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

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Grade 8 Overview The Number System • Know that there are numbers that are not rational, and approximate them by rational numbers. Expressions and Equations • Work with radicals and integer exponents. • Understand the connections between proportional relationships, lines, and linear equations. • Analyze and solve linear equations and pairs of simultaneous linear equations. Functions • Define, evaluate, and compare functions. • Use functions to model relationships between quantities. Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Geometry • Understand congruence and similarity using physical models, transparencies, or geometry software. • Understand and apply the Pythagorean Theorem. • Solve real-world and mathematical problems involving volume of cylinders, cones and spheres. Statistics and Probability • Investigate patterns of association in bivariate data. Disclaimer: This document is up-to-date as of 11/17/2010. The language provided may not be Page 54 of 98 modified in any way. The most current Iowa Core can be found at http://iowacore.educateiowa.gov.
The Number System 8.NS Know that there are numbers that are not rational, and approximate them by rational numbers. 1. Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. (8.NS.1.) 2. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π 2 ). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. (8.NS.2.) Expressions and Equations 8.EE Work with radicals and integer exponents. 1. Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3 2 × 3 –5 = 3 –3 = 1/3 3 = 1/27. (8.EE.1.) 2. Use square root and cube root symbols to represent solutions to equations of the form x 2 = p and x 3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. (8.EE.2.) 3. Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 10 8 and the population of the world as 7 × 10 9 , and determine that the world population is more than 20 times larger. (8.EE.3.) 4. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. (8.EE.4.) Understand the connections between proportional relationships, lines, and linear equations. 5. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. (8.EE.5.) 6. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. (8.EE.6.) Analyze and solve linear equations and pairs of simultaneous linear equations. 7. Solve linear equations in one variable. a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. (8.EE.7.) Disclaimer: This document is up-to-date as of 11/17/2010. The language provided may not be Page 55 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
Page 3 and 4: Introduction Iowa Core Mathematics
Page 5 and 6: These Standards endeavor to follow
Page 7 and 8: How to read the grade level standar
Page 9 and 10: 4. Model with mathematics. Mathemat
Page 11 and 12: Mathematics | Kindergarten In Kinde
Page 13 and 14: Counting and Cardinality K.CC Know
Page 15 and 16: Mathematics | Grade 1 In Grade 1, i
Page 17 and 18: Operations and Algebraic Thinking 1
Page 27 and 28: 2. Measure and estimate liquid volu
Page 33 and 34: Understand decimal notation for fra
Page 39 and 40: 7. Apply and extend previous unders
Page 43 and 44: Ratios and Proportional Relationshi
Page 45 and 46: Expressions and Equations 6.EE Appl
Page 49 and 50: Ratios and Proportional Relationshi
Page 51 and 52: Geometry 7.G Draw, construct, and d
Page 53: Mathematics | Grade 8 In Grade 8, i
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
Page 73 and 74: Mathematics | High School—Modelin
Page 75 and 76: Mathematics | High School—Geometr
Page 77 and 78: Geometry Overview Congruence • Ex
Page 79 and 80: Similarity, Right Triangles, and Tr
Page 81 and 82: (IA) Use diagrams consisting of ver
Page 83 and 84: Statistics and Probability Overview
Page 85 and 86: 4. Use data from a sample survey to
Page 87 and 88: Note on courses and transitions The
Page 89 and 90: First quartile. For a data set with
Page 91 and 92: Tape diagram. A drawing that looks
Page 93 and 94: Table 2. Common multiplication and
Page 95 and 96: Sample of Works Consulted Existing
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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