# Division of Special Education LAUSD, June Grade 4 Math 156

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1 Use the four operations with whole numbers to solve problems. 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 Interpret Multiplication Equation as a Comparison <STUDENT> will 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) <UNDER_WHAT_CONDITION> as measured <MEASURE> in <NUMBER1> out of Use the four operations with whole numbers to solve problems. 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 Word Problems - Multiplicative Comparison <STUDENT> will multiply to solve word problems involving multiplicative comparison <UNDER_WHAT_CONDITION> as measured <MEASURE> in <NUMBER1> out of 4.OA.2 Divide to Solve Word Problems - Multiplicative Comparison Standard 3 Use the four operations with whole numbers to solve problems. <STUDENT> will solve multistep word problems posed with whole numbers and having whole- number answers using the four operations, including problems in which remainders must be interpreted <UNDER_WHAT_CONDITION> as measured <MEASURE> in <NUMBER1> out of <NUMBER2> trials with <PERCENT>% accuracy <STUDENT> will divide to solve word problems involving multiplicative comparison <UNDER_WHAT_CONDITION> as measured <MEASURE> in <NUMBER1> out of 4.OA.3 Solve Multistep Word Problems <STUDENT> will solve multistep word problems posed with whole numbers and having whole- number answers using the four operations, including problems in which remainders must be interpreted <UNDER_WHAT_CONDITION> as 4.OA.3 Represent Multistep Word Problems with Equations <Students> will represent multistep word problems with equations with a letter standing in for the unknown quantity, assess the reasonableness of answers, and solve the problems <UNDER_WHAT_CONDITION> as measured <MEASURE> in <NUMBER1> out of Grade 4 Math 156

2 Gain familiarity with factors and multiples. 4.OA.4 Find Factor Pairs for Whole Numbers Standard 4 Find all factor pairs for a whole number in the range Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range is a multiple of a given one- digit number. Determine whether a given whole number in the range is prime or composite. <STUDENT> will find all factor pairs for a whole number in the range and will recognize that a whole number is a multiple of each of its factors 4.OA.4 Determine Multiples of Whole Numbers Standard 5 Generate and analyze patterns. Generalize place value understanding for multi- digit whole numbers. 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. 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 = 10 by applying concepts of place value and division. <STUDENT> will determine whether a given whole number in the range is a multiple of a given one- digit number <UNDER_WHAT_CONDITION> as 4.OA.5 Generate Number of Shape Pattern that Follows Rule <STUDENT> will generate a number or shape pattern that follows a given rule and/or identify apparent features of the pattern <UNDER_WHAT_CONDITION> as 4.NBT.1 Understand Place Value for Multidigit Whole Numbers <STUDENT> will 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 Grade 4 Math 157

3 Generalize place value understanding for multi- digit whole 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 >, =, 4.NBT.2 Read and Write Multidigit Whole Numbers numbers. and < symbols to record the results of comparisons. <STUDENT> will read and write multi- digit whole numbers using one or combination of the following: base- ten numerals, number names or expanded form <UNDER_WHAT_CONDITION> as measured <MEASURE> in <NUMBER1> out of 4.NBT.2 Compare Two Multidigit Whole Numbers <STUDENT> will compare two multi- digit whole numbers based on the meaning of digits in each place, using <, =, and > symbols to record the results of comparisons <UNDER_WHAT_CONDITION> as measured <MEASURE> in <NUMBER1> out of Standard 3 Standard 4 Generalize place value understanding for multi- digit whole numbers. Use place value understanding and properties of operations to perform multi- digit arithmetic. Use place value understanding to round multi- digit whole numbers to any place. Fluently add and subtract multi- digit whole numbers using the standard algorithm. 4.NBT.3 Round Multidigit Whole Numbers Using Place Value <STUDENT> will use place value understanding to round multi- digit whole numbers to any place <UNDER_WHAT_CONDITION> as measured <MEASURE> in <NUMBER1> out of 4.NBT.4 Add Multidigit Whole Numbers <STUDENT> will add multi- digit whole numbers using the standard algorithm 4.NBT.4 Subtract Multidigit Whole Numbers <STUDENT> will subtract multi- digit whole numbers using the standard algorithm <UNDER_WHAT_CONDITION> as measured <MEASURE> in <NUMBER1> out of Grade 4 Math 158

4 4.NBT.5 Multiply Whole Number with 1-4 Digits by 1 Digit Standard 5 Use place value understanding and properties of operations to perform multi- digit arithmetic. 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. <STUDENT> will 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 and illustrate and explain the calculation by using equations, rectangular arrays or area models <UNDER_WHAT_CONDITION> as measured 4.NBT.5 Multiply Two 2- Digit Numbers Standard 6 Use place value understanding and properties of operations to perform multi- digit arithmetic. 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. <STUDENT> will multiply two two- digit numbers using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays or area models 4.NBT.6 Divide Whole Numbers with 1-4 Digits by 1 Digit Divisors <STUDENT> will find whole- number quotients and remainders with up to four- digit dividends and one- digit divisors, using strategies based on place value, properties of operations, or the relationship between multiplication and division Extend understanding of fraction equivalence and ordering. 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 Explain Equivalent Using Visual Fraction Models <STUDENT> will 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 4.NF.1 Use Visual Fraction Models to Generate Equivalent <STUDENT> will use visual fraction models to recognize and generate equivalent fractions <UNDER_WHAT_CONDITION> as measured <MEASURE> in <NUMBER1> out of Grade 4 Math 159

