Common Core State Standards 1 st Edition. Math Pacing Guide


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1 Common Core State Standards 1 st Edition Math Pacing Guide Fourth Grade 2 nd Nine Week Period 1 st Edition Developed by: Christy Mitchell, Amy Moreman, Natalie Reno `````````````````````````````````````````````````````````````````````````````````````` Mr. Stan Rounds, Superintendent Dr. Steven Sanchez, Deputy Superintendent Prepared By: Lydia Polanco, Coordinator of Elementary Instruction Fourth Grade  2 nd Nine Weeks 1
2 Math Pacing Guide Las Cruces Public Schools Understanding Mathematics: The standards define what students should understand and be able to do in their study of mathematics. Asking a student to understand something means asking a teacher to assess whether the student has understood it. 1 Mathematical understanding and procedural skill are equally important. 2 Description of the Pacing Guide: A pacing guide is an interval based description of what teachers teach in a particular grade or course; the order in which it is taught, and the amount of time dedicated to teaching the content. Purpose of a Pacing Guide: The purpose of a pacing guide is to ensure that all of the standards are addressed during the academic year. Each pacing guide is nine weeks in duration. Components of the Pacing Guide: Critical Areas Each grade level has identified Critical Areas. These areas are woven throughout the standards and should receive additional time and attention. Mathematical Practice Standards (8) Based on the NCTM Process Standards, these standards describe the variety of "processes and proficiencies" students should master while working with the Grade Level Content Standards. Domains are larger groups of related Content Standards. Standards from different domains may sometimes be closely related. 3 Clusters are groups of related standards. Note that standards from different clusters may sometimes be closely related, because mathematics is a connected subject. 4 Grade level standards define what students should know and be able to do by the end of each grade level. Unpacked standards provide a clear picture for the teacher as he/she implements the CCSS Resources includes but not limited to current district core resources Depth of Knowledge (DOK) Criteria for systematically analyzing the alignment between standards and standardized assessments. Understanding Mathematics: The standards define what students should understand and be able to do in their study of mathematics. Asking a student to understand something means asking a teacher to assess whether the student has understood it Mathematics, Introduction, p. 4 2 See #1 3 See #1 4 Mathematics, Introduction, p Mathematics, Introduction, p. 4 Fourth Grade  2 nd Nine Weeks 2
3 STANDARDSBASED, STANDARDSDRIVEN LCPS Pacing Guides Other Resources Common Core State Standards Core Program envision Math Supplemental Technology Based program to prepare for PARCC (First in Math, FASTT Math, etc.) Fourth Grade  2 nd Nine Weeks 3
4 Grade Level: 4 Quarter: 2 nd Nine Weeks Standard Q1 Q2 Q3 Q4 4.0A.1 X P R R 4.0A.2 X P R R 4.0A.3 X P R R 4.0A.4 X P R R Domain: Operations and Algebraic Thinking Cluster: Use the four operations with whole numbers to solve problems. Critical Areas: #1: Strong Connection #2: No Connection #3: No Connection #4: No Connection Grade Level Content Standard Mathematical Practice Standard 4.OA.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.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.3. Solve multistep word problems posed with whole numbers and having wholenumber 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.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 onedigit number. Determine whether a given whole number in the range is prime or composite. MP.1. Make sense of problems and persevere in solving them. MP.3. Construct viable arguments and critique the reasoning of others. MP.4. Model with mathematics. MP.7. Look for and make use of structure. MP.4. Model with mathematics. MP.7. Look for and make use of structure. MP.1. Make sense of problems and persevere in solving them. MP.4. Model with mathematics. MP.7. Look for and make use of structure. MP.7. Look for and make use of structure. Unpacked Content Standard: 4.OA.1. Students should be given opportunities to write and identify equations and statements for multiplicative comparisons. 5 x 8 = 40. Sally is five years old. Her mom is eight times older. How old is Sally s Mom? 5 x 5 = 25. Sally has five times as many pencils as Mary. If Sally has 5 pencils, how many does Mary have? 4.OA.2 This standard calls for students to translate comparative situations into equations with an unknown and solve. Fourth Grade  2 nd Nine Weeks 4
