BREATHITT COUNTY SCHOOLS 4th Grade Math Curriculum Week Standard Key Vocabulary Learning Target Resources Assessment

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1 Operations and Algebraic Thinking OA.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.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. (Note: See Glossary, Table 2.) 4.OA.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 Product, factors, array, Multiple, Commutative, Zero, Identity Property of Multiplication Distributive Property, Inverse operations, fact family, I can recognize multiplication as repeated addition of equal groups used in arrays and comparisons. I can use patterns to find products with factors of 2, 5, and 9. I can use multiplication properties to simplify computations. I can use the distributive property to find products of the factors of 3, 4, 6, 7, and 8 by breaking apart problems into simpler problems. I can recognize patterns and continue the pattern. I can use arrays to write and complete multiplication and division fact families. EnVision Math Core Standards Lessons 1/1-10 Manipulatives needed for the lesson--see list of technology resources used for each unit. Summative Assessment-Topic 1 multiple choice/constructed response test Performance Task p36 1

2 number. Determine whether a given whole number in the range is prime or composite OA.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. Repeating pattern, input, output I can identify a repeating pattern. I can identify number sequences. I can extend a table and generate a number that follows a given rule. I can write a rule for a situation. I can extend geometric patterns. EnVision Math Core Standards Lessons 2/1-6 Manipulatives needed for the lesson--see list of technology resources used for each unit. Summative Assessment-Topic 2 multiple choice/constructed response test Performance Task p62 Number and Operations in Base Ten NBT.1: Recognize that in a multidigit 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.2: Read and write multi-digit Digits, place value, standard form, expanded form, word form, compare, I can read and write numbers in standard, expanded, and word form. I can recognize that a digit in one place represents ten times what it represents in the place to its right. I can compare two numbers using <, >, or =. Lessons 3/1-6 Manipulatives needed for the lesson--see list of technology resources used for each unit. Summative Assessment-Topic 3 multiple choice/constructed 2

3 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. I can order numbers. I can round whole numbers. response test Performance Task p86 4.NBT.3: Use place value understanding to round multi-digit whole numbers to any place NBT.3: Use place value understanding to round multidigit whole numbers to any place. 4.NBT.4: Fluently add and subtract multi-digit whole numbers using the standard algorithm. Breaking apart, compensation, counting on, commutative, associative, and identity properties of addition, inverse operations I can use mental math to add and subtract whole numbers. I can fluently add and subtract whole numbers. I can estimate sums and differences. Lessons 4/1-6 Manipulatives needed for the lesson--see list of technology resources used for each unit. Summative Assessment-Topic 4 multiple choice/constructed response test Performance Task p112 3

4 NBT.5: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. product factors multiple multiplication array Lesson 5-1 Arrays and Multiplying by 10 and 100 I can use arrays to multiply by 10 and 100. I can make an array with place-value blocks to help me visualize and find products Lesson 5-2 Multiplying by Multiples of 10 and 100 I can use multiplication facts and number patterns to multiply by multiples of 10 and 100. envision Math Lesson 5-1/5-5 Daily Common Core Reviews Quick Check Masters Student Workbook place value blocks grid paper Daily Common Core Review Quick Check Masters partial products Lesson 5-3 Breaking Apart to Multiply I can break apart numbers and use arrays to multiply 2- digit by 1-digit numbers. lattice method Introduce and Practice Lattice Method for Multiplication I can use the lattice method to multiply 2-digit numbers. Lesson 5-4 Using Mental Math to Multiply I can use compensation to multiply numbers mentally. 4

5 9 10 Cont. 4.NBT.5: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 4.OA.3 Solve multi-step 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. 4.NBT.5: Multiply a whole number of up compensation Lesson 5-5 Using Rounding to Estimate I can use rounding to estimate solutions to multiplication problems. Lesson 5-6 Problem Solving: Reasonableness I can check for reasonableness by making sure my calculations answer the question asked. I can use estimation to make sure the calculation was performed correctly. Lesson 6-1 Arrays and Using an Expanded Algorithm I can record multiplication using an expanded algorithm. envision Math Lesson 5-1/5-5 Daily Common Core Reviews Quick Check Masters Student Workbook place value blocks grid paper Daily Common Core Review Quick Check Masters Topic 5 Reteaching pg 130 Summative Assessments Number Sense: Multiplying by 1-digit Numbers Topic Test pg 132, 133 Performance Assessment pg 134 Extended Response 5

