4 th GRADE MATH PACING GUIDE: 1st Nine Weeks UNIT 1: NUMBERS AND OPERATIONS IN BASE TEN, PART 1 Week Lesson Standards Learning Target Vocabulary
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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. 10 Lesson 0 Lessons for the 1 st 5 Days Refer to the Mathematical Practices - Set up rules and expectations - Pre-assessments WEEK 2 Aug. 14 Continue Lesson 0 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 using standard form, word form, and expanded form (the expanded form of 4256 is written as 4 x 1, x x 10 6 x 1). Compare 2 multi-digit based on meanings of the digits in each place and use the symbols >, =, and < to show the relationship. - I can identify the value of a digit based on its location in the number. - I can demonstrate how moving from one place-value 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 - I can use symbols (>, <, =) to show the relationship between two multidigit Value Period Word Form Standard Form Expanded Form Compare Greater Than Less Than WEEK 3 Aug. 21 Lesson 3 Add and Subtract Whole Numbers 4.NBT.B4 Fluently add and subtract within 1,000,000 using appropriate strategies and algorithms. - I can use the standard algorithm to add multi-digit whole - I can use the standard algorithm to subtract multi-digit whole Sum Difference Regroup WEEK 4 Aug. 28 Lesson 4 Round Whole Numbers 4.NBT.A.3 Round multi-digit whole to any place (up to and including the hundred-thousand place) using understanding of place value. - I can use appropriate tools to round multi-digit whole - I can explain how a multi-digit whole number is rounded to a specific place value. Round To Estimate An Estimate WEEK 5 Sept. 5 WEEK 6 Sept. 11 Lesson 5 Understand Multiplication Lesson 7 Multiples and Factors 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. 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 hole number in the range is prime or composite. 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. - 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. Multiplication Product Factors Equation - Review place value Factor Pair Multiple Composite Numbers Prime Numbers subtraction of whole
2 WEEK 7 Sept. 18 Lesson 6 Multiplication and Division in Word Problems 4.OA.A.2 Multiply or divide to solve contextual problems involving multiplicative comparison, and distinguishing multiplicative comparison from additive comparison. Task Arcs 1:Pattern Blocks 2: Playing Baseball 3: Jack and the Beanstalk 4: House of Cards 7: Generations - 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 Factor Equation subtraction of whole WEEK 8 Sept. 25 Lesson 9 Model Multi-Step Problems Lesson 10 Solve Multi-Step Problems 4.OA.A.3 Solve multistep word problems posed with whole 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. Expression Unknown Equation Remainder Reasonable - Review Rounding - Review and assess Units 1 and 2 Week 9 Oct. 2 FLEX WEEK
3 4 th GRADE MATH PACING GUIDE: 2nd Nine Weeks UNIT 3: NUMBER AND OPERATIONS IN BASE TEN, PART 2 WEEK 10 Oct. 16 WEEK 11 Oct. 23 Lesson 11 Multiply Whole Numbers 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, 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.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit, 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 of up to four digits by one-digit whole - I can multiply a two-digit number by a two-digit number. - I can multiply whole of up to four digits by one-digit whole - I can multiply a two-digit number by a two-digit number. Partial Products Multiplication Product Factor Multiple -Review multiplicative comparison - Review factors and multiples WEEK 12 Oct. 30 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 of up to four digits by one-digit whole - I can multiply a two-digit number by a two-digit number. - I can divide up to four-digit dividends by one-digit divisors, with remainders. - I can recognize the relationship between multiplication and division. Quotient Dividend Divisor Remainder Partial Quotient Division subtraction WEEK 13 Nov. 6 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 of up to four digits by one-digit whole - I can multiply a two-digit number by a two-digit number. - I can divide up to four-digit dividends by one-digit divisors, with remainders. - I can recognize the relationship between multiplication and division. Quotient Dividend Divisor Remainder Partial Quotient Division subtraction
