Iowa Core K-12 Mathematics (PDF) - Green Hills AEA

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Table 3. The properties of operations. Here a, b and c stand for arbitrary numbers in a given number system. The properties of operations apply to the rational number system, the real number system, and the complex number system. Associative property of addition (a + b) + c = a + (b + c) Commutative property of addition a + b = b + a Additive identity property of 0 a + 0 = 0 + a = a Existence of additive inverses For every a there exists –a so that a + (–a) = (–a) + a = 0. Associative property of multiplication (a × b) × c = a × (b × c) Commutative property of multiplication a × b = b × a Multiplicative identity property of 1 a × 1 = 1 × a = a Existence of multiplicative inverses For every a ≠ 0 there exists 1/a so that a × 1/a = 1/a × a = 1. Distributive property of multiplication over addition a × (b + c) = a × b + a × c Table 4. The properties of equality. Here a, b and c stand for arbitrary numbers in the rational, real, or complex number systems. Reflexive property of equality a = a Symmetric property of equality If a = b, then b = a. Transitive property of equality If a = b and b = c, then a = c. Addition property of equality If a = b, then a + c = b + c. Subtraction property of equality If a = b, then a – c = b – c. Multiplication property of equality If a = b, then a × c = b × c. Division property of equality If a = b and c ≠ 0, then a ÷ c = b ÷ c. Substitution property of equality If a = b, then b may be substituted for a in any expression containing a. Table 5. The properties of inequality. Here a, b and c stand for arbitrary numbers in the rational or real number systems. Exactly one of the following is true: a < b, a = b, a > b. If a > b and b > c then a > c. If a > b, then b < a. If a > b, then –a < –b. If a > b, then a ± c > b ± c. If a > b and c > 0, then a × c > b × c. If a > b and c < 0, then a × c b and c > 0, then a ÷ c > b ÷ c. If a > b and c < 0, then a ÷ c Iowa Core can be found at http://iowacore.educateiowa.gov.
Sample of Works Consulted Existing state standards documents. Research summaries and briefs provided to the Working Group by researchers. National Assessment Governing Board, Mathematics Framework for the 2009 National Assessment of Educational Progress. U.S. Department of Education, 2008. NAEP Validity Studies Panel, Validity Study of the NAEP Mathematics Assessment: Grades 4 and 8. Daro et al., 2007. Mathematics documents from: Alberta, Canada; Belgium; China; Chinese Taipei; Denmark; England; Finland; Hong Kong; India; Ireland; Japan; Korea; New Zealand; Singapore; Victoria (British Columbia). Adding it Up: Helping Children Learn Mathematics. National Research Council, Mathematics Learning Study Committee, 2001. Benchmarking for Success: Ensuring U.S. Students Receive a World- Class Education. National Governors Association, Council of Chief State School Officers, and Achieve, Inc., 2008. Crossroads in Mathematics (1995) and Beyond Crossroads (2006). American Mathematical Association of Two-Year Colleges (AMATYC). Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence. National Council of Teachers of Mathematics, 2006. Focus in High School Mathematics: Reasoning and Sense Making. National Council of Teachers of Mathematics. Reston, VA: NCTM. Foundations for Success: The Final Report of the National Mathematics Advisory Panel. U.S. Department of Education: Washington, DC, 2008. Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report: A PreK-12 Curriculum Framework. How People Learn: Brain, Mind, Experience, and School. Bransford, J.D., Brown, A.L., and Cocking, R.R., eds. Committee on Developments in the Science of Learning, Commission on Behavioral and Social Sciences and Education, National Research Council, 1999. Mathematics and Democracy, The Case for Quantitative Literacy, Steen, L.A. (ed.). National Council on Education and the Disciplines, 2001. Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity. Cross, C.T., Woods, T.A., and Schweingruber, S., eds. Committee on Early Childhood Mathematics, National Research Council, 2009. The Opportunity Equation: Transforming Mathematics and Science Education for Citizenship and the Global Economy. The Carnegie Corporation of New York and the Institute for Advanced Study, 2009. Online: http://www.opportunityequati on.org/ Principles and Standards for School Mathematics. National Council of Teachers of Mathematics, 2000. The Proficiency Illusion. Cronin, J., Dahlin, M., Adkins, D., and Kingsbury, G.G.; foreword by C.E. Finn, Jr., and M. J. Petrilli. Thomas B. Fordham Institute, 2007. Ready or Not: Creating a High School Diploma That Counts. American Diploma Project, 2004. A Research Companion to Principles and Standards for School Mathematics. National Council of Teachers of Mathematics, 2003. Sizing Up State Standards 2008. American Federation of Teachers, 2008. A Splintered Vision: An Investigation of U.S. Science and Mathematics Education. Schmidt, W.H., McKnight, C.C., Raizen, S.A., et al. U.S. National Research Center for the Third International Mathematics and Science Study, Michigan State University, 1997. Stars By Which to Navigate? Scanning National and International Education Standards in 2009. Carmichael, S.B., Wilson. W.S, Finn, Jr., C.E., Winkler, A.M., and Palmieri, S. Thomas B. Fordham Institute, 2009. Askey, R., “Knowing and Teaching Elementary Mathematics,” American Educator, Fall 1999. Aydogan, C., Plummer, C., Kang, S. J., Bilbrey, C., Farran, D. C., & Lipsey, M. W. (2005). An investigation of prekindergarten curricula: Influences on classroom characteristics and child engagement. Paper presented at the NAEYC. Blum, W., Galbraith, P. L., Henn, H- W. and Niss, M. (Eds) Applications and Modeling in Mathematics Education, ICMI Study 14. Amsterdam: Springer. Brosterman, N. (1997). Inventing kindergarten. New York: Harry N. Abrams. Disclaimer: This document is up-to-date as of 11/17/2010. The language provided may not be Page 95 of 98 modified in any way. The most current Iowa Core can be found at http://iowacore.educateiowa.gov.
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Mathematics November 17, 2010
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Introduction Iowa Core Mathematics
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These Standards endeavor to follow
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How to read the grade level standar
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4. Model with mathematics. Mathemat
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Mathematics | Kindergarten In Kinde
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Counting and Cardinality K.CC Know
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Mathematics | Grade 1 In Grade 1, i
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Operations and Algebraic Thinking 1
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2. Measure and estimate liquid volu
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Understand decimal notation for fra
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7. Apply and extend previous unders
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Page 55 and 56: The Number System 8.NS Know that th
Page 57 and 58: 3. Describe the effect of dilations
Page 59 and 60: Mathematics | High School—Number
Page 61 and 62: The Real Number System N-RN Extend
Page 63 and 64: Mathematics | High School—Algebra
Page 65 and 66: Seeing Structure in Expressions A-S
Page 67 and 68: 6. Solve systems of linear equation
Page 69 and 70: Functions Overview Interpreting Fun
Page 71 and 72: 9. Compare properties of two functi
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Page 77 and 78: Geometry Overview Congruence • Ex
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Page 83 and 84: Statistics and Probability Overview
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Page 89 and 90: First quartile. For a data set with
Page 91 and 92: Tape diagram. A drawing that looks
Page 93: Table 2. Common multiplication and
Page 97 and 98: Schmidt, W., Houang, R., and Cogan,
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Iowa Core K-12 Mathematics (PDF) - Green Hills AEA

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