1: NUMBERS AND OPERATIONS IN BASE TEN, PART

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1 4 th GRADE MATH PACING GUIDE: 1st Nine Weeks UNIT 1: NUMBERS AND OPERATIONS IN BASE TEN, PART 1 WEEK 1 Aug. 8 FLEX Week Set up classroom rules and expectations Review 3 rd Grade Material Pre-Assessments WEEK 2 Aug. 15 Lesson 1 Understand Place Value Lesson 2 Compare Whole Numbers 4NBT.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 multidigit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. - I can identify the value of a digit based on its location in the number. - I can demonstrate how moving from one placevalue position to the next changes the value by a multiple of ten. - I can use standard form, word form, and expanded form to read and write multi-digit whole numbers. - I can use symbols (>, <, =) to show the relationship between two multi-digit numbers. Value Period Word Form Standard Form Expanded Form Compare Greater Than Less Than For additional support and to dig deeper into the standards for this unit, refer to the following resources: Lessons and Interactive Engage New York engageny.org Illuminations illuminations.nctm.org Tasks TN Task Arcs Illustrative Mathematics illustrativemathematics.org Video Tutorials and Practice Learn Zillion Brain Pop Khan Academy Study Jams / Discovery Education Sheppard Software Promethean Planet Books Teaching Student Centered Mathematics: Grades 3-5 Volume 2 by John A. Van de Walle and Lou Ann H. Lovin (Jun 11, 2005)

2 WEEK 3 Aug. 22 Lesson 3 Add and Subtract Whole Numbers 4.NBT.B4 Fluently add and subtract multi-digit whole numbers using the standard algorithm. - I can use the standard algorithm to add multi-digit whole numbers. - I can use the standard algorithm to subtract multidigit whole numbers. WEEK 4 Aug. 29 Lesson 4 Round Whole Numbers 4.NBT.A.3 Use place value understanding to round multi-digit whole numbers to any place. - I can use appropriate tools to round multi-digit whole numbers. - I can explain how a multi-digit whole number is rounded to a specific place value. - Unit 1 Assessment WEEK 5 Sept. 6 Lesson 5 Understand Multiplication 4.OA.A.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. UNIT 2: OPERATIONS AND ALGEBRAIC THINKING - I can find the key words in a word problem that indicate a multiplicative comparison. - I can write an equation to represent a multiplicative comparison indicated by a word problem. Multiplication Product Factors Equation Brainpop Multiplication: Be Fruitful and Multiply

3 WEEK 6 Sept. 12 WEEK 7 Sept. 19 WEEK 8 Sept. 26 Lesson 7 Multiples and Factors Lesson 6 Multiplication and Division in Word Problems Lesson 9 Model Multi-Step Problems 4.O.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 onedigit number. Determine whether a given hole number in the range is prime or composite. 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 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. - I can use understanding of multiplication facts to list all the factors of a given whole number. - I can use understanding of multiplication and division facts to determine if a whole number is a multiple of another number. - I can apply understanding of multiples and factors to solving problems. Factor Pair Multiple Composite and Prime Numbers - I can use drawings and symbols to represent a multiplicative comparison problem. - I can use an equation to solve for the unknown in a multiplicative comparison problem. Unknown Symbol Product Factors Equation - I can use equations with a letter standing for the unknown to represent multi-step word problems. - I can solve multi-step word problems. - I can interpret the remainder in a division word problem. - I can use estimation strategies to make sure the answer makes sense. Unknown Expression Brainpop Factoring: What are numbers made of? Numbers of Course WEEK 9 Oct. 3 Lesson 10 Solve Multi-Step 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. - I can use equations with a letter standing for the unknown to represent multi-step word problems. - I can solve multi-step word problems. - I can interpret the remainder in a division word problem. - I can use estimation strategies to make sure the answer makes sense. Remainder Reasonable - Unit 2 Assessment

