# 4 Unit 7: Fractions and Decimals (19 days)

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1 Elementary Pacing Guide by Quarter Content Area: Mathematics Grade: 4 th Quarter Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8 Week 9 1 Unit 1: Place Value and Multi digit Addition and Subtraction (20 ) 2 Unit 2: Multiplication with Whole Numbers (26 ) Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8 Week 9 (Continued) Unit 2: Multiplication with Whole Numbers (26 ) Unit 3: Division with Whole Numbers (17 ) 3 Unit 4: Equations and Word Problems (20 ) Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8 Week 9 (Continued) Unit 4: Equations and Word Problems (20 ) Unit 5: Measurement (13 ) Unit 6: Fraction Concepts and Operations (16 ) 4 Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8 Week 9 Unit 7: Fractions and Decimals (19 ) Unit 8: Geometry (19 ) Grade 4 Raytown Quality Schools

2 4 th Grade Pacing Guide Unit Title Pacing Missouri Learning Standards Unit 1: Place Value and Multi digit Addition and Subtraction Unit 2: Multiplication with Whole Numbers Unit 3: Division with Whole Numbers Unit 4: Equations and Word Problems Unit 5: Measurement Unit 6: Fraction Concepts and Operations Unit 7: Fractions and Decimals Unit 8: Geometry *Glossary Table OA.A.3 4.NBT.A.1 4.MD.A.2 4.NBT.A.2 4.NBT.A.3 4.NBT.B.4 4.OA.A.3 4.NBT.A.1 4.MD.A.2 4.NBT.A.2 4.NBT.A.3 4.NBT.B.5 4.OA.A.3 4.NBT.A.3 4.NBT.B.6 4.OA.A.1 4.NBT.B.4 4.MD.A.2 4.OA.A.2 * 4.NBT.B.5 4.OA.A.3 4.NBT.B.6 4.OA.B.4 4.OA.C.5 4.MD.A.1 4.MD.A.2 4.MD.A.3 4.MD.B.4 4.NF.A.2 4.NF.B.3 4.NF.B.3a 4.NF.B.3b 4.NF.B.3c 4.NF.B.3d 4.NF.B.4 4.NF.B.4a 4.NF.B.4b 4.NF.B.4c 4.NF.A.1 4.NF.A.2 4.NF.C.5 4.NF.C.6 4.NF.C.7 4.MD.A.2 4.MD.B.4 4.MD.A.2 4.MD.B.4 4.OA.C.5 4.MD.C.5 4.G.A.1 4.MD.C.5a 4.G.A.2 4.MD.C.5b 4.G.A.3 4.MD.C.6 4.MD.C.7 Grade 4 Raytown Quality Schools

3 4th Grade Math MLS 4th Grade Math: Math Expressions and Math MLS Correlations Units U1 U2 U3 U4 U5 U6 U7 U8 Place Value & Multi digit Addition & Subtraction (20 ) Multiplication with Whole Numbers (26 ) Division with Whole Numbers (17 ) Equations & Word Problems (20 ) Measurement (13 ) Fraction Concepts & Operations (16 ) Fractions & Decimals (19 ) Operations and Algebraic Thinking 4.OA.A.1 S 4.OA.A.2* P 4.OA.A.3 P 4.OA.B.4 S 4.OA.C.5 P Number and Operations in Base Ten 4.NBT.A.1 S 4.NBT.A.2 P 4.NBT.A.3 S 4.NBT.B.4 P 4.NBT.B.5 P 4.NBT.B.6 P Number and Operations in Base Ten: Fractions 4.NF.A.1 S 4.NF.A.2 P 4.NF.B.3 P 4.NF.B.3a S 4.NF.B.3b S 4.NF.B.3c P 4.NF.B.3d P 4.NF.B.4 P 4.NF.B.4a S 4.NF.B.4b S 4.NF.B.4c P 4.NF.C.5 S 4.NF.C.6 S 4.NF.C.7 P Measurement and Data 4.MD.A.1 S 4.MD.A.2 P 4.MD.A.3 P 4.MD.B.4 S 4.MD.C.5 P 4.MD.C.5a P 4.MD.C.5b S 4.MD.C.6 S 4.MD.C.7 S Geometry 4.G.A.1 S 4.G.A.2 P 4.G.A.3 S *See Glossary Table Geometry (20 ) Grade 4 Raytown Quality Schools

4 Unit 1: Place Value & Multi digit Addition & Subtraction (20 ) Use the four operations with whole numbers to solve problems. Fourth Grade Standards by Unit 4.OA.A.3 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. 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. Generalize place value understanding for multi digit whole numbers. (Limited to whole numbers less than or equal to 1,000,000) 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 = 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. 4.NBT.A.3 Use place value understanding to round multi digit whole numbers to any place. Use place value understanding and properties of operations to perform multi digit arithmetic. (Limited to whole numbers less than or equal to 1,000,000) 4.NBT.B.4 Fluently add and subtract multi digit whole numbers using the standard algorithm. 4.MD.A.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. Unit 2: Multiplication with Whole Numbers (26 ) Use the four operations with whole numbers to solve problems. 4.OA.A.3 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. 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. Generalize place value understanding for multi digit whole numbers. (Limited to whole numbers less than or equal to 1,000,000) 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 = 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. 4.NBT.A.3 Use place value understanding to round multi digit whole numbers to any place. Use place value understanding and properties of operations to perform multi digit arithmetic. (Limited to whole numbers less than or equal to 1,000,000) 4.NBT.B.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. 4.MD.A.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. Grade 4 Raytown Quality Schools

