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Mathematics Pacing Resource Document 4.G.4 Standard: 4.G.4: Identify, describe, and draw rays, angles (right, acute, obtuse), and perpendicular and parallel lines using appropriate tools (e.g., ruler, straightedge and technology). Identify these in two-dimensional figures. Teacher Background Information: 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. Examples of points, line segments, lines, angles, parallelism, and perpendicularity can be seen daily. Students may not easily identify lines and rays because they are more abstract. Student should be able to use side length to classify triangles as equilateral, equiangular, isosceles, or scalene; and can use angle size to classify them as acute, right, or obtuse. They then learn to cross-classify, for example, naming a shape as a right isosceles triangle. Thus, students develop explicit awareness of and vocabulary for many concepts they have been developing, including points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Such mathematical terms are useful in communicating geometric ideas, but more important is that constructing examples of these concepts, such as drawing angles and triangles that are acute, obtuse, and right, help students form richer concept images connected to verbal definitions. That is, students have more complete and accurate mental images and associated vocabulary for geometric ideas (e.g., they understand that angles can be larger than 90 and their concept images for angles include many images of such obtuse angles). Similarly, students see points and lines as abstract objects: Lines are infinite in extent and points have location but no dimension. Grids are made of points and lines and do not end at the edge of the paper. Students also learn to apply these concepts in varied contexts. For example, they learn to represent angles that occur in various contexts as two rays, explicitly including the reference line, e.g., a horizontal or vertical line when considering slope or a “line of sight” in turn contexts. They understand the size of the angle as a rotation of a ray on the reference line to a line depicting slope or as the “line of sight” in computer environments. Analyzing the shapes in order to construct them requires students to explicitly formulate their ideas about the shapes. For instance, what series of commands would produce a square? How many degrees are the angles? What is the measure of the resulting angle? What would be the commands for an equilateral triangle? How many degrees are the angles? What is the measure of the resulting angle? Such experiences help students connect what are often initially isolated ideas about the concept of angle. (Progressions for the CCSSM, Geometry, CCSS Writing Team, June 2012, page 14) Indianapolis Public Schools Curriculum and Instruction Mathematics Pacing Resource Document 4.G.4 Standard: 4.G.4: Identify, describe, and draw rays, angles (right, acute, obtuse), and perpendicular and parallel lines using appropriate tools (e.g., ruler, straightedge and technology). Identify these in two-dimensional figures. Teacher Background Information: Example: 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. Example: How many acute, obtuse and right angles are in this shape? 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. Indianapolis Public Schools Curriculum and Instruction Mathematics Pacing Resource Document 4.G.4 Standard: 4.G.4: Identify, describe, and draw rays, angles (right, acute, obtuse), and perpendicular and parallel lines using appropriate tools (e.g., ruler, straightedge and technology). Identify these in two-dimensional figures. Lesson Plans/Print Activities: Web-based Practice: Math Expressions o o http://www.aplusmath.com/cgi-bin/games/geopicture A+ Math Hidden Picture http://www.aplusmath.com/cgi-bin/flashcards/geoflash A+ Math Geometry Flash Cards http://quizlet.com/15453601/parallel-and-perpendicular-lines-vocab-flashcards/ Flash Cards https://cccmedia.ips.k12.in.us/NDM/ Smart Math: parallel & perpendicular lines (Search: parallel lines and perpendicular lines U2 Lesson 2 U4 Lesson 1 https://www.engageny.org/resource/grade-4-mathematicsmodule-4-topic-lesson-1 Identify and draw points, lines, line segments, rays, and angles and recognize them in various contexts and familiar figures. https://www.engageny.org/resource/grade-4-mathematicsmodule-4-topic-lesson-2 Use right angles to determine whether angles are equal to, greater than, or less than right angles. Draw right, obtuse, and acute angles. https://www.engageny.org/resource/grade-4-mathematicsmodule-4-topic-lesson-3 Identify, define, and draw perpendicular lines. http://www.mangahigh.com/en_us/maths_games/shape/understanding_prop erties_of_shape/recognise_perpendicular_and_parallel_lines Recognize parallel and perpendicular lines https://www.engageny.org/resource/grade-4-mathematicsmodule-4-topic-lesson-4 Identify, define, and draw parallel lines. https://learnzillion.com/lessonsets/757 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. https://learnzillion.com/lesson_plans/474 Identify geometric attributes in two-dimensional figures by examining their