4 4 th GRADE MATH PACING GUIDE: 2 nd Nine Weeks WEEK 11 Oct. 24 Lesson 11 Multiply Whole Numbers WEEK 10 Oct. 17 FLEX Week 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. UNIT 3: NUMBER AND OPERATIONS IN BASE TEN, PART 2 - I can multiply whole numbers of up to four digits by onedigit whole numbers. - I can multiply a two-digit number by a two-digit number. - I can use equations, rectangular arrays, and area models to illustrate and explain calculations. Multiple WEEK 12 Oct. 31 Lesson 11 Multiply Whole Numbers 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. - I can multiply whole numbers of up to four digits by onedigit whole numbers. - I can multiply a two-digit number by a two-digit number. - I can use equations, rectangular arrays, and area models to illustrate and explain calculations. WEEK 13 Nov. 7 Lesson 12 Divide Whole Numbers 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. - I can multiply whole numbers of up to four digits by one-digit whole numbers. - I can multiply a two-digit number by a two-digit number. - I can use equations, rectangular arrays, and area models to illustrate and explain calculations. - I can divide up to four-digit dividends by one-digit divisors, with remainders. - I can use equations, rectangular arrays, and area models to illustrate and explain calculations. - I can recognize the relationship between multiplication and division. Quotient Dividend Divisor Remainder Khan Academy Introduction to Long Division Multi-digit Division without Remainders Dividing Numbers: Intro to Remainders Dividing Numbers: Example with Remainders Dividing Numbers: Long Division with Remainders Division with Remainders Dividing by Two Digits Example 2 Brainpop - Division: Divide and Conquer

5 WEEK 14 Nov. 14 Lesson 12 Divide Whole Numbers 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. - I can divide up to four-digit dividends by one-digit divisors, with remainders. - I can use equations, rectangular arrays, and area models to illustrate and explain calculations. - I can recognize the relationship between multiplication and division. Khan Academy Introduction to Long Division Multi-digit Division without Remainders Dividing Numbers: Intro to Remainders Dividing Numbers: Example with Remainders Dividing Numbers: Long Division with Remainders Division with Remainders Dividing by Two Digits Example 2 - Unit 3 Assessment WEEK 15 Nov. 28 WEEK 16 Dec. 5 Lesson 13 Understand Equivalent Fractions Lesson 14 Compare Fractions 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. UNIT 4: NUMBER AND OPERATIONS FRACTIONS - I can understand the value of a fraction. - I can understand how a fraction model represents a fraction. - I can represent fractions on a number line. - I can understand how two fractions are equivalent. - I can understand how different models can represent the same value. Denominator Numerator Divide Equivalent Fractions - I can use symbols (>,<,=) to compare fractions with the same denominator and different numerators. - I can recognize that fractions with different denominators and the same numerators represent different values. - I can use benchmark fractions to compare fractions. - I can recognize that you can only compare two fractions when both refer to the same whole. Study Jams - Equivalent Fractions Learn Zillion - Interactive Fractions on a Number Line interactive Identify with Lines: Identify Fractions on a Number Line Khan Academy More on Equivalent Fractions

6 WEEK 17 Dec. 12 Lesson 15 Understand Fraction Addition and Subtraction 4.NF.B.3 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. - I can understand addition as joining parts. - I can understand subtraction as separating parts. - I can understand addition and subtraction of fractions. - I can use fraction models to add and subtract fractions with like denominators. Khan Academy Adding and Subtracting Fractions (the first 3 minutes is about like denominators) WEEK 18 Dec. 19 FLEX Week 4 th GRADE MATH PACING GUIDE: 3 rd Nine Weeks WEEK 19 Jan. 9 WEEK 20 Jan. 17 Lesson 16 Add and Subtract Fractions FLEX Week 4.NF.B.3 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. 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. - I can add fractions with like denominators. - I can subtract fractions with like denominators. - I can use fraction models, number lines, and equations to represent word problems. Brainpop Adding and Subtracting Fractions: Working with Pieces of Things

7 WEEK 21 Jan. 23 Lesson 17 Add and Subtract Mixed Numbers 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. - I can join fractions (same denominators) by adding. -I can separate fractions (same denominators) by subtracting. - I can break apart fractions with a numerator greater than 1 into smaller parts. - I can write a decomposed fraction using an equation. - I can add and subtract mixed numbers with like denominators. - I can determine whether to use addition or subtraction when solving word problems involving fractions. Mixed Number WEEK 22 Jan. 30 Lesson 18 Understand Fraction Multiplication 4.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. 1. 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? - I can multiply a unit fraction (numerator of 1) by a whole number. - I can multiply a fraction with a numerator greater than one by a whole number. Fraction