5 Students need many opportunities to solve contextual problems. Examples: Unknown Product: A blue scarf costs $3. A red scarf costs 6 times as much. How much does the red scarf cost? (3 x 6 = p). Group Size Unknown: A book costs $18. That is 3 times more than a DVD. How much does a DVD cost? (18 p = 3 or 3 x p = 18). Number of Groups Unknown: A red scarf costs $18. A blue scarf costs $6. How many times as much does the red scarf cost compared to the blue scarf? (18 6 = p or 6 x p = 18). 4.OA.3 The focus in this standard is to have students use and discuss various strategies. It refers to estimation strategies, including using compatible numbers (numbers that sum to 10 or 100) or rounding. Problems should be structured so that all acceptable estimation strategies will arrive at a reasonable answer. Students need many opportunities solving multistep story problems using all four operations. On a vacation, your family travels 267 miles on the first day, 194 miles on the second day and 34 miles on the third day. How many miles did they travel total? Some typical estimation strategies for this problem: Student 1 response: I first thought about 267 and 34. I noticed that their sum is about 300. Then I knew that 194 is close to 200. When I put 300 and 200 together, I get 500. Student 2 response: I first thought about 194. It is really close to 200. I also have 2 hundreds in 267. That gives me a total of 4 hundreds. Then I have 67 in 267 and the 34. When I put 67 and 34 together that is really close to 100. When I add that hundred to the 4 hundreds that I already had, I end up with 500. Student 3 response: I rounded 267 to 300. I rounded 194 to 200. I rounded 34 to 30. When I added 300, 200 and 30, I know my answer will be about OA.4 Requires students to demonstrate understanding of factors and multiples of whole numbers. This standard also refers to prime and composite numbers. Prime numbers have exactly two factors, the number one and their own number. For example, the number 17 has the factors of 1 and 17. Composite numbers have more than two factors. For example, 8 has the factors 1, 2, 4, and 8. A common misconception is that the number 1 is prime, when in fact; it is neither prime nor composite. Another common misconception is that all prime numbers are odd numbers. This is not true, since the number 2 has only 2 factors, 1 and 2, and is also an even number. Vocabulary: multiply, divide, unknown, algebraic thinking, equation, remainders, reasonableness, mental computation, estimation strategies, factor pairs, multiple, factors, prime, composite, rounding, product, array, fact family, inverse operations, commutative property of multiplication, zero property of multiplication, identity property of multiplication, distributive property Resources: Depth of Knowledge envisionmath 4.OA.1: Topic 1: Multiplication and Division: Meanings and Facts 11 Meanings of Multiplication 13 Multiplication Properties 17 Relating Multiplication & Division 4.OA.1. DOK 1: What is number 3 times larger than 4? 4.OA.1 DOK 2: Write an equation that shows 8 times as many as OA.2. DOK 1: Jenny has 5 dolls. Susie has 3 times as many dolls as Jenny. How many dolls does Susie have in all? Fourth Grade  2 nd Nine Weeks 5
6 4.OA.2: Topic 1: Multiplication and Division: Meanings and Facts 16 Meaning of Division 18 Special Quotients 19 Using Multiplication Facts to find Division Facts 110 Problem Solving: Draw a picture and write an equation 4.OA.3: Topic 1: Multiplication and Division: Meanings and Facts 15 Look for a Pattern 4.OA.3: Topic 5: Number Sense: Multiplying by 1Digit Numbers 56 Problem Solving: Reasonableness 4.OA.4: Topic 1: Multiplication and Division: Meanings and Facts 14 3, 4, 6, 7, and 8 as Factors 4.OA.4: Topic 11: Fraction Equivalence and Ordering 111 Factors 112 Prime and Composite Numbers 113 Multiples 4.OA.2. DOK 2: Joan works on a loading dock. She can load 45 boxes in one hour. Write an equation that can be used to find b, the number of boxes she can load in 2 hours. 4.OA.3. DOK 1: Identify the equation used to solve this word problem. Noah is planning a birthday party. 24 girls are attending and 28 boys plan to attend. He is serving the cake that will feed 75 people. How many more people can Noah invite to his party before he runs out of cake? 75(24+28) = 4.OA.3. DOK 2: Solve: Mary had 3 apple trees with 12 apples on each tree. She had 4 orange trees with 16 oranges on each tree. Write an equation with a letter standing for the unknown quantity that shows how much fruit she has in all. 4.OA.3. DOK 3: Write and solve a twostep word problem that uses 2 different operations. 4.OA.4. DOK 1: Identify the prime number. Which number is a composite? What are the factors of 25? List the multiples of 7 up to 70. Fourth Grade  2 nd Nine Weeks 6