4 UNIT 4: NUMBER AND OPERATIONS FRACTIONS 4.OA.A.3 Solve multistep word problems posed with whole - I can use equations with a letter standing for the unknown to represent Expression and having whole-number answers using the four operations, multi-step word problems. Unknown including problems in which remainders must be interpreted. - I can solve multi-step word problems. Equation Represent these problems using equations with a letter standing for - I can interpret the remainder in a division word problem. Remainder the unknown quantity. Assess the reasonableness of answers using - I can use estimation strategies to make sure the answer makes sense. Reasonable mental computation and estimation strategies including rounding. WEEK 14 Nov. 13 Solve Multi-Step Problems Task Arcs Task Arcs 5: Fair Tickets 6: Smoky Mts. 8: Earning Money WEEK 15 Nov. 27 Lesson 13 Understand Equivalent s 4.NF.A.1 Explain why a fraction is equivalent to a fraction by using visual fraction models, with attention to how the or 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. For example, = =. - 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. Divide Equivalent s - Review factors and multiples WEEK 16 Dec. 4 Lesson 14 Compare s 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. 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. - 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. Benchmark Common Compare > < - Review comparing whole
5 4.NF.B.3 Understand a fraction with a > 1 as a sum of fractions. - I can understand addition as joining parts. a. Understand addition and subtraction of fractions as joining and - I can understand subtraction as separating parts. separating parts referring to the same whole. - I can understand addition and subtraction of fractions. b. Decompose a fraction into a sum of fractions with the same - I can use fraction models to add and subtract fractions with like Unit denominator in more than one way, recording each decomposition denominators. Line Plots by an equation. Justify decompositions, e.g., by using a visual - I can add fractions with like denominators. fraction model. Examples: = + + ; = + ; 2 = = - I can subtract fractions with like denominators. - Review multi digit - I can use fraction models, number lines, and equations to multiplication + +. represent word problems. - I can make a line plot that displays data in fractional units. - I can solve addition and subtraction problems by using a line plot. WEEK 17 Dec. 11 WEEK 18 Dec. 18 Lesson 15 Understand Addition and Subtraction Lesson 16 Add and Subtract s Lesson 27 Line Plots Lesson 16 Add and Subtract s 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. 4.MD.B.4 Make a line plot to display a data set of measurements in fractions of a unit (,, ). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. 4.NF.B.3 Understand a fraction with a > 1 as a sum of fractions. 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: = + + ; = + ; 2 = = + +. 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. Unit - Review long division
6 4 th GRADE MATH PACING GUIDE: 3 rd Nine Weeks CRA Tasks: Pizza Task More or Less Than One? Task The Cake Shop Task Orange Juice Task Cottage Cheese Task WEEK 19 Jan. 8 FLEX WEEK WEEK 20 Jan. 16 WEEK 21 Jan. 22 Lesson 17 Add and Subtract Mixed Numbers Lesson 18 Understand Multiplication 4.NF.B.3c Add and subtract mixed with like denominators, 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.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. 1. a. Understand a fraction as a multiple of. For example, use a visual fraction model to represent as the product 5 ( ), recording the conclusion by the equation = 5 ( ). b. Understand a multiple of as a multiple of, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 ( ) as 6 (), recognizing this product as. (In general, n ( ( ) ) =.) 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 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 does your answer lie? - 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 with like denominators. - I can determine whether to use addition or subtraction when solving word problems involving fractions. - 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. Mixed Number subtraction of whole Product - Review rounding
7 4.NF.B.4 Apply and extend previous understandings of multiplication to - I can solve word problems that involve multiplying a fraction multiply a fraction by a whole number. 1. by a whole number. WEEK 22 Jan. 29 WEEK 23 Feb. 5 Lesson 19 Multiply s Lesson 20 s as Tenths and Hundredths a. Understand a fraction as a multiple of. For example, use a visual fraction model to represent as the product 5 ( ), recording the conclusion by the equation = 5 ( ). b. Understand a multiple of as a multiple of, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 ( ) as 6 (), recognizing this product as. (In general, n ( ( ) ) =.) 