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4th 4th Grade Nine Weeks Math Domain: Geometry Cluster: Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Common Core Standards: 4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. 4.G.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.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 the line-symmetric figures and draw lines of symmetry. Key Vocabulary Line Symmetry Plane Congruent Congruence Similar Line of Symmetry Reflection Line of Reflection Line Horizontal Line Segment Ray Angle Vertex Oblique Perpendicular Right Angle Parallel Quadrilateral Vertical Trapezoid Isosceles Trapezoid Parallelogram Rhombus Rectangle Square Acute Angle Edge Diagonal Equivalent Intersecting lines Obtuse angle Parallel lines Perpendicular Lines Plane Point Straight Angle Symmetric Two-Dimensional 1 Habits of Mind Persistence Striving for Accuracy Remaining Open to Continuous Learning Thinking/Communication with Clarity & Precision 2 Domain: Geometry Cluster: Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Common Core Standard: 4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. What does this mean? This standard asks students to draw two-dimensional geometric objects 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. Math Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Essential Question: How does geometry better describe objects? How do geometric shapes help with problem solving? How are angles categorized? How are shapes categorized by their angles? Learning Targets (KUD) K: vocabulary associated with lines and angles; U: criteria for categorizing lines and angles D: use measurements to categorize lines and angles, draw Criteria for Success for Mastery Students should be able to: Identify (by name) points, lines, line segments, rays, angles 3 examples of a point, line, line segment, ray, right angle, acute angle, obtuse angle, perpendicular lines, and parallel lines; use pictures to explain lines and angles I can: draw an example of a point, line, line segment, ray, right angle, acute angle, obtuse angle, perpendicular lines, and parallel lines. look for and identify the following in a given twodimensional figure: point, line, line segment, ray, right angle, acute angle, obtuse angle, perpendicular lines, and parallel lines. use pictorial representations to explain lines and angles. (acute, right, and obtuse), parallel lines, and perpendicular lines within diagrams and two-dimensional figures. Draw points, lines, line segments, rays, angles, and perpendicular and parallel lines in two-dimensional figures. Examples Right angle Segment Acute angle Line Obtuse angle Ray Straight angle Parallel Lines Perpendicular Lines 4 Textbook Resources Houghton Mifflin Harcourt Unit 6 Chapter 12: Motion Geometry 378A-378B. 378-381 Math Expression: 215J, 220-224, 226-238, 437J, 438-446, 456-457, 461-463, 774 Houghton Mifflin (Turtle) Chapter 16, Lesson 1, 2, 4, 5-404-409, 412-417,; Chapter 17, Lesson 4-440-443 Supplemental Resources STAMS Math Madness Buckle Down Houghton Mifflin Math Chapter Challenges North Carolina Mathematics Coach Math Intensive Intervention (Houghton Mifflin) Houghton Mifflin Harcourt Strategic Intervention Houghton Mifflin Harcourt Assessment Guide Houghton Mifflin Harcourt Problem Solving Practice Book Houghton Mifflin Harcourt Resource Book Media Resources Geometry by John Burstein Sir Cumference and the Great Knight of Angleland : A Math Adventure by Cindy Neuschwander What's your angle, Pythagoras? : A Math Adventure by Julie Ellis Web Resources http://www.math-drills.com http://www.brainpop.com/ 5 Domain: Geometry Cluster: Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Common Core Standard: 4.G.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. What does this mean? Two-dimensional figures may be classified using different characteristics such as, parallel or perpendicular lines or by angle measurement. Math Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Essential Question: How does geometry better describe objects? What characteristics can be used to categorize two-dimensional shapes? What primary characteristic identifies a right triangle? Learning Targets (KUD) K: vocabulary associated with lines and angles U: criteria for categorizing lines, angles, right triangles, and Criteria for Success for Mastery Students should be able to: 6 two-dimensional shapes; the use of a protractor when classifying shapes by their attributes D: use 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; identify right triangles I can: classify two-dimensional shapes into the following categories: those with parallel lines, those with perpendicular lines, those with both parallel and perpendicular lines, those with no parallel or perpendicular lines. classify two-dimensional shapes into categories based on the presence or absence of acute, obtuse, or right angles. identify a right triangle. recognize right triangles. determine attributes of specific shapes using a protractor. Classify shapes by attributes such as presence of right angles, parallel and perpendicular line segments, number of sides, and congruency. Identify and classify triangles based on properties such as angles and side lengths. 