6 11 12 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. product array factor rounding Lesson 6-2 Connecting the Expanded and Standard Algorithms I can multiply 2-digit numbers by 1-digit numbers using paper-andpencil methods. Lesson 6-3 Multiplying 2-Digit by 1-Digit Numbers I can multiply 2-digit numbers by 1-digit numbers using the standard algorithm and estimate to check for reasonableness. Lesson 6-4 Multiplying 3- and 4- Digit by 1-Digit Numbers I can use the standard algorithm to multiply 3- and 4-digit numbers by 1-digit numbers. envision Math Lesson 6-1/6-6 Daily Common Core Reviews Quick Check Masters Student Workbook place value blocks Daily Common Core Review Quick Check Masters Summative assessments Review what you know pg NBT.5: Multiply a whole number of up to four digits by a one-digit whole Lesson 6-5 Multiplying by 1- Digit Numbers I can multiply 2, 3, and 4-digit numbers by 1- digit numbers using the standard algorithm. I can estimate to check for reasonableness. 6

7 11 12 Cont. 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. product array factor rounding Lesson 6-6 Problem Solving: Missing or Extra Information I can identify what information in a problem is missing or is not needed. envision Math Lesson 6-1/6-6 Daily Common Core Reviews Quick Check Masters Daily Common Core Review Student Workbook Quick Check Masters place value blocks Summative Assessments Developing Fluency: Multiplying by 1-Digit Numbers Topic Test pg 160, NBT.5: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit Lesson 7-1 Arrays and Multiplying 2-Digit Numbers by Multiples of 10 I can use arrays to multiply 2-digit numbers by multiples of 10. Lesson 7-2 Using Mental Math Performance Assessment pg 162 Extended Response 7

8 13 14 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 equation factors product round array to Multiply 2-Digit Numbers I can use patterns to multiply by multiples of 10. I can use basic facts and place-value patterns to mentally multiply a twodigit number by a multiple of 10 or 100. envision Math Lesson 7-1/7-5 Daily Common Core Reviews Quick Check Masters Daily Common Core Review 4.NBT.3 Use place value understanding to round multi-digit whole numbers to any place. Lesson 7-3 Using Rounding to Estimate I can use rounding to estimate solutions to multiplication problems involving two 2-digit numbers. Student Workbook grid paper place value blocks Quick Check Masters 4.NBT.5: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers using strategies based on place value and the properties of Lesson 7-4 Using Compatible Numbers to Estimate I can use compatible numbers and rounding to estimate solutions to multiplication problems involving two 2-digit numbers. 8

9 13 14 Cont. operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models equation factors product round array compatible numbers Lesson 7-5 Problem Solving: Multiple-Step Problems I can identify and answer hidden questions to solve multistep problems with operations. envision Math Lesson 7-1/7-5 Daily Common Core Reviews Quick Check Masters Daily Common Core Review Student Workbook Quick Check Masters Summative Assessments Number Sense: Multiplying by 2-Digit Numbers Topic Test pg 180, NBT.5: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models Lesson 8-1 Arrays and Multiplying 2-Digit Numbers I can use arrays to multiply two-digit numbers by twodigit numbers to find the product. Performance Assessment pg 182 Extended Response 9

10 15 16 Cont. 4.NBT.5: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models rounding Commutative Property compatible Distributive Property rounding Commutative Property compatible Distributive Property Lesson 8-2 Arrays and an Expanded Algorithm I can use an expanded algorithm to multiply twodigit numbers to find the product Lesson 8-3 Multiplying 2-Digit Numbers by Multiples of 10 I can use grids and patterns to multiply 2-digit numbers and multiples of 10. Lesson 8-4 Multiplying 2-Digit by 2-Digit Numbers I can use partial products to multiply 2-digit numbers by 2-digit numbers and find the products. Lesson 8-5 Problem Solving: Two-Question Problems I can solve two-question problems. envision Math Lesson 8-1/8-5 Daily Common Core Reviews Quick Check Masters Student Workbook grid paper Daily Common Core Review Quick Check Masters Summative Assessments Number Sense: Multiplying by 2-Digit Numbers Topic Test pg 200, 201 Performance Assessment pg 202 Extended Response 10

11 Number Operations/Fractions/Algebraic Expressions NBT.6: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 4.OA.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 Divide Divisor Quotient Remainder Dividend Estimate Multiplication equation I can use mental math to divide. I can estimate quotients. I can estimate quotients for greater dividends. I can divide with remainders. I can decide whether to multiply or divide in a math story. I can draw a picture and write an equation to solve a problem. EnVision Math Core Standards Lessons 9-1/9-6 Manipulatives needed for the lesson--see list of technology resources used for each unit. Summative Assessment-Topic 9 multiple choice/constructed response test 4.OA.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. (Note: See 11