7 Grade Level: 4 Quarter: 2 nd Nine Weeks Domain: Number and Operations in Base Ten (4.NBT) Standard Q1 Q2 Q3 Q4 4.NBT.5 X P P R 4.NBT.6 X P P R Cluster: Use place value understanding and properties of operations to perform multidigit arithmetic. Critical Areas: #1: Strong Connection #2: No Connection #3: No Connection #4: No Connection Grade Level Content Standard Mathematical Practice Standard 4.NBT.5. Multiply a whole number of up to four digits by a onedigit whole number, and multiply two twodigit 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.6 Find wholenumber quotients and remainders with up to fourdigit dividends and onedigit 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. MP.3. Construct viable arguments and critique the reasoning of others. MP.4. Model with mathematics. MP.7. Look for and make use of structure. MP.3. Construct viable arguments and critique the reasoning of others. MP.4. Model with mathematics. MP.7. Look for and make use of structure. Unpacked Content Standard: 4.NBT.5. Students who develop flexibility in breaking numbers apart (decomposing numbers) have a better understanding of the importance of place value and the distributive property in multidigit multiplication. Students use base ten blocks, area models, partitioning, compensation strategies, etc. when multiplying whole numbers and use words and diagrams to explain their thinking. They use the terms factor and product when communicating their reasoning. Multiple strategies enable students to develop fluency with multiplication and transfer that understanding to division. Use of the standard algorithm for multiplication and understanding why it works, is an expectation in the 5th grade. This standard calls for students to multiply numbers using a variety of strategies. There are 25 dozen cookies in the bakery. What is the total number of cookies at the bakery? Student 1 25 x 12 I broke 25 up into 5 groups of 5 5 x 12 = 60 I have 5 groups of 5 in x 5 = 300 Student 2 25 x 12 I doubled 25 and cut 12 in half to get 50 x 6 = 300 Student 3 25 x12 I broke 12 up into 10 and 2 25 x 10 = x 2 = = NBT.6 In fourth grade, students build on their third grade work with division within 100. Students need opportunities to develop their understandings by using problems in and out of context. Fourth Grade  2 nd Nine Weeks 7
8 Examples : A 4th grade teacher bought 4 new pencil boxes. She has 260 pencils. She wants to put the pencils in the boxes so that each box has the same number of pencils. How many pencils will there be in each box? Using Base 10 Blocks: Students build 260 with base 10 blocks and distribute them into 4 equal groups. Some students may need to trade the 2 hundreds for tens but others may easily recognize that 200 divided by 4 is 50. Using Place Value: = (200 4) + (60 4) Using Multiplication: 4 x 50 = 200, 4 x 10 = 40, 4 x 5 = 20; = 65; so = 65 This standard calls for students to explore division through various strategies. Student divided by 8 There are 70 8 s in = 32 There are 4 8 s in = 74 Student divided by 8 I know that 10 8 s is 80 If I take out 50 8 s that is = 192 I can take out 20 more 8 s which is = 32 8 goes into 32 4 times I have none left I took out 50, then 20 more, then 4 more That s 7 Student 3 I want to get to x 25 = x 25 = x 25 = = = 592 I had 75 groups of 8 and took one away, so there are 74 teams Vocabulary: partial products, quotients, remainders, dividends, divisors, multiplication, division, equations, rectangular arrays, area models, compatible numbers, Resources: Depth of Knowledge envisionmath 4.NBT.5 Topic 5: Number Sense: Multiplying by 1Digit Numbers 51 Arrays and Multiplying by 10 and Multiplying by Multiples of 10 and Breaking Apart to Multiply 54 Using Mental Math to Multiply 55 Using Rounding to Estimate 56 Problem Solving: Reasonableness 4.NBT.5 Topic 6: Developing Fluency: Multiplying by 1Digit Numbers 61 Arrays and Using an Expanded Algorithm, 62 Connecting the Expanded and Standard Algorithms 63 Multiplying 2Digit by 1Digit Numbers 4.NBT.5. DOK 1: Solve: 124 x 7 =, 53 x 25 =, 2531 x 4 = 4.NBT.5. DOK 2: Find the product of 45 x 23 using a strategy other than the standard algorithm. Fourth Grade  2 nd Nine Weeks 8