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 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 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 100. For example, express + " = " "" "" " as, and add " "". (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 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. Product - Review multi-digit multiplication Tenths Hundredths Equivalent s - Review long division WEEK 24 Feb. 12 Lesson 21 Relate Decimals and s 4.NF.C.6 Read and write decimal notation for fractions with denominators 10 or 100. Locate the decimals on a number line. - I can convert decimals into fractions, with denominators of 10 or I can convert fractions into decimals, with denominators of 10 or 100. Decimal Decimal Point - Review equivalent fractions WEEK 25 Feb. 20 Lesson 22 Compare Decimals Lesson 27 Line Plots 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. Use the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. 4.MD.B.4 Make a line plot to display a data set of measurements in fractions of a unit (,, ). 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. - I can compare two decimals up to hundredths, using the >, <, and = symbols. - I can make a line plot that displays data in fractional units. - I can solve addition and subtraction problems by using a line plot. Decimal Compare > < Line Plots - Review comparing fractions
8 WEEK 26 Feb. 26 Lesson 23 Convert Measurements Customary UNIT 5: MEASUREMENT AND DATA 4.MD.A.1 Measure and estimate to determine relative sizes of measurement - I can measure the length, volume, and/or mass of an object. Convert units within a single system of measurement involving length, liquid volume, - I can estimate relative length, volume, and/or mass of an Metric System and mass/weight of objects using customary and metric units. object. Customary System WEEK 27 Mar. 5 Lesson 25 Length, Liquid, Volume, 4.MD.A.2 Solve one-or-two step real-world problems involving whole number measurements with all four operations within a single system of measurement including problems involving simple fractions. - Review adding/subtracting fractions Liquid Volume Mass - Review adding subtracting mixed
9 4 th GRADE MATH PACING GUIDE: 4 th Nine Weeks WEEK 28 Mar. 12 WEEK 29 Mar. 19 Lesson 26 Perimeter and Area Lesson 24 Time and Money 4.MD.A.3 Know and 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.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. - I can use the formulas for perimeter and area to solve problems. - I can determine which operation to use when solving word problems involving length, liquid, volume, mass, time, and money. Area Perimeter Formula - Review multi digit multiplication and long division Convert subtraction of whole WEEK 30 Apr. 2 Lesson 31 Points, Lines, Rays, and Angles UNIT 6: Geometry 4.G.A.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse, straight, reflex), and perpendicular and parallel lines. Identify these in twodimensional figures. - 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 twodimensional figures. Point Line Segment Line Ray Angle Parallel Perpendicular Acute Obtuse - Review rounding WEEK 31 Apr. 9 Lesson 28 (Unit 5) Understand Angles Lesson 32 Classify 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 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. G.A.3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. - 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. - I can identify a triangle based on the size of its angles (acute, obtuse, right). - I can recognize the lines of symmetry in two-dimensional figures. - I can draw lines of symmetry in two-dimensional figures. Angle Ray Vertex Degree Right Angle Acute Angle Obtuse Angle Polygon Rectangle Equilateral, Isosceles Scalene, Acute Right, and Obtuse Triangles Quadrilateral Parallelogram Rhombus Trapezoid - Review equivalent and comparing fractions
10 WEEK 32 Apr. 16 WEEK 33 Apr. 23 Unit 5 Lesson 29 Measure and Draw Angles Lesson 30 Add and Subtract with Angles FLEX WEEK 4.MD.C.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. 4.MD.C.7 Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. - 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. Protractor Angle Ray Vertex Degree Right Angle Compose Decompose - Review adding and subtracting fractions - Review adding and subtracting mixed WEEK 34 Apr. 30 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 and draw lines of symmetry for two-dimensional figures. - 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 two-dimensional 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 - Review relating fractions to decimals WEEK 35 May 7 Unit 2 Lesson 8 Number and Shape 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 Explain informally why the will continue to alternate in this way. - I can use rules to make or extend a number pattern. - I can analyze and describe patterns in and shapes. Rule Pattern - Review comparing decimals WEEKs May 14 and May 21 FLEX WEEK - Refer to the Math in Action for Units 1 6
1: NUMBERS AND OPERATIONS IN BASE TEN, PART
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