12 Glossary, Table 2.) 4.NBT.5: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models NBT.6: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 4.NBT.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. Repeat Subtraction Division Quotient Divisor Dividend Remainder Multiples Operation digit I can show division as repeated subtraction. I can divide using repeated subtraction. I can use objects to divide. I can divide 2 digit by one digit numbers. I can divide 3 digit by one digit numbers. I can decide where to start dividing. I can divide 4 digit by one digit numbers. I can solve multiple-step problems. EnVision Lessons 10-1/10-8 Manipulatives needed for the lesson--see list of technology resources used for each unit. Summative: Topic 10 test Multiple Choice/constructed response test Performance Task Topic 10 Create an array or use division to help solve the task. 4.NBT.5: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the 12

13 properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 4.OA.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 OA.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. 4.OA.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 fraction Numerator Denominator Factors Multiples Prime Composite Equivalent Compare Order Common denominator benchmark I can use multiplication to find all the factors of a number. I can find prime and composite numbers. I can find multiples of a number. I can find equivalent fractions. I can find equivalent fractions on a number line. I can use the number line or fraction strips to find equivalent fractions. I can order fractions. EnVision Lessons 11-1/11-8 Manipulatives needed for the lesson--see list of technology resources used for each unit. Standardized test with Summative Test-Topic 11-Multiple Choice and Constructed response 13

14 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. 4.NF.1: Explain why a fraction a/b is equivalent to a fraction (n a)/(n b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. 4.NF.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. I can compare fractions with different numerators and denominators. 14

15 NF.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. 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. Fractions Denominators Numerators Number line Improper Mixed number Compose Decompose equation I can model addition of fractions. I can add fractions with like denominators. I can model subtraction of fractions. I can subtract fractions with like denominators. I can add and subtract fractions on a number line. I can write an improper fraction as a mixed number. I can write a mixed number as an improper fraction. I can model addition and subtraction of mixed numbers. I can add mixed numbers. I can subtract mixed numbers. I can compose and decompose fractions. I can draw a picture and write an equation to solve a problem using fractions. EnVision Lessons 12-1/12-11 Manipulatives needed for the lesson--see list of technology resources. Summative: Pages Performance Task Topic 12-page

16 25, 26 Topic 13 Extending Fraction Concepts 4.NF.4a Understand a fraction a/b as a multiple of 1/b. 4.NF.4b Understand a fraction a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. 4.NF.4c Solve word problems involving multiplication of a fraction by a whole number. 4.NF.5 Express a fraction with denominator 10 as an equivalent fraction with a denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. Unit Fraction Decimal Point Hundredth Tenth I can show fractions as multiples of unit fractions by using models. I can multiply a fraction by a whole number by using models. I can multiply a fraction by a whole number using symbols to solve problems. I can write a fraction as a decimal. I can write a decimal as a fraction. I can locate and name fractions on a number line. I can locate and name decimals on a number line. I can use equivalent fractions to write fractions as decimals. I can use models and placevalue charts to represent decimals to hundredths. EnVision Lessons 13-1 through Manipulatives needed for the lesson--see list of technology resources used for each unit. : bell ringers exit slips quick check quizzes for each lesson participation and success during wholegroup activities and discussion and lesson practice problems ability to teach/share/lead during small-group activities journaling, Summative: ( quick check quizzes for each lesson) Topic 13 Test: multiple choice and short answer, student text pages Alternate test master for Topic 13 from assessment book Topic 13 Performance Task student text page

17 4.NF.6 Use decimal notation with denominators 10 or 100. I can read and write decimals to the hundredths in expanded, standard, and word form. 27, 28 Topic 14: Measurement Units and 4.NF.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. 4.MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. 4.MD.1 Know relative sizes of measurements unit 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 measurements equivalents in a Inch Foot Yard Mile I can use models and placevalue charts to compare decimals to the hundredths. I can use the four operations to solve word problems involving decimals (money) and problems that require expressing measurements given in a larger unit in terms of a smaller unit. I can solve problems with fractions and decimals by drawing a picture. I can estimate and measure length by choosing the appropriate unit of length. I can measure length with customary units. EnVision Lessons 14-1 through Manipulatives needed for the lesson--see list of technology resources used for each unit : bell ringers exit slips quick check quizzes for each lesson participation and success 17

