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Grade 6 – Math –3rd Nine Weeks Standard(s): Mathematical Processes & Geometry and Measurement GLE 0606.4.1 Understand and use basic properties of triangles, quadrilaterals, and other polygons. SPI 0606.4.1 Identify, define or describe geometric shapes given a visual representation or a written description of its properties. 0606.4.3 Verify the basic properties of triangles and quadrilaterals using a protractor and ruler. 0606.4.4 Classify triangles by side lengths (scalene, isosceles, and equilateral) and angle measure (acute, right, obtuse, isosceles and equiangular). 0606.1.10 Use various methods (such as dynamic geometry software) to explore properties of triangles and quadrilaterals. SPI 0606.4.2 Find a missing angle measure in problems involving interior/exterior angles and/or their sums. 0606.4.1 Investigate the sum of the angles in a triangle and a quadrilateral using various methods. 0606.4.2 Relate the sum of the angles in a triangle to the sum of the angles in polygons. 0606.4.6 Use the properties of interior and exterior angles of polygons to solve problems. SPI 0606.4.3 Solve problems using the Triangle Inequality Theorem. 0606.4.5 Model and use the Triangle Inequality Theorem. Activities/Strategies “Which nets form a cube” interactive site: “Net Tools”: Illuminations http://illuminations.nctm.org/activitydetail.aspx?ID=84 Navigating through Geometry Grades 6-8 “Indirect Measurement” “In Your Shadow” Indirect Measurement Activity Lesson from http://illuminations.nctm.org/LessonDetail.aspx?ID=L515 Literature: “Measuring Penny” (Standard and nonstandard measurement) Navigating Through Geometry Grades 6-8 Patty Paper “Area Activity” Deriving Area Formulas for Trapezoids, parallelograms, triangles, and circles. Online Area of a Triangle Practice http://www.mathgoodies.com/lessons/vol1/area_triangle.html Triangle Inequality Activities and Lesson Ideas http://www.deltastate.edu/docs/math/lp3lclark.pdf http://mathscience.dadeschools.net/geo/pdf/lessons/Triangle_Inequal ity.pdf Literature: “Grandfather Tang’s Story” (polygons, tangrams, area) Literature: “The Warlords Puzzle” (Tangrams- Marilyn Burns Math and Literature grades 4-6 Literature: “The Greedy Triangle” (polygons) SpringBoard: “Play Area” (Geometry) SpringBoard: “What’s My Name” (Geometry, figures, angles, lines) SpringBoard: “Triangle Trivia” (classification of triangles) OCS: Sum of Interior & Exterior Angles of Polygons http://regentsprep.org/Regents/math/mathtopic.cfm?TopicCode=poly IC Teachers: Shapes - Polygons http://icteachers.co.uk/children/sats/polygons.htm Literature: “Shape Up!” By David Adler Literature: “What’s your Angle Pythagoras? :A math adventure” by Julie Ellis. Have students draw their own line diagrams including the notation. Resources Chapter 7 Sec 1 pg 322 Chapter 7 Sec 2 pg 326 Chapter 7 Sec 3 pg 332 Chapter 7 Sec 4 pg 336 Chapter 7 Sec 5 pg 344 Chapter 7 Sec 6 pg 348 Chapter 7 Sec 7 pg 352 SuperSource Cuisenaire Rods and Resource book SuperSource Tangram and Resource book About Teaching Mathematics by Marilyn Burns Teaching Student-Centered Mathematics Grades 5-8 by John A. Van de Walle See PortaPortal resources Grade 6 – Math –3rd Nine Weeks 0606.4.2 Use the concepts of translation, rotation, reflection, and symmetry to understand congruence in the plane. 0606.4.7 Work with transformations in a plane and explore their meanings through drawings and manipulatives. 0606.4.8 Understand scaling, dilation and their relation to similarity. 0606.4.9 Analyze the differences between congruence and similarity. 0606.4.10 Describe the effect of a transformation on a 2-dimensional figure and the resulting symmetry. 0606.4.3 Develop and use formulas to determine the circumference and area of circles, and the area of trapezoids, and develop strategies to find the area of composite shapes. SPI 0606.4.4 Calculate with circumferences and areas of circles. 0606.4.11 Relate the circumference of a circle with the perimeter of a polygonal figure. 0606.4.12 Derive the meaning of Pi using concrete models and/or appropriate technology. 