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

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Find arc lengths and areas of sectors of circles 5. Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. (G-C.5.) Expressing Geometric Properties with Equations G-GPE Translate between the geometric description and the equation for a conic section 1. Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. (G-GPE.1.) 2. Derive the equation of a parabola given a focus and directrix. (G-GPE.2.) 3. (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. (G-GPE.3.) Use coordinates to prove simple geometric theorems algebraically 4. Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2). (G-GPE.4.) 5. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). (G-GPE.5.) 6. Find the point on a directed line segment between two given points that partitions the segment in a given ratio. (G-GPE.6.) 7. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. ★ (G-GPE.7.) Geometric Measurement and Dimension G-GMD Explain volume formulas and use them to solve problems 1. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments. (G-GMD.1.) 2. (+) Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures. (G-GMD.2.) 3. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. ★ (G-GMD.3.) Visualize relationships between two-dimensional and three-dimensional objects IA.7.Plot points in three-dimensions. 4. Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. (G-GMD.4.) Modeling with Geometry G-MG Apply geometric concepts in modeling situations 1. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). ★ (G-MG.1.) 2. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). ★ (G-MG.2.) 3. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). ★ (G-MG.3.) Disclaimer: This document is up-to-date as of 11/17/2010. The language provided may not be Page 80 of 98 modified in any way. The most current Iowa Core can be found at http://iowacore.educateiowa.gov.
(IA) Use diagrams consisting of vertices and edges (vertex-edge graphs) to model and solve problems related to networks. IA.8.Understand, analyze, evaluate, and apply vertex-edge graphs to model and solve problems related to paths, circuits, networks, and relationships among a finite number of elements, in real-world and abstract settings. ★ IA.9.Model and solve problems using at least two of the following fundamental graph topics and models: Euler paths and circuits, Hamilton paths and circuits, the traveling salesman problem (TSP), minimum spanning trees, critical paths, vertex coloring. ★ IA.10.Compare and contrast vertex-edge graph topics and models in terms of: ★ • properties • algorithms • optimization • types of problems that can be solved Disclaimer: This document is up-to-date as of 11/17/2010. The language provided may not be Page 81 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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Page 33 and 34: Understand decimal notation for fra
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Page 45 and 46: Expressions and Equations 6.EE Appl
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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
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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 87 and 88: Note on courses and transitions The
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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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