characteristics. https://learnzillion.com/lessonsets/381 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. https://learnzillion.com/lesson_plans/1064 Draw and identify angles by comparing them to known right angles. Indianapolis Public Schools Curriculum and Instruction Mathematics Pacing Resource Document https://learnzillion.com/lesson_plans/471 Identify and draw parallel and perpendicular line segments by examining their characteristics. http://www.edhelper.com/math/geometry3.htm Edhelper activity sheet http://www.onlinemathlearning.com/pairs-of-lines.html May be projected for whole or small group instruction http://illuminations.nctm.org/Lesson.aspx?id=665 Polygon Capture http://bridges1.mathlearningcenter.org/media/Bridges_Gr4_O nlineSupplement/B4SUP-C1_GeomParallel_0409.pdf Bridges to Mathematics lesson Indianapolis Public Schools Curriculum and Instruction Mathematics Pacing Resource Document 4.G.4 (Readiness Form I) Indianapolis Public Schools Curriculum and Instruction Mathematics Pacing Resource Document 4.G.4 (Readiness Form II) Indianapolis Public Schools Curriculum and Instruction Mathematics Pacing Resource Document 4.G.4 Look at angle BAN. Is BAN a right, acute, or obtuse angle? ___________________________________ Add segment BK that is perpendicular to segment BA. Explain how you know that segment BK is perpendicular to segment BA. _________________________________________________________________________________________________ _________________________________________________________________________________________________ _________________________________________________________________________________________________ [Howard County Public Schools, Maryland] Indianapolis Public Schools Curriculum and Instruction Mathematics Pacing Resource Document 4.G.4 Look at the following pictures. Find examples of: Points Line segments Rays Angles Parallel lines (segments) Perpendicular lines (segments) Indianapolis Public Schools Curriculum and Instruction Mathematics Pacing Resource Document 4.G.4 Which figures below show pairs of lines that appear to be parallel? A. Figure 1 only B. Figure 3 only C. Figure 1 and figure 2 D. Figure 2 and figure 3 Indianapolis Public Schools Curriculum and Instruction Mathematics Pacing Resource Document 4.G.4 Which shapes contain parallel lines? Indianapolis Public Schools Curriculum and Instruction Mathematics Pacing Resource Document 4.G.4 The map below shows four highways that connect five towns. Each town is labeled by a point on the map. What are the labels for the five towns? Which roads are line segments? Which roads are rays? Which roads are lines? Name two pairs of perpendicular roads. Name two pairs of parallel roads. Indianapolis Public Schools Curriculum and Instruction Mathematics Pacing Resource Document 4.G.4 The map below shows three towns (A, B, and C). 1) Draw three roads that connect the 3 towns. The roads should include 1 line, 1 line segment, and 1 ray. 2) Make a town D so that the road between A and D is perpendicular to the road between C and D. 3) Make 2 more towns (E and F) and connect the towns with 1 line and 1 ray. One of the roads should be parallel to another road that you already have. 4) If you were in charge of the road system, and wanted to leave open the possibility of building more towns in the future, should most of your roads be line segments, lines, or rays? Indianapolis Public Schools Curriculum and Instruction Mathematics Pacing Resource Document 4.G.4 Letters can be thought of as geometric figures. a) How many line segments are needed to make the letter A? How many angles are there? Are they acute, obtuse, or right angles? Are any of the line segments perpendicular? Are any of the line segments parallel? b) We can build all of these letters from line segments and arcs of circles. Build all of the capital letters with the smallest number of "pieces," where each piece is either a line segment or an arc of a circle. c) Which letters have perpendicular line segments? d) Which letters have parallel line segments? e) Which letters have no line segments? f) Do any letters contain both parallel and perpendicular lines? g) What makes the lower case letters "i" and "j" different than all of the capital letters? Indianapolis Public Schools Curriculum and Instruction Mathematics Pacing Resource Document 4.G.4 The students in Ms. Sun's class were drawing geometric figures. First she asked them to draw some points, and then she asked them to draw all the line segments they could that join two of their points. Joni drew 4 points and then drew 4 line segments between them: Are there other line segments that Joni could have drawn? Tony drew 3 points and then drew 3 line segments between them: Are there other line segments that Tony could have drawn? Here are 5 points. Draw all the line segments you can connecting pairs of them. Starting with just two points, how many line segments can you draw between them? Tony decided that he could actually draw two line segments between two points, and maybe even more. This is what he drew: What do you think of Tony's idea? Discuss it with a partner. Indianapolis Public Schools Curriculum and Instruction