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. Examples Which figure in the Venn diagram below is in the wrong place? Explain how you know. at least one set of parallel sides A at least one right angle B 7 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. Textbook Resources Houghton Mifflin Harcourt Unit 6 Chapter 12: Motion Geometry 378A-378B. 378-381 Math Expression: 215J, 220-224, 226-238, 437J, 438-446, 456-457, 461-463, 774 Houghton Mifflin (Turtle) Chapter 16, Lesson 1, 2, 4, 5-404-409, 412-417,; Chapter 17, Lesson 4-440-443 Supplemental Resources STAMS Math Madness Buckle Down Houghton Mifflin Math Chapter Challenges North Carolina Mathematics Coach Math Intensive Intervention (Houghton Mifflin) Houghton Mifflin Harcourt Strategic Intervention Houghton Mifflin Harcourt Assessment Guide Houghton Mifflin Harcourt Problem Solving Practice Book Houghton Mifflin Harcourt Resource Book Media Resources Geometry by John Burstein Sir Cumference and the Great Knight of Angleland : A Math Adventure by Cindy Neuschwander What's your angle, Pythagoras? : A Math Adventure by Julie Ellis Web Resources http://www.math-drills.com 8 http://www.brainpop.com/ TEACHER NOTE: In the U.S., the term “trapezoid” may have two different meanings. Research identifies these as inclusive and exclusive definitions. The inclusive definition states: A trapezoid is a quadrilateral with at least one pair of parallel sides. The exclusive definition states: A trapezoid is a quadrilateral with exactly one pair of parallel sides. With this definition, a parallelogram is not a trapezoid. North Carolina has adopted the exclusive definition. (Progressions for the CCSSM: Geometry, The Common Core Standards Writing Team, June 2012.) Domain: Geometry Cluster: Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Common Core Standard: 4.G.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 the line-symmetric figures and draw lines of symmetry. What does this mean? Students need experiences with figures which are symmetrical and non-symmetrical. Figures include both regular and non-regular polygons. Folding cut-out figures will help students determine whether a figure has one or more lines of symmetry. **This standard only includes line symmetry not rotational symmetry. Math Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Essential Question: How does geometry better describe objects? 9 How can lines of symmetry be drawn for two-dimensional figures? How can you identify examples and non-examples of lines of symmetry in two-dimensional figures? Learning Targets (KUD) K: vocabulary associated with lines and angles U: criteria for categorizing lines, angles, right triangles, and two-dimensional shapes D: find lines of symmetry using symmetrical and nonsymmetrical figures; determine whether a figure has one or more lines of symmetry; explore lines of symmetry using cutout figures I can: find lines of symmetry using cut-out figures. define line symmetry. draw lines of symmetry in two-dimensional figures. identify examples and non-examples of line symmetry in two-dimensional figures. Criteria for Success for Mastery Students should be able to: Define line symmetry. Identify examples and non-examples of line symmetry in twodimensional figures. Draw lines of symmetry in two-dimensional figures. Examples 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 have lines of symmetry that go from a midpoint of a side through a vertex. Textbook Resources 10 Houghton Mifflin Harcourt Unit 6 Chapter 12: Motion Geometry 378A-378B. 378-381 Math Expression: 215J, 220-224, 226-238, 437J, 438-446, 456-457, 461-463, 774 Houghton Mifflin (Turtle) Chapter 16, Lesson 1, 2, 4, 5-404-409, 412-417,; Chapter 17, Lesson 4-440-443 Supplemental Resources STAMS Math Madness Buckle Down Houghton Mifflin Math Chapter Challenges North Carolina Mathematics Coach Math Intensive Intervention (Houghton Mifflin) Houghton Mifflin Harcourt Strategic Intervention Houghton Mifflin Harcourt Assessment Guide Houghton Mifflin Harcourt Problem Solving Practice Book Houghton Mifflin Harcourt Resource Book Media Resources Geometry by John Burstein Sir Cumference and the Great Knight of Angleland : A Math Adventure by Cindy Neuschwander What's your angle, Pythagoras? : A Math Adventure by Julie Ellis Web Resources http://www.math-drills.com http://www.brainpop.com/ 11 Domain: Measurement and Data Cluster: Geometric measurement: Understand concepts of angle and measure angles Common Core Standards: 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 “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. 