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2016-2017 Mathematics Curriculum Map Grade 7, Q4 Unifying Concept: Comparing Populations and Geometry Quarter 4 Target Standards are emphasized every quarter and used in formal assessment to evaluate student mastery. Highly-Leveraged Standards1 - There are no Highly-Leveraged Target standards for this quarter. Additional Standards Complementary Standards: (Standards to be assessed in classroom and/or future benchmarks) Supporting Standards2 7.SP.B.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. 7.SP.B.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. 7.G.A.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. 7.G.A.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions* determine a unique triangle, more than one triangle, or no triangle. *Conditions may involve points, line segments, angles, parallelism, congruence, angles, and perpendicularity. 7.G.A.3 Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. 7.G.B.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. 7.G.B.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. 7.G.B.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Standards for Mathematical Practice: (quarterly focus) Mathematically proficient students: SMP 1. Make sense of problems and persevere in solving them. SMP 2. Reason abstractly and quantitatively. SMP 3. Construct viable arguments and critique the reasoning of others. SMP 4. Model with mathematics. SMP 5. Use appropriate tools strategically. SMP 7. Look for and make use of structure. Mathematical Practices Poster 6th – 12th Grade Literacy in History/Social Studies, Science, and Technical Subjects Focus Standards: (http://www.azed.gov/standardspractices/files/2015/04/accs-6-12-ela-contentliteracy-standards-final10_28_2013.pdf) 1 Highly-Leveraged Standards are the most essential for students to learn because they have endurance, leverage and essentiality. This definition for highly-leveraged standards was adapted from the website of Millis Public Schools, K-12, in Massachusetts, USA. http://www.millis.k12.ma.us/services/curriculum_assessment/brochures Specifically for mathematics, the Highly-Leveraged Standards are the Major Content/Clusters as defined by the AZCCRS Grade Level Focus documents. They should encompass a range of at least 65%-75% for Major Content/Clusters and a range of 25%-35% for Supporting Cluster Instruction. See the Grade Level Focus documents at: http://www.azed.gov/azccrs/files/2015/01/k-8-major-and-supporting-content-emphasis.pdf 2 Supporting Standards are related standards that support the highly-leveraged standards in and across grade levels. *Highly-Leveraged standards in bold and supporting standards are normal text. TUSD Department of Curriculum and Instruction Curriculum 3.0 Revised 5/18/2016 10:12 AM Page 1 2016-2017 Mathematics Curriculum Map Grade 7, Q4 Adopted and Supplemental Texts Eureka Math/ Engage NY: Module 5 Topic D Module 6 Holt: 7.SP.B.3 Holt: Mathematics Course 2 Must be supplemented for this standard 7.SP.B.4 Holt: Mathematics Course 2 Must be supplemented for this standard 7.G.A.1 Holt: Mathematics Course 2 Chapter 5 - Section 9 7.G.A.2 Holt: Mathematics Course 2 Must be supplemented for this standard 7.G.A.3 Holt: Mathematics Course 2 Chapter 10 Extension, page 612 7.G.B.4 Holt: Mathematics Course 2 Must be supplemented for this standard 7.G.B.5 Holt: Mathematics Course 2 8-3 Must be supplemented for this standard 7.G.B.6 Holt: Mathematics Course 2 Must be supplemented for this standard Additional Resources: https://www.illustrativemathematics.org/ www.insidemathematics.org https://learnzillion.com/ http://maccss.ncdpi.wikispaces.net/Middle+School http://www.pbslearningmedia.org/standards/1 http://nlvm.usu.edu/en/nav/vlibrary.html http://nymathstandards.pbworks.com/ http://www.geogebra.org/ http://map.mathshell.org/lessons.php TUSD Department of Curriculum and Instruction Big Ideas Curriculum 3.0 Essential Concepts: Measures of center and measures of variability are used to determine informal (generalizations) or formal (numerical) differences between two data sets with similar variability. (7.SP.B3-4) Scale drawings are proportional to actual objects and can be used to find actual measurements. (7.G.A.1) Given constraints for triangles will determine whether a unique triangle, more than one triangle, or no triangle can be constructed. (7.G.A.2) When you slice through a solid, you create a cross section that can be described as a two-dimensional figure. (7.G.A.3) Pi is derived by finding the ratio of the circumference to the diameter for any circle. (7.G.B.4) The circumference of a circle is 2r or d . (7.G.B.4) Using the fact that circumference of a circle is 2r ; the area formula of a circle can be derived to be r 2 . (7.G.B.4) Equations can be written and used to find the value of missing angles in multi-step problems involving complementary, supplementary, adjacent and vertical angles. (7.G.B.5) The volume of a prism is calculated by taking the area of the base times the height (V = B x h). (7.G.B.6) Surface area of prisms and pyramids is calculated