5 Extend understanding of fraction equivalence and 4.NF.2 Compare 2 with Different Numerators and Denominators ordering. Standard 3 Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. 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. 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. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = /8 =8/8 + 8/8 + 1/8. c. 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. d. 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. <STUDENT> will compare two fractions with different numerators and different denominators, record the results of the comparisons with <, =, and > symbols, and justify the conclusions <UNDER_WHAT_CONDITION> as measured 4.NF.3 Decompose Fraction into Sum of <STUDENT> will demonstrate that a fraction a/b with a > 1 is a sum of fractions 1/b by decomposing a fraction into a sum of fractions with the same denominator <UNDER_WHAT_CONDITION> as measured <MEASURE> in <NUMBER1> out of 4.NF.3 Word Problems - Addition/Subtraction of <STUDENT> will solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators 4.NF.3 Add/Subtract Mixed Numbers with Like Denominators <STUDENT> will add and subtract mixed numbers with like denominators Grade 4 Math 160

6 4.NF.4 Multiply Fraction by Whole Number Standard 4 Standard 5 Standard 6 Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. Understand decimal notation for fractions, and compare decimal fractions. Understand decimal notation for fractions, and compare decimal fractions. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. a. 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). 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. For example, use a visual fraction model to express 3 (2/5) as 6 (1/5), recognizing this product as 6/5. (In general, n (a/b) = (n a)/b.) 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. 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? 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 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. 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. <STUDENT> will multiply a fraction by a whole number 4.NF.4 Solve Word Problems - Multiplication of <STUDENT> will solve word problems involving multiplication of a fraction by a whole number <UNDER_WHAT_CONDITION> as measured <MEASURE> in <NUMBER1> out of 4.NF.5 Decimal Notation for Adding Equivalent <STUDENT> will 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 <UNDER_WHAT_CONDITION> as 4.NF.6 Use Decimal Notation with with Denominators 10 or 100 <STUDENT> will use decimal notation for fractions with denominators 10 or 100 Grade 4 Math 161

7 Standard 7 Understand decimal notation for fractions, and compare decimal fractions. 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 the number line or another visual model. 4.NF.7 Compare 2 Decimals to the Hundredths Place <STUDENT> will compare two decimals to the hundredths place by reasoning about their size, record the results of comparisons with the symbols <, =, or >, and justify the conclusions <UNDER_WHAT_CONDITION> as measured Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. 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),... 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. 1 Identify Relative Sizes of Units <STUDENT> will identify relative sizes of measurement units within one system of units <UNDER_WHAT_CONDITION> as measured <MEASURE> in <NUMBER1> out of 4.MD.1 Record Equivalents in a Table <STUDENT> will record measurement equivalents in a two column table 4.MD.2 Solve Word Problems Involving <STUDENT> will use any of the four operations to solve word problems involving one or combination of the following: distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals <UNDER_WHAT_CONDITION> as measured <MEASURE> in <NUMBER1> out of 4.MD.2 Use Conversion to Solve Word Problems <STUDENT> will use any of the four operations to solve problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit Grade 4 Math 162

8 4.MD.3 Apply Area and Perimeter Formulas to Solve Word Problems Standard 3 Standard 4 Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Represent and interpret data. 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. 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. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. <STUDENT> will apply the area and perimeter formulas for rectangles in real world and mathematical problems <UNDER_WHAT_CONDITION> as measured 4.MD.4 Make Line Plot to Display of a Unit <STUDENT> will make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8) <UNDER_WHAT_CONDITION> as measured 4.MD.4 Solve Problems Involving Using Line Plots Standard 5 Geometric measurement: understand concepts of angle and measure 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 b. An angle that turns through n one- degree angles is said to have an angle measure of n degrees. <STUDENT> will solve problems involving addition and subtraction of fractions by using information presented in line plots <UNDER_WHAT_CONDITION> as 4.MD.5 Identify Angles/Explain Angle <STUDENT> will identify angles as geometric shapes that are formed wherever two rays share a common endpoint and explain concepts of angle measurement Grade 4 Math 163

9 Measure angles in whole- number degrees using a protractor. Sketch angles of specified measure. 4.MD.6 Measure Angles in Degrees with Protractor Standard 6 Geometric measurement: understand concepts of angle and measure <STUDENT> will measure angles in whole- number degrees using a protractor and/or will sketch angles of specified measure <UNDER_WHAT_CONDITION> as Standard 7 Geometric measurement: understand concepts of angle and measure 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.7 Recognize Angle Measure as Additive <STUDENT> will recognize angle measure as additive that 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 <UNDER_WHAT_CONDITION> as 4.MD.7 Addition/Subtraction Problems with Unknown Angles <STUDENT> will solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (G) Geometry (G) Geometry Draw and identify lines and angles, and classify shapes by properties of their lines and Draw and identify lines and angles, and classify shapes by properties of their lines and Draw points, lines, line segments, rays, angles (right, acute, obtuse), 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 of a specified size. Recognize right triangles as a category, and identify right tri 4.G.1 Draw and Identify Lines and Angles <STUDENT> will draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines and identify these in two- dimensional figures <UNDER_WHAT_CONDITION> as measured <MEASURE> in <NUMBER1> out of 4.G.2 Classify 2- Dimensional Figures <STUDENT> will classify two- dimensional figures based on one or more of the following: the presence or absence of parallel lines, perpendicular lines, or angles of a certain size, and <UNDER_WHAT_CONDITION> as measured Grade 4 Math 164

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