8 WEEK 23 Feb. 6 WEEK 24 Feb. 13 Lesson 19 Multiply Fractions Lesson 20 Fractions as Tenths and Hundredths 4.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. 1. 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? 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 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. (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.) - I can solve word problems that involve multiplying a fraction by a whole number. - I can rewrite a fraction that has a denominator of 10 as an equivalent fraction with a denominator of I can rewrite a fraction that has a denominator of 100 as an equivalent fraction with a denominator of I can explain the relationship between tenths and hundredths. - I can add two fractions with denominators of 10 or 100. WEEK 25 Feb. 21 Lesson 21 Relate Decimals and Fractions 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. - I can convert decimals into fractions, with denominators of 10 or I can convert fractions into decimals, with denominators of 10 or 100. Brainpop Converting Fractions to Decimals & Decimals: Thinking in Tenths

9 4.NF.C.7 Compare two decimals to hundredths by - I can compare two decimals up to hundredths, using - Unit 4 Assessment reasoning about their size. Recognize that the >, <, and = symbols. comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and Decimal justify the conclusions, e.g., by using a visual model. **Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. WEEK 26 Feb. 27 WEEK 27 Mar. 6 Lesson 22 Compare Decimals Lesson 23 Convert Measurements Customary 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),... UNIT 5: MEASUREMENT AND DATA - I can identify customary units of measurement. - I can convert customary measurements from a larger unit to a smaller unit. - I can create a conversion table showing equivalent customary measurements. WEEK 29 Mar. 27 Lesson 25 Length, Liquid, Volume, and Mass Lesson 24 Time and Money WEEK 28 Mar. 13 FLEX Week 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 features a measurement scale. 4 th GRADE MATH PACING GUIDE: 4 th Nine Weeks - I can determine which operation to use when solving word problems involving length, liquid, volume, mass, time, and money.

10 4.MD.B.4 Make a line plot to display a data set of - I can make a line plot that displays data in fractional units. measurements in fractions of a unit (1/2, 1/4, 1/8). - I can solve addition and subtraction problems by using a line plot. Solve problems involving addition and subtraction of fractions by using information presented in line Line Plot plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. WEEK 30 Apr. 3 WEEK 31 Apr. 10 WEEK 32 Apr. 17 WEEK 33 Apr. 24 Lesson 27 Line Plots Lesson 26 Perimeter and Area Unit 6 Lesson 31 Points, Lines, Rays, and Angles Lesson 28 Understand Angles 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. 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. 4.MD.5 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. - I can use the formulas for perimeter and area to solve problems. Area Perimeter - I can identify and draw points, lines, line segments, rays, and angles, and identify them in two-dimensional figures. - I can identify and draw parallel and perpendicular lines, distinguish between the two, and identify them in two-dimensional figures. Point Line Segment Line Ray Angle Parallel Perpendicular Acute Obtuse - I can recognize an angle as a geometric shape. - I can identify acute, right, and obtuse angles. - I can recognize the relationship between an angle and a circle. Right

11 4.MD.C.6 Measure angles in whole-number degrees - Unit 5 Assessment using a protractor. Sketch angles of specified measure. WEEK 34 May 1 Lesson 29 Measure and Draw Angles Lesson 30 Add and Subtract with Angles 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. - I can measure an angle correctly using a protractor. - I can draw an angle of a specific degree. - I can explain how one angle can be broken down into smaller angles. - I can explain how several smaller angles can be put together to form one large angle. - I can solve addition and subtraction problems to find unknown angles. Vertex Decompose WEEK 35 May 8 Unit 6 Lesson 32 Classify Two-Dimensional Figures Lesson 33 Symmetry 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. 4.G.A.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. - I can sort two-dimensional figures based on parallel or perpendicular lines. - I can sort two-dimensional figures based on acute, obtuse, or right angles. - I can recognize that triangles can be classified based on the lengths of their sides (isosceles, equilateral, scalene). - I can identify a triangle based on the size of its angles (acute, obtuse, right). - I can recognize the lines of symmetry in twodimensional figures. - I can draw lines of symmetry in two-dimensional figures. Equilateral Triangle Isosceles Triangle Scalene Triangle Acute Triangle Right Triangle Obtuse Triangle Line of Symmetry - Polygon Song - Unit 6 Assessment

12 4.OA.C.5. Generate a number or shape pattern that - I can use rules to make or extend a number pattern. follows a given rule. Identify apparent features of the - I can analyze and describe patterns in numbers and pattern that were not explicit in the rule itself. For shapes. 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. WEEK 36 May 15 Lesson 8 Number and Shape Patterns