by finding the sum of the area of each of its faces. (7.G.B.6) Essential Questions: What statistical processes help gain understanding about the relationship of two populations? (7.SP.B.3-4) What measure of center or measure of variability would you use to compare two data sets and why? ? (7.SP.B.3-4) How can you use a proportion to help determine the actual measurements of a scaled object? (7.G.A.1) How are scale drawings used in the real world? (7.G.A.1) How do you know if the conditions you have been given will produce one triangle, two triangles, or no triangle? (7.G.A.2) What shapes are created when planar cuts are made diagonally, perpendicularly, and parallel to the base in a rectangular prism or rectangular pyramid? (7.G.A.3) How do you derive the value of pi given any circle? (7.G.B.4) How do you derive the area formula for a circle from the formula for the circumference of a circle? (7.G.B.4) What is a real-world situation in which you use the area and/or Revised 5/18/2016 10:12 AM Page 2 2016-2017 Mathematics Curriculum Map Grade 7, Q4 Cutting shapes with a plane: http://intermath.coe.uga.edu/dictnary/descript.asp?termID=95 Cross sections: http://www.learner.org/courses/learningmath/geometry/session9/part_c/ index.html http://threeacts.mrmeyer.com https://www.tenmarks.com/signup circumference of a circle? (7.G.B.4) What are efficient strategies for finding an unknown angle in a figure? (7.G.B.5) What is a real-world situation in which you would need to calculate the volume and surface area of a three dimensional figure? (7.G.B.6) Vocabulary SP Vocab: data distribution lower extreme (minimum) lower quartile mean average deviation measures of center measures of variability similar variabilities standard deviation upper extreme (maximum) upper quartile variance variation/variability Additional Resource: http://www.graniteschools.org/mathvocabulary/ Geometry Vocab: adjacent angles perpendicular angle pairs pi (π) base plane sections circumference prism complementary angles pyramids congruent angles radius correspondence right rectangular prism corresponding angles right rectangular pyramids cylinder scale drawing diameter scale factor dimensions supplementary angles edge surface area face transversal inscribed unique triangle net vertex parallel vertical angles Interdisciplinary Connections Multicultural Math Connections: Literacy Connections: Articles: Reading: A Course in Multicultural Mathematics Integrating Mathematics of Worldwide Cultures into K-12 Teaching Mathematics through Multicultural Literature http://msms.ehe.osu.edu/2010/05/20/teaching-with-trade-books-math/ The Librarian Who Measured the Earth by: Kathryn Lasky Sir Cumference and the Dragon of Pi (A Math Adventure) by Cindy Neuschwander Sir Cumference and the Sword in the Cone by: Cindy Neuschwander Flatland: A Romance of Many Dimensions by: Edwin A. Abbott Mathematicians Are People, Too: Stories from the Lives of Great Mathematicians by: Luetta Reimer and Wilbert Reimer Mathematicians Are People, Too, Volume Two by: Luetta Reimer and Wilbert Reimer Math and Literature by Jennifer Bay-Williams and Sherri Martinie (pp. 42-46, 111-112, 65, 90-93) Books: (some titles available at LIRC) The Multicultural Math Classroom: Bringing in the World by Claudia Zaslavsky Math and Science Across Cultures: Activities and Investigations from the Exploratorium by Maurice Bazin Multicultural Mathematics: Interdisciplinary Cooperative-Learning Activities by Claudia Zaslavsky Multicultural Mathematics by Claudia Zaslavsky. Websites: TUSD Department of Curriculum and Instruction Curriculum 3.0 Revised 5/18/2016 10:12 AM Page 3 2016-2017 Mathematics Curriculum Map Grade 7, Q4 http://www.radicalmath.org/ http://www.nea.org/tools/lessons/47756.htm Writing: http://mathcomm.org/ (This site addresses diverse aspects of mathematical communication.) http://www.edutopia.org/blog/four-tips-writing-math-classroom-heatherwolpert-gawron http://mathsolutions.com/wpcontent/uploads/1995_Writing_in_Elem_Grades.pdf http://files.eric.ed.gov/fulltext/ED544239.pdf http://www-tc.pbs.org/teacherline/courses/rdla230/docs/session_1_burns.pdf Writing Prompts for Math http://writingfix.com/wac/numberfix.htm Writing in Math Class by Marilyn Burns Assessment Guides and Resources Performance Level Descriptors http://www.azed.gov/assessment/files/2015/12/math-pld-grade-7.pdf AZMERIT Resources: http://www.azed.gov/assessment/azmeritsupportmaterials/ Performance tasks: http://www.insidemathematics.org/performance-assessment-tasks Howard County- Assessment tasks by standard: https://hcpss.instructure.com/courses/127 Mathematics Assessment Project: http://map.mathshell.org/stds.php?standardid=1559 TUSD Department of Curriculum and Instruction Curriculum 3.0 Instructional Resources DOK Levels http://www.azed.gov/assessment/files/2014/11/dok-levels.pdf DOK Stems http://www.azed.gov/assessment/files/2014/11/dok-question-stems.pdf Hess’s Matrix http://static.pdesas.org/content/documents/M2-Activity_2_Handout.pdf Bloom’s Taxonomy http://www.bloomstaxonomy.org/Blooms%20Taxonomy%20questions.pdf Revised 5/18/2016 10:12 AM Page 4