9 64 Multiplying 3 and 4Digit by 1Digit Numbers 65 Multiplying by 1Digit Numbers 66 Problem Solving: Missing or Extra Information 4.NBT.5 Topic 7: Number Sense: Multiplying by 2Digit Number 71 Arrays and Multiplying 2Digit Numbers by Multiples of Using Mental Math to Multiply 2digit Numbers 74 Using Compatible Numbers to Estimate 75 Problem Solving: MultipleStep Problems 4.NBT.6: DOK 1: Solve: = =. 4.NBT.6: DOK 2: Jenny has 36 brownies. She would like to share them with her 6 friends. Which operation shows how many brownies each friend will receive? 4.NBT.6: DOK 2: Henry had 491 baseball cards. He wanted to split them equally between his 5 friends. How many would each friend get, and is there a remainder? 4.NBT.5 Topic 8: Developing Fluency: Multiplying by 2Digit Numbers 81 Arrays and Multiplying 2Digit Numbers 82 Arrays and an Expanded Algorithm 83 Multiplying 2Digit Numbers by Multiples of Ten 84 Multiplying 2Digit by 2Digit Numbers 85 Problem Solving: TwoQuestion Problems 4.NBT.6 Topic 9: Number Sense: Dividing by 1Digit Divisors 91 Using Mental Math to Divide 92 Estimating Quotients 93 Estimating Quotients for greater Dividends 94 Dividing with Remainders 95 Multiplication and Division Stories, 96 Problem Solving: Draw a Picture and Write an Equation. 4.NBT.6 Topic 10: Developing Fluency: Dividing by 1Digit Divisors 101 Using Object to Divide: Division as Repeated Subtraction 102 Division as Repeated Subtraction 103 Using Object to Divide: Division as Sharing 104 Dividing 2Digit by 1Digit Numbers 105 Dividing 3Digit by 1Digit Numbers 106 Deciding Where to Start Dividing, 107 Dividing 4Digit by 1 Digit Dividing 4Digit by 1Digit Numbers Fourth Grade  2 nd Nine Weeks 9
10 Grade Level: 4 Quarter: 2 nd Nine Weeks Domain: Operations and Algebraic Thinking (OA) Standard Q1 Q2 Q3 Q4 4.MD.3 (area) I/P I/P R R Cluster: Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Critical Areas: #1: Strong Connection #2: No Connection #3: No Connection #4: No Connection Grade Level Content Standard Mathematical Practice Standard 4.MD.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. 2nd quarter area MP.4. Model with mathematics. MP.7.Look for and make use of structure. Unpacked Content Standard: 4.MD.3 Students developed understanding of area in 3rd grade by using visual models. While students are expected to use a formula to calculate the area of rectangles, they need to understand and be able to communicate their understanding of why the formula works. The formula for area is I x w and the answer will always be in square units. This standard calls for students to generalize their understanding of area by connecting the concept to a mathematical formula. The formula should be developed through experience not just memorization. Mrs. Fields is covering the miniature golf course with an artificial grass. The length is 12ft and the width is 9ft. How many 1foot squares of carpet will she need to cover the entire course? Vocabulary: rectangles, area, formula, length, width, perimeter Resources: envision Math 4.MD.3 Topic 15: Solving Measurement Problems 151 Solving Area and Perimeter Problems Depth of Knowledge 4.MD.3. DOK 1: Find the area of a regular polygon with length and width given. 4.MD.3. DOK 2: The rectangular sign has an area of 32 in. The length of the sign is 8 in. How wide is the sign? 4.MD.3. DOK 3: Create 2 different polygons with an area of 64 in. Fourth Grade  2 nd Nine Weeks 10
11 Grade Level: 4 Quarter: 2 nd Nine Weeks Domain: Measurement and Data (4.MD) Standard Q1 Q2 Q3 Q4 4.MD.5a X P R R 4.MD.5b X P R R 4.MD.6 X P R R 4.MD.7 X P R R Cluster: Geometric measurement: understand concepts of angle and measure angles. Critical Areas: #1: No Connection #2: No Connection #3: Strong Connection #4: No Connection Grade Level Content Standard Mathematical Practice Standard 4.MD.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: 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 "onedegree angle," and can be used to measure angles. 4.MD.5b An angle that turns through n onedegree angles is said to have an angle measure of n degrees. 4.MD.6 Measure angles in wholenumber degrees using a protractor. Sketch angles of specified measure. 