4.MD.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. 4.MD.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. 12 Key Vocabulary Degrees Protractor Acute angle Obtuse angle Right angle Straight angle Center Radius Diameter Chord Ray End point Intersect One degree angle Vertex Angle Parallel lines Intersecting lines Perpendicular lines Measure Point Decompose Circle Habits of Mind Persistence Striving for Accuracy Thinking Flexibly Remaining Open to Continuous Learning Thinking/Communication with Clarity & Precision Questioning and Posing Problems 13 Domain: Measurement and Data Cluster: Geometric measurement: Understand concepts of angle and measure angles Common Core 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 “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. What does this mean? 5a Use a circle to measure angles and determine that an angle measurement is not related to an area. An angle is the union of two rays, a and b, with the same initial point P. 5b Determine that the number of times you turn one degree is the measure of the angle. This standard calls for students to explore an angle as a series of “one-degree turns.” Math Practices: 14 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Essential Question: How do you determine an angle measurement in reference to a circle? How is the measurement of an angle related to the area of a circle? How are one-degree angles used to measure the total angle measurement? Why does “what” we measure influence “how” we measure? Why display data in different ways? Learning Targets (KUD) K: vocabulary associated with geometric measurement and data U: how to use appropriate tools for measurement D: use a circle to measure angles and determine that the angle measurement is not related to an area I can: identify the parts of an angle. explain that an angle is measured in degrees related to the 360 degrees in a circle. demonstrate how to measure angles using a circle. demonstrate that a 1/360 is a one degree angle. determine angle measurements in reference to a circle by using given angle measurements. determine that three 30-degree angles make a 90-degree Criteria for Success for Mastery Students should be able to: Demonstrate how to measure angles using a circle (right, acute, and obtuse). Demonstrate that a 1/360 is a one degree angle. (A 30 degree angle is 30/360 degree angle which simplified is 1/12 of the circle. o Example: Create small groups of students and give each group a 30, 45, and 90 degree angle. Give students a variety of sizes of circles. Have students place one angle over two different sizes of circles and discuss if the angle measurement changed or not. Have students practice this over and over again to determine that the angle measurement does not change no matter the size of the circle it is placed over. Demonstrate an understanding that 25 one degree angles 15 angle AND two 45-degree angles make a 90-degree angle AND two 90-degree angles make 180 degrees which is a straight angle. determine that a circle has 360 degrees. demonstrate an understanding that 25 one-degree angles measures the same as a 25-degree angle. measures the same as a 25 degree angle. Examples a. 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. b. A water sprinkler rotates one-degree at each interval. If the sprinkler rotates a total of 100º, how many one-degree turns has the sprinkler made? Textbook Resources Math Expression: 226, 229,438-446, 437K Houghton Mifflin (Turtle) Chapter 16, Lesson 16.3 and Lesson 16.7—410-411, 422-425 Supplemental Resources STAMS Math Madness Buckle Down Houghton Mifflin Math Chapter Challenges North Carolina Mathematics Coach Math Intensive Intervention (Houghton Mifflin) Houghton Mifflin Harcourt Strategic Intervention Houghton Mifflin Harcourt Assessment Guide 16 Houghton Mifflin Harcourt Problem Solving Practice Book Houghton Mifflin Harcourt Resource Book Media Resources Geometry by John Burstein Sir Cumference and the Great Knight of Angleland : A Math Adventure by Cindy Neuschwander What's Your Angle, Pythagoras? : A Math Adventure by Julie Ellis Web Resources http://www.math-drills.com http://www.brainpop.com/ Domain: Measurement and Data Cluster: Geometric measurement: Understand concepts of angle and measure angles Common Core Standard: 4.MD.