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Grade 4 Math Unit 5 Title Suggested Time Frame th 5 and 6 Six Weeks Suggested Duration: 30 days Guiding Questions Unit 5 – Geometry Big Ideas/Enduring Understandings • • th Relationships between geometric figures can be described and compared. Geometric figures can be described, compared, and transformed using symmetry and congruence. • • • • • • What angles are formed by each set of lines? Can lines be both intersecting and perpendicular? How do you differentiate between angles? How do you differentiate between transformations? How can you determine if a figure has symmetry? What are the attributes of a two-dimensional or three-dimensional shape? Vertical Alignment *TEKS one level below* *TEKS one level below* th TEA MATH VERTICAL ALIGNMENT—K-6 Grade Sample Assessment Question Coming soon! CISD Math Grade 4-Unit 5 Updated May18, 2015 The resources included here provide teaching examples and/or meaningful learning experiences to address the District Curriculum. In order to address the TEKS to the proper depth and complexity, teachers are encouraged to use resources to the degree that they are congruent with the TEKS and research-based best practices. Teaching using only the suggested resources does not guarantee student mastery of all standards. Teachers must use professional judgment to select among these and/or other resources to teach the district curriculum. Some resources are protected by copyright. A username and password is required to view the copyrighted material. District Specificity/Examples TEKS clarifying examples are a product of the Austin Area Math Supervisors TEKS Clarifying Documents. Ongoing TEKS 4.01 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (A) apply mathematics to problems arising in everyday life, society, and the workplace; • Focus is on application • Students should assess which tool to apply rather than trying only one or all • Students should evaluate the effectiveness of representations to ensure they are communicating mathematical ideas clearly Students are expected to use appropriate mathematical vocabulary and phrasing when communicating ideas Students are expected to form conjectures based on patterns or sets of examples and non-examples (B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution; (C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems; (D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate; (E) create and use representations to organize, record, and communicate mathematical ideas; • (F) analyze mathematical relationships to connect and communicate mathematical ideas; and • (G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication • CISD Math Grade 4-Unit 5 Updated May18, 2015 Precise mathematical language is expected. Knowledge and Skills with Student Expectations District Specificity/ Examples Vocabulary Resources Resources listed and categorized to indicate suggested uses. Any additional resources must be aligned with the TEKS. GEOMETRY---15 days MAT.4.06 Geometry and measurement. The student applies mathematical process standards to analyze geometric attributes in order to develop generalizations about their properties. The student is expected to: (A) Identify points, lines, line segments, rays, angles, and perpendicular and parallel lines Supporting vocabulary – straight angle 4.06A 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. • • • • • • • • • • • • • • • • • • **Visual Representations…next page. • • CISD Math Grade 4-Unit 5 Updated May18, 2015 Angles Geometric attributes Lines Line segments Parallel line Perpendicular line Points Rays Congruent Lines of symmetry Symmetry Two-dimensional Acute angles Obtuse angles Right angles Attributes Polygons Rhombus, parallelogram, trapezoid, rectangle, square, quadrilateral Sides Vertex (vertices) HMH GoMath Module 13 Region 11 Livebinder http://illuminations .nctm.org/ (B) Identify and draw one or more lines of symmetry, if they exist, for a twodimensional figure CISD Math Grade 4-Unit 5 Updated May18, 2015 4.06B Students need experiences with figures which are symmetrical and on-symmetrical. Figures include both regular and on-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. (C) Apply knowledge of right angles to identify acute, right, and obtuse triangles; 4.06C Given a set of different triangles, students measure the angles (using a protractor or geometry exploration software) and classify triangles according to their properties. Students organize their data in a table and analyze patterns to match triangles with the most appropriate name. Right triangles can be a category for classification. A right triangle has one right angle. There are different types of right triangles. An isosceles right triangle has two or more congruent sides and a scalene right triangles has no congruent sides. (D) Classify two-dimensional 4.06D figures based on the Two-dimensional figures may be classified using different characteristics such as, parallel or perpendicular or by angle presence or absence of measurement. parallel or perpendicular lines or the presence or Parallel or Perpendicular Lines: absence of angles of a Students should become familiar with the concept of parallel and perpendicular lines. Two lines are parallel if they never intersect specified size and are always equidistant. Two lines are perpendicular if they intersect in right angles. CISD Math Grade 4-Unit 5 Updated May18, 2015 CISD Math Grade 4-Unit 5 Updated May18, 2015 MAT.4.07 Geometry and measurement. The student applies mathematical process standards to solve problems involving angles less than or equal to 180 degrees. The student is expected to: (A) Illustrate the measure of an angle as the part of a circle whose center is at the vertex of the angle that is "cut out" by the rays of the angle. Angle measures are limited to whole numbers CISD Math Grade 4-Unit 5 Updated May18, 2015 4.07A o Grade 4 introduces illustrating the measure of an angle as the part of a circle whose center is at the vertex of the angle that is "cut out" by the rays of the angle. Angle measures are limited to whole numbers. Before students begin measuring angles with protractors, they need to have some experiences with benchmark angles. They transfer their understanding that a rotation about a point makes a complete circle to recognize and sketch angles that measure approximately and . They extend this understanding and recognize and sketch angles that measure approximately and . They use appropriate terminology (acute, right and • • • • • • • • • • • • • • • • Center Measure of an angle Part of a circle Rays Vertex of an angle Angle Angle vertex Degrees 1/360 of a circle One degree Center mark Inner scale Line Outer scale Protractor Zero adge HMH GoMath Module 14 Region 11 Livebinder http://illuminations .nctm.org/ obtuse) to describe angles and rays (perpendicular). • This standard brings up a connection between angles and circular • measurement (360 degrees). 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. (B) Illustrate degrees as the units used to measure an angle, where 1/360 of any circle is one degree and an angle that "cuts" n/360 out of any circle whose center is at the angle's vertex has a measure of n degrees. Angle measures are limited to whole numbers 4.07B o Grade 4 introduces illustrating degrees as the units used to measure an angle, where of any circle is one degree and an angle that "cuts" out of any circle whose center is at the angle's vertex has a measure of n degrees. Angle measures are limited to whole numbers. 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 “one-degree angle,” and degrees are the unit used to measure angles in elementary school. A full rotation is thus 360 degrees. Two angles are called 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 (ie share a side) are called adjacent angles. These terms may come up in classroom discussion. This concept is developed thoroughly in middle school. CISD Math Grade 4-Unit 5 Updated May18, 2015 Adjacent angles Non-overlapping Like length, area and volume, angle measure is additive. The sum of 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 , thus they are complementary. Two adjacent angles that compose a “straight angle” of 180 must be supplementary. (Source: Kaufman ISD Clarifying Docs) CISD Math Grade 4-Unit 5 Updated May18, 2015 (C) Determine the approximate measures of angles in degrees to the nearest whole number using a protractor (D) Draw an angle with a given measure CISD Math Grade 4-Unit 5 Updated May18, 2015 4.07C & 4.07D • Grade 4 introduces determining the approximate measures of angles in degrees to the nearest whole number using a protractor. (E) Determine the measure of an unknown angle formed by two nonoverlapping adjacent angles given one or both angle measures REVIEW – 15 days CISD Math Grade 4-Unit 5 Updated May18, 2015 4.07E