0606.4.13 Understand the relationships among the radius, diameter, circumference and area of a circle, and that the ratio of the circumference to the diameter is the same as the ratio of the area to the square of the radius, and that this ratio is called Pi. 0606.4.14 Relate the area of a trapezoid to the area of a parallelogram. Origami fold Activities Alphabet Transformations with Virtual Practice http://www.misterteacher.com/abc.html Literature: “A Cloak for the Dreamer” (Properties of Shapes, tessellations) SpringBoard: “The Dot Game” (Area and Perimeter) InterMath: Angle of Rotation http://intermath.coe.uga.edu/dictnary/descript.asp?termID=35 PBS Kids-Cyberchase: Vortex http://pbskids.org/cyberchase/games/timelapse/timelapse.html Regents Prep: Working with Reflections http://regentsprep.org/Regents/math/coreflec/Prac1.htm Chapter 7 Sec 9 pg 362 Chapter 7 Sec 10 pg 365 Chapter 7 Sec 11 pg 369 Chapter 12 Sec 3 pg 610 Chapter 12 Sec 4 pg 613 Chapter 12 Sec 5 pg 616 Area of a circle with Wikki Stix Activity Literature: “Sir Cumference and the Dragon of Pi” SERIES books Literature: “ Spaghetti and Meatballs for All” (Area & perimeter) http://www.baylor.edu/content/services/document.php/27178.ppt Circumference of A Circle http://www.aaamath.com/geo612-circumference-circle.html#pgtp NCTM: Circle String - Circumference http://illuminations.nctm.org/ActivityDetail.aspx?ID=115 Chapter 10 Sec 1 pg 500 Chapter 10 Sec 2 pg 504 Chapter 10 Sec 3 pg 508 Chapter 10 Sec 4 pg 511 Chapter 10 Sec 5 pg 516 SuperSource Geoboards Grade 6 – Math –3rd Nine Weeks 0606.4.4 Develop and use formulas for surface area and volume of 3-dimensional figures. SPI 0606.4.5 Determine the surface area and volume of prisms, pyramids and cylinders. SPI 0606.4.6 Given the volume of a cone/pyramid, find the volume of the related cylinder/prism or vice versa. 0606.3.4 Generate data and graph relationships concerning measurement of length, area, volume, weight, time, temperature, money, and information. 0606.4.15 Find lengths given areas or volumes, and vice versa. 0606.4.16 Solve contextual problems involving area and circumference of circles, surface areas and volumes of prisms, pyramids, cones, and cylinders. 0606.4.17 Use manipulatives to discover the volume of a pyramid is one-third the volume of the related prism (the heights and base areas are equal). 0606.4.18 Use manipulatives to discover the volume of a cone Navigating Through Geometry in Grades 6-8 “Constructing ThreeDimensional Figures” Navigating through Measurement in Grades 6-8 “Ratios –Surface Areas and Volumes” Hangman Puzzles on Nets and 3-D Figures http://www.compasslearningodyssey.com/sample_act/math3_4/MA3 CA05a-package_preloader.swf Literature: “Counting on Frank” (Proportional Reasoning, volume Marilyn Burns Math & Literature grades 4-6) Math Central: Irregular Surface Area Exercise http://mathcentral.uregina.ca/RR/database/RR.09.97/hermsmeier1.ht ml Compare Volumes of 3D Shapes http://www.analyzemath.com/Geometry/compare_volume_3D.html Chapter 10 Sec 6 pg 524 Chapter 10 Sec 7 pg 530 Chapter 10 Sec 8 pg 534 Chapter 10 Sec 9 pg 538 SuperSource Snap Cubes and resource book 3-D Solid Figures Suggested Integrated Activities Social Studies: Geography Link – Map making/line relationships (Math textbook pg 325) Social Studies Link – African Culture/geometric patterns (Math textbook pg 359) Social Studies Link – Map skills/estimating area (Math textbook pg 507) Social Studies Textbook Geography handbook pgs GH11-GH13 Science: Earth Science Link – Space exploration/algebraic expressions (Math textbook pg 55) Physical Science Link – Density & Mass/Volume (Math textbook pg 537) Science Textbook Appendix pg 483-489 Reading and Language: Focus on Problem-Solving “Solve” pg 343 Focus on Problem-Solving “Make a Plan” pg 361 Math Journals Chapter 7 pg 325 (diagrams), pg 329 (angles), pg 335 (angles), pg 339 (lines), pg 347 (triangles), pg 351 (quads), pg 355 (polygons), pg 359 (geometric patterns), pg 368 (transformations), pg 372 (symmetry) Write about It: last page of each lesson Focus on Problem-Solving “Solve” pg 521 Math Journals Chapter 10 pg 503 (polygons), 507 (area), 519 (compass), 527 (vertex), 533 (surface area), 537 (formulas), 541 (cylinders) Focus on Problem-Solving “Solve” pg 609 Math Journals Chapter 12 pg 601 (functions), pg 607 (functions), pg 619 (coordinate grids), pg 623 (grid)