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. What does this mean? Use a protractor to measure and create angles. Math Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 17 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Essential Question: Why does “what” we measure influence “how” we measure? Why display data in different ways? How do you use a protractor to measure and create angles? Learning Targets (KUD) K: vocabulary associated with geometric measurement and data; measure of benchmark angles (45º, 90º, 180º) U: how to use appropriate tools for measurement D: use a protractor to measure angles; create pictorial representations of benchmark angles Criteria for Success for Mastery Students should be able to: I can: understand how to use a protractor and measure a given angle in whole-number degrees. determine that obtuse angles are greater than 90 degrees. determine that acute angles are less than 90 degrees. determine that right angles are 90 degrees. determine that a straight angle is 180 degrees. create pictorial representations of angles. sketch angles with a given measurement. Measure given angles using a protractor. Create obtuse angles and give the angle measurement using a protractor. Create acute angles and give the angle measurement using a protractor. Create right angles and give the angle measurement using a protractor. Create straight angles and give the angle measurement using a protractor. Examples Students should measure angles and sketch angles 18 120 degrees 135 degrees As with all measurable 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 come to associate all slanted lines with 45º measures and horizontal and vertical lines with measures of 90º. Textbook Resources Math Expression: 226, 229,438-446, 437K Houghton Mifflin (Turtle) Chapter 16, Lesson 16.3 and Lesson 16.7—410-411, 422-425 Supplemental Resources STAMS Math Madness Buckle Down Houghton Mifflin Math Chapter Challenges North Carolina Mathematics Coach Math Intensive Intervention (Houghton Mifflin) 19 Houghton Mifflin Harcourt Strategic Intervention Houghton Mifflin Harcourt Assessment Guide Houghton Mifflin Harcourt Problem Solving Practice Book Houghton Mifflin Harcourt Resource Book Media Resources Geometry by John Burstein Sir Cumference and the Great Knight of Angleland : A Math Adventure by Cindy Neuschwander What's Your Angle, Pythagoras? : A Math Adventure by Julie Ellis Web Resources http://www.math-drills.com http://www.brainpop.com/ Domain: Measurement and Data Cluster: Geometric measurement: Understand concepts of angle and measure angles Common Core Standard: 4.MD.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. What does this mean? This standard addresses the idea of decomposing (breaking apart) an angle into smaller parts. Use angle measurements to solve word problems. 20 Math Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Essential Question: Why does “what” we measure influence “how” we measure? Why display data in different ways? How do you solve multi-step word problems using measurement? How do you decompose a specific benchmark angle? Learning Targets (KUD) K: vocabulary associated with geometric measurement and data; measure of benchmark angles (45º, 90º, 180º) U: how to use appropriate tools for measurement D: solve word problems involving unknown angles; use addition and subtraction to solve for missing angle measurements I can: determine how to break apart or decompose an angle. explain that the angle measurement of a larger angle is the sum of the angle measures of its decomposed parts. write an equation with an unknown angle measurement. use addition and subtraction to solve for the missing angle Criteria for Success for Mastery Students should be able to: Demonstrate how to solve addition and subtraction problems using angles and decompose those angles. Demonstrate how to solve addition and subtraction problems using angles, a variable, and an equation and decompose those angles. o Example: A 10 degree angle is made up of 10 one degree angles. o Example: You have a pie that half of the pie has been eaten. You have three pieces of the pie left. One piece of the pie shows a 30 degree angle. How many one degree angles make up that 30 degree angle? You have another 21 measurements. piece that shows a 90 degree angle. How many one solve word problems involving unknown angles. degree angles make up that 90 degree angle? Use the measurements of the given pieces of pie to determine the other piece of pie. (30+90=120, THEN 180-120=60) Examples 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 25 degree cycles will it go through for the rotation to reach at least 90 degrees? Textbook Resources Math Expression: 226, 229,438-446, 437K Houghton Mifflin (Turtle) Chapter 16, Lesson 16.3 and Lesson 16.7—410-411, 422-425 Supplemental Resources STAMS Math Madness Buckle Down Houghton Mifflin Math Chapter Challenges North Carolina Mathematics Coach Math Intensive Intervention (Houghton Mifflin) 22 Houghton Mifflin Harcourt Strategic Intervention Houghton Mifflin Harcourt Assessment Guide Houghton Mifflin Harcourt Problem Solving Practice Book Houghton Mifflin Harcourt Resource Book Media Resources Geometry by John Burstein Sir Cumference and the Great Knight of Angleland : A Math Adventure by Cindy Neuschwander What's Your Angle, Pythagoras? : A Math Adventure by Julie Ellis Web Resources http://www.math-drills.com http://www.brainpop.com/ 23