18 Conversions two-column table. For example, know that 1 frt is 12 times as long as 1 in. Express the length of a 4ft snake as 48 inches. Generate a conversion talbe for feet and inches listing the number pairs: (1,12), (2,24), (3,36). Capacity I can measure lengths with metric units. I can estimate fluently with customary units: cups, pints, quarts, and gallons. I can compare the relative sizes of capacity measurements. during wholegroup activities and discussion and lesson practice problems ability to teach/share/lea d during smallgroup activities journaling, Weight Ounce Pound Ton I can estimate fluently and measure with units of weight: ounces, pounds, and tons. I can convert between customary units of measure for length and capacity. I can solve and explain word problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Summative: ( quick check quizzes for each lesson) Topic 14 Test: multiple choice and short answer, student text pages Alternate test master for Topic 14 from assessment book Topic 14 18

19 4.MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Millimeter Centimeter Decimeter Meter Kilometer Milliliter Liter Mass Gram Kilogram I can estimate and measure length to the nearest centimeter, and choose the most appropriate metric unit for measuring length. I can estimate fluently with milliliters and liters. I can measure capacity with milliliters and liters. I can estimate and measure with units of mass: grams and kilograms. Performance Task student text page 398 I can convert between metric units. I can compare several different units of time and freely convert from one unit of time to another. I can solve word problems that require finding the original times, measurements, or quantities that led to a result that is given. 19

20 29, 30 Topic 15 Solving Measurement Problems 31, 32 4.MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. 4.MD.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. 4.MD.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in linie 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.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and Perimeter Area Line plot Point Line Plane I can use the formulas for the perimeter and area of rectangles to solve real-world problems. I can use diagrams to show data and analyze how the quantities are related to solve real-world measurement problems. I can solve real-world problems that involve money and giving change by counting. I can construct line plots using given data and use the line plot to answer questions about the data set. I can break a problem into smaller, more manageable pieces and find a pattern to fit. I can identify and describe points, lines, and planes. EnVision Lessons 15-1 through 15-5 Manipulatives needed for the lesson--see list of technology resources used for each unit EnVision Lessons 16-1 through : bell ringers exit slips quick check quizzes for each lesson participation and success during wholegroup activities and discussion and lesson practice problems ability to teach/share/lead during small-group activities journaling, Summative: ( quick check quizzes for each lesson) Topic 15 Test: multiple choice and short answer, student text pages Alternate test master for Topic 15from assessment book Topic 15 Performance Task student text page 418 : bell ringers 20

21 Topic 16 Lines, Angles, and Shapes perpendicular and parallel lines. Identify these in two-dimensional figures. 4.G.2 I can 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. Parallel lines Intersecting lines Perpendicular lines Line segment Ray Angle Right angle Acute angle Obtuse angle Straight angle Polygon Side Vertex Triangle Quadrilateral Pentagon Hexagon Octagon Equilateral triangle Isosceles triangle Scalene triangle Right triangle Acute triangle Obtuse triangle I can use geometric terms to describe parts of lines and types of angles. I can learn to identify polygons. I can learn to identify triangles. I can learn to identify quadrilaterals.. I can solve problems by making and testing generalizations. Manipulatives needed for the lesson--see list of technology resources used for each unit exit slips quick check quizzes for each lesson participation and success during whole-group activities and discussion and lesson practice problems ability to teach/share/lead during small-group activities journaling, Summative: ( quick check quizzes for each lesson) Topic 15 Test: multiple choice and short answer, student text pages Alternate test master for Topic 16 from assessment book Topic 16 Performance Task student text page 450 Rhombus Trapezoid Parallelogram 21

22 4.G.3 Recognize a line of symmetry for a twodimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Rectangle Square Symmetric Line of symmetry I can determine if a plane figure has line symmetry and, if so, how many lines of symmetry it has. 4.MD.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.5b An angle that turns through n one-degree angles is said to have an angle measure of n degrees. Degree Unit angle Angle measure I can use unit angles and fractions of a circle to find angle measures. I can find the measure of an unknown angle by adding and subtracting. I can use a smaller angle to measure a larger angle by repeating the unit 4.MD.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. I can measure and draw angles. 22

23 4.MD.7 Recognize angle measure as additive. When an angle is decomposed into nonoverlapping 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 angels on a diagram in real world and mathematical problems. Protractor I can find the measure of an unknown angle by adding and subtracting 23

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