS.3) INCC 4.NF.4: 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. a. Understand a fraction a/b as a multiple of 1/b. b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole Now in 5 th grade (5.C.5) number. c. 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. INCC 4.MD.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 No longer taught in Indiana Academic Standards 2014 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. IAS 4.1.9: Round two-place decimals to tenths or to the nearest whole number. Now in 5 th grade (5.NS.5) IAS 4.2.8: Add and subtract simple fractions with different denominators, using objects or pictures. Now in 5 th grade (5.C.4) IAS 4.2.10: Use a standard algorithm to add and subtract decimals (to hundredths). Now in 5 th grade (5.C.8) IAS 4.3.7: Relate problem situations to number sentences involving multiplication and division. Now in 5 th grade (5.AT.1) IAS 4.4.4: Identify congruent quadrilaterals and give reasons for congruence using sides, angels, parallels and No longer taught in Indiana Academic Standards 2014 perpendiculars. Indianapolis Public Schools Curriculum and Instruction Page 10 of 10