5 Unit 3: Division with Whole Numbers (17 ) Use the four operations with whole numbers to solve problems. 4.OA.A.3 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. 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. Generalize place value understanding for multi digit whole numbers. (Limited to whole numbers less than or equal to 1,000,000) 4.NBT.A.3 Use place value understanding to round multi digit whole numbers to any place. Use place value understanding and properties of operations to perform multi digit arithmetic. (Limited to whole numbers less than or equal to 1,000,000) 4.NBT.B.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. Unit 4: Equations & Word Problems (20 ) Use the four operations with whole numbers to solve problems. 4.OA.A.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. 4.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. (See Glossary) 4.OA.A.3* 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. 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. Gain familiarity with factors and multiples. 4.OA.B.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. 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. Use place value understanding and properties of operations to perform multi digit arithmetic. (Limited to whole numbers less than or equal to 1,000,000) 4.NBT.B.4 Fluently add and subtract multi digit whole numbers using the standard algorithm. 4.NBT.B.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. 4.NBT.B.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. 4.MD.A.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. Grade 4 Raytown Quality Schools

6 Unit 5: Measurement (13 ) 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),... 4.MD.A.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. 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. Represent and interpret data. 4.MD.B.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. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. Unit 6: Fraction Concepts & Operations (16 ) Extend understanding of fraction equivalence and ordering. (Limited to fractions with denominators 2,3,4,5,6,8,10,12, and 100) 4.NF.A.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. (Limited to fractions with denominators 2,3,4,5,6,8,10,12, and 100) 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. 4.NF.B.3b 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. 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.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.4b 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.) 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.MD.A.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. Represent and interpret data. 4.MD.B.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. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. Grade 4 Raytown Quality Schools

7 Unit 7: Fractions & Decimals (19 ) Extend understanding of fraction equivalence and ordering. (Limited to fractions with denominators 2,3,4,5,6,8,10,12, and 100) 4.NF.A.1 Explain why a fraction a/b is equivalent to a fraction (n a)/(n b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. 4.NF.A.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. Understand decimal notation for fractions, and compare decimal fractions. (Limited to fractions with denominators 2,3,4,5,6,8,10,12, and 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. (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.) For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/ 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.MD.A.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. Represent and interpret data. 4.MD.B.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. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. Unit 8: Geometry (20 ) 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. 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.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.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. Draw and identify lines and angles, and classify shapes by properties of their lines and angles. 4.G.A.1 4.G.A.2 4.G.A.3 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 triangles. 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. Grade 4 Raytown Quality Schools

8 Grade 4 Raytown Quality Schools

9 Mathematical Practices See individual lessons in Math Expressions to include Math Practices in daily lessons. It is important to emphasize not only the content contained in the expectations presented but also the importance of mathematical practices for all students at all grades. If content expectations are not implemented within a view of the mathematical processes/practices that should be developed by students, the ultimate impact mathematical power may be minimal. The following Mathematical Practices describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. They are consistent with the Show-Me process standards and these practices rest on important processes and proficiencies with longstanding importance in mathematics education. The first of these are the National Council of Teachers of Mathematics process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council s report Adding It Up; adaptive reasoning, strategic competence, conceptual understanding, procedural fluency, and productive disposition. The Mathematical Practices describe ways in which developing students should engage with the subject matter. A mathematically literate student can: 1. Make sense of problems and persevere in solving them. Relate a problem to prior knowledge. Recognize that there may be multiple entry points to a problem and more than one path to a solution. Analyze what is given, what is not given, what is being asked, and what strategies are needed, and make an initial attempt to solve a problem. Evaluation the success of an approach to solve a problem and refine it if necessary. Evaluate the reasonableness of a solution to a problem. 2. Reason both contextually and abstractly. Make sense of quantities and their relationships in mathematical and real-world situations. Describe a given situation using multiple mathematical representations. Translate among multiple mathematical representations and compare the meanings each representation conveys about the situation. Connect the meaning of mathematical operations to the context of a given situation. 3. Use critical thinking skills to justify mathematical reasoning and critique the reasoning of others. Construct and justify a solution to a problem. Compare and discuss the validity of various reasoning strategies. Make conjectures and explore their validity. Reflect on and provide thoughtful responses to the reasoning of others. 4. Connect mathematical ideas and real-world situations through modeling. Identify relevant quantities and develop a model to describe their relationships. Interpret mathematical models in the context of the situation. Make assumptions and estimates to simplify complicated situations. Evaluate the reasonableness of a model and refine if necessary. 5. Use a variety of mathematical tools effectively and strategically. Select and use appropriate tools when solving a mathematical problem. Use technological tools and other external mathematics resources to explore and deepen understanding of concepts. Grade 4 Raytown Quality Schools

10 6. Communicate mathematically and approach mathematical situations with precision. Express numerical answers with the degree of precision appropriate for the context of a situation. Represent numbers in an appropriate form according to the context of the situation. Use appropriate and precise mathematical language. Use appropriate units, scales, and labels. 7. Identify and utilize structure and patterns. Recognize complex mathematical objects as being composed of more than one simple object. Recognize mathematical repetition in order to make generalizations. Look for structures to interpret meaning and develop solution strategies. 8. Look for and express regularity in repeated reasoning. Notice if calculations are repeated and look for generalizations in methods. Maintain oversight of the process while paying attention to the details. Draw general results from trying multiple examples. Grade 4 Raytown Quality Schools

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