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 angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. MP.5. Use appropriate tools strategically MP.7. Look for and make use of structure. MP.5. Use appropriate tools strategically MP.7. Look for and make use of structure. MP.1. Make sense of problems and persevere in solving them. MP.4. Model with mathematics. Unpacked Content Standard: 4.MD.5a Angle measure is a turning point in the study of geometry. Students often find angles and angle measure to be difficult concepts to learn, but that learning allows them to engage in interesting and important mathematics. An angle is the union of two rays, a and b, with the same initial point P. The rays can be made to coincide by rotating one to the other about P; this rotation determines the size of the angle between a and b. The rays are sometimes called the sides of the angles. Another way of saying this is that each ray determines a direction and the angle size measures the change from one direction to the other. Angles are 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 onedegree angle, and degrees are the unit used to measure angles in elementary school. A full rotation is thus 360º. Two angles are called Fourth Grade  2 nd Nine Weeks 11
12 complementary if their measurements have the sum of 90º. Two angles are called supplementary if their measurements have the sum of 180º. Two angles with the same vertex that overlap only at a boundary (i.e., share a side) are called adjacent angles. These terms may come up in classroom discussion, they will not be tested. This concept is developed thoroughly in middle school (7th grade). Like length, area, and volume, angle measure is additive: The sum of the measurements of adjacent angles is the measurement of the angle formed by their union. This leads to other important properties. If a right angle is decomposed into two adjacent angles, the sum is 90º, thus they are complementary. Two adjacent angles that compose a straight angle of 180º must be supplementary. The diagram below will help students understand that an angle measurement is not related to an area since the area between the 2 rays is different for both circles yet the angle measure is the same. 4.MD.5b This standard calls for students to explore an angle as a series of onedegree turns. A water sprinkler rotates onedegree at each interval. If the sprinkler rotates a total of 100º, how many onedegree turns has the sprinkler made? 4.MD.6 Before students begin measuring angles with protractors, they need to have some experiences with benchmark angles. They transfer their understanding that a 360º rotation about a point makes a complete circle to recognize and sketch angles that measure approximately 90º and 180º. They extend this understanding and recognize and sketch angles that measure approximately 45º and 30º. They use appropriate terminology (acute, right, and obtuse) to describe angles and rays (perpendicular). Students should measure angles and sketch angles Fourth Grade  2 nd Nine Weeks 12
13 As with all measureable attributes, students must first recognize the attribute of angle measure, and distinguish it from other attributes. As with other concepts students need varied examples and explicit discussions to avoid learning limited ideas about measuring angles (e.g., misconceptions that a right angle is an angle that points to the right, or two right angles represented with different orientations are not equal in measure). If examples and tasks are not varied, students can develop incomplete and inaccurate notions. For example, some students come to associate all slanted lines with 45º measures and horizontal and vertical lines with measures of 90º. Others believe angles can be slanted lines with 45º measures and horizontal and vertical lines with measures of 90º. Others believe angles can be read off a protractor in standard position, that is, a base is horizontal, even if neither ray of the angle is horizontal. Measuring and then sketching many angles with no horizontal or vertical ray, perhaps initially using circular 360º protractors, can help students avoid such limited conceptions. 4.MD.7 This standard addresses the idea of decomposing (breaking apart) an angle into smaller parts. A lawn water sprinkler rotates 65 degrees and then pauses. It then rotates an additional 25 degrees. What is the total degree of the water sprinkler rotation? To cover a full 360 degrees how many times will the water sprinkler need to be moved? If the water sprinkler rotates a total of 25 degrees then pauses. How many 25degree cycles will it go through for the rotation to reach at least 90 degrees? If the two rays are perpendicular, what is the value of m? Vocabulary: rays, circular arc, center point, angle, vertex, end point, one degree angle, circle, measure angles, protractor, decompose, acute, obtuse, right, straight angle. Resources: Depth of Knowledge Fourth Grade  2 nd Nine Weeks 13
14 envision Math 4.MD.5a Topic 16: Lines, Angles, and Shapes 163 Understanding Angles and Unit Angles 4.MD.5a DOK 1: Classify the following angles. What is the measurement of the shaded portion of the following angles? 4.MD.5b Topic 16: Lines, Angles, and Shapes 165 Measuring Angles 4.MD.6 Topic 16: Lines, Angles, and Shapes 165 Measuring Angles 4.MD. 7 Topic 16: Lines, Angles, and Shapes 166 Adding and Subtracting Angle Measures 4.MD.5b DOK 1: What is the measure of each angle of a yellow hexagon pattern block? 4.MD.6 DOK 1: Use a protractor to measure the following angle. 4.MD.7 DOK 1: Find the value of X. 4.MD.7 DOK 2: Construct a 90 angle and separate the angle into 2 smaller angles. Fourth Grade  2 nd Nine Weeks 14
15 Grade Level: 4 Quarter: 2 nd Nine Weeks Domain: Geometry Standard Q1 Q2 Q3 Q4 4.G.1 X P R R 4.G.2 X P R R 4.G.3 X P R R Cluster: Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Critical Areas: #1: No Connection #2: No Connection #3: Strong Connection #4: No Connection Grade Level Content Standard Mathematical Practice Standard 4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. 4.G.2 Classify twodimensional 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.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 linesymmetric figures and, draw lines of symmetry. MP.4. Model with mathematics. MP.7.Look for and make use of structure. Unpacked Content Standard: 4.G.1 This standard asks students to draw two dimensional geometric objects (points, lines, line segments, rays, angles [right, acute, obtuse], and perpendicular and parallel lines) and to also identify them in two dimensional figures. This is the first time that students are exposed to rays, angles, and perpendicular and parallel lines. Draw two different types of quadrilaterals that have two pairs of parallel sides. Is it possible to have an acute right triangle? Justify your reasoning using pictures and words. How many acute, obtuse and right angles are in this shape? Fourth Grade  2 nd Nine Weeks 15
16 Draw and list the properties of a parallelogram. Draw and list the properties of a rectangle. How are your drawings and lists alike? How are they different? Be ready to share your thinking with the class. Figures from previous grades: polygon, rhombus/rhombi, rectangle, square, triangle, quadrilateral, pentagon, hexagon, trapezoid, half/quarter circle, circle 4.G.2 This standard calls for students to sort objects based on parallelism, perpendicularity and angle types. Do you agree with the label on each of the circles in the Venn diagram above? Describe why some shapes fall in the overlapping sections of the circles. Draw and name a figure that has two parallel sides and exactly 2 right angles. 4.G.3 This standard only includes line symmetry. For each figure, draw all of the lines of symmetry. What pattern do you notice? How many lines of symmetry do you think there would be for regular polygons with 9 and 11 sides. Sketch each figure and check your predictions. Polygons with an odd number of sides, such as a triangle and hexagon, have lines of symmetry that go from a midpoint of a side through a vertex. Vocabulary: acute angle, right angle, obtuse angle, points, lines, line segments, rays, perpendicular lines, right triangles, isosceles triangle, scalene Fourth Grade  2 nd Nine Weeks 16
17 triangle, equilateral triangle, acute triangle, obtuse triangle, line of symmetry, line symmetrical figures, parallel lines, intersecting lines, polygon, vertex, side, quadrilateral, pentagon, octagon, hexagon, rhombus, trapezoid, parallelogram, rectangle, square, triangle Resources: Depth of Knowledge envision Math 4.G.1 Topic 16: Lines, Angles, and Shapes 161 Point, Lines, and Planes 162 Line Segments, Rays, and Angles 4.G.2 Topic 16: Lines, Angles, and Shapes 167 Polygons 168 Triangles 169 Quadrilaterals Problem Solving: Make and Test Generalizations 4.G.3 Topic 16: Lines, Angles, and Shapes Line Symmetry 4.G.1 DOK 1: Use the image below to answer the questions. 1. Name two parallel lines 2. Name two perpendicular lines 3. Name two lines that make a right angle 4. Name two intersecting lines 4.G.2 DOK 2: I am a polygon with four sides. I have one pair of parallel lines. I have two acute angles and two obtuse angles. What shape am I? Draw, name, and label the angles. 4.G.3 DOK 1: 4.G.3 DOK 2: Draw a figure with exactly two lines of symmetry. Fourth Grade  2 nd Nine Weeks 17
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