A Correlation of Pearson Mathematics Geometry Common Core, 2015 To the Missouri Learning Standards for Mathematics Geometry
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1 A Correlation of Pearson Mathematics Common Core, 2015 To the Missouri Learning Standards for Mathematics
2 A Correlation of Common Core 2015 To the Introduction This document demonstrates how Pearson, Common Core Edition 2015 meets the standards of the Missouri Learning Standards for Mathematics,. Correlation references are to the pages of the Student and Teacher s Editions. Pearson, Common Core Edition 2015 balances conceptual understanding, procedural fluency, and the application of mathematics to solve problems and formulate models. Each lesson begins with Interactive Learning, the Solve It!, which immediately engages students in their daily learning according to the Standards for Mathematical Practice. The second step of the lesson, Guided Instruction, uses visual learning principles and a Thinking/Reasoning strand (seen in the Know/Need/Plan and Think/Plan/Write boxes) to introduce the Essential Understanding of the lesson by teaching THROUGH and FOR problem-solving. In the third step of the lesson, the Lesson Check, Do you know HOW? exercises measure students procedural fluency, while Do you UNDERSTAND? problems measure students conceptual understanding. In the fourth step of the lesson, Practice problems are designed to develop students fluency in the Content Standards and proficiency with the Mathematical Practices. Real-world STEM problems as well as problems designed to elicit the use of one or more of the Standards for Mathematical Practice are clearly labeled in the Practice step of the lesson. The final phase of the lesson, Assess and Remediate, features a Lesson Quiz to measure students understanding of lesson concepts. By utilizing the balanced and proven-effective approach of Pearson s 5-step lesson design, you can teach with confidence. Copyright 2016 Pearson Education, Inc. or its affiliate(s). All rights reserved.
3 A Correlation of Common Core 2015 To the Grade-Level Expectations Congruence A Experiment with transformations in the plane. 1 Define angle, circle, perpendicular line, parallel line, line segment and ray based on the undefined notions of point, line, distance along a line and distance around a circular arc. SE/TE: 4-7, 11-16, 20-23, 27-31, 34-37, 43-46, , TE: 10A-10B, 19A-19B, 26A-26B, 33A-33B, 40A-40B, 48A-48B, 146A-146B, 657A-657B 2 Represent transformations in the plane, and describe them as functions that take points in the plane as inputs and give other points as outputs. SE/TE: CB 544, , , , , TE: 552A-552B, 560A-560B, 567A-567B, 576A- 576B, 593A-593B 3 Describe the rotational symmetry and lines of symmetry of two-dimensional figures. SE/TE: CB Develop definitions of rotations, reflections and translations in terms of angles, circles, perpendicular lines, parallel lines and line segments. SE/TE: , , TE: 552A-552B, 560A-560B, 567A-567B 5 Demonstrate the ability to rotate, reflect or SE/TE: , CB 553, , , translate a figure, and determine a possible sequence of transformations between two TE: 552A-552B, 560A-560B, 567A-567B, 576A-576B congruent figures. B Understand congruence in terms of rigid motions. 1 Develop the definition of congruence in terms of rigid motions. SE/TE: , , , , TE: 552A-552B, 560A-560B, 567A-567B, 576A- 576B, 585A-585B 2 Develop the criteria for triangle congruence from the definition of congruence in terms of rigid motions. SE/TE: TE: 585A-585B C Prove geometric theorems. 1 Prove theorems about lines and angles. SE/TE: , , , , TE: 127A-127B, 146A-146B, 155A-155B, 163A- 163B, 294A-294B
4 A Correlation of Common Core 2015 To the Grade-Level Expectations 2 Prove theorems about triangles. SE/TE: , , , , , , TE: 178A-178B, 256A-256B, 291A-291B, 315A- 315B, 322A-322B, 331A-331B, 339A-339B 3 Prove theorems about polygons. SE/TE: , , , TE: 366A-366B, 374A-374B, 382A-382B, 388A-388B D Make geometric constructions. 1 Construct geometric figures using various tools and methods. SE/TE: CB 42, 43-46, CB 49, CB 147, , , CB 249, , , CB 413, CB 470, TE: 48A-48B, 188A-188B, 248A-248B, 256A-256B, 291A-291B, 634A-634B Similarity, Right Triangles, and Trigonometry A Understand similarity in terms of similarity transformations. 1 Construct and analyze scale changes of SE/TE: CB 586, geometric figures. TE: 593A-593B 2 Use the definition of similarity to decide if figures are similar and to solve problems involving similar figures. SE/TE: TE: 600A-600B 3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. B Prove theorems involving similarity. 1 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. SE/TE: TE: 600A-600B SE/TE: , CB 225, , , CB 242, , , , , , , , CB 352, , , , , , , , , CB , , TE: 224A-224B, 233A-233B, 241A-241B, 248A- 248B, 256A-256B, 264A-264B, 271A-271B, 291A- 291B, 299A-299B, 315A-315B, 358A-358B, 366A- 366B, 374A-374B, 382A-382B, 388A-388B, 397A- 397B, 438A-438B, 447A-447B, 458A-458B, 467A- 467B
5 A Correlation of Common Core 2015 To the Grade-Level Expectations C Define trigonometric ratios, and solve problems involving right triangles. 1 Understand that side ratios in right SE/TE: CB 506, triangles define the trigonometric ratios for acute angles. TE: 513A-513B 2 Explain and use the relationship between the sine and cosine of complementary angles. SE/TE: , CB 514 TE: 513A-513B 3 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles. SE/TE: , , , TE: 498A-498B, 505A-505B, 513A-513B, 521A-521B 4 Derive the formula A = 1/2 ab sin(c) for the area of a triangle. SE/TE: TE: 648A-648B Circles A Understand and apply theorems about circles. 1 Prove that all circles are similar using SE/TE: similarity transformations. TE: 657A-657B 2 Identify and describe relationships among inscribed angles, radii and chords of circles. SE/TE: , , CB 770, , , CB 789, TE: 657A-657B, 769A-769B, 779A-779B, 787A- 787B, 797A-797B 3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. SE/TE: CB 300, TE: 307A-307B B Find arc lengths and areas of sectors of circles. 1 Derive the formula for the length of an arc SE/TE: of a circle. TE: 657A-657B
6 A Correlation of Common Core 2015 To the Grade-Level Expectations 2 Derive the formula for the area of a sector of a circle. SE/TE: TE: 666A-666B Exploring Geometric Properties with Equations A Translate between the geometric description and the equation for a conic section. 1 Derive the equation of a circle. SE/TE: Derive the equation of a parabola given a focus and directrix. TE: 803A-803B SE/TE: CB B Use coordinates to prove geometric theorems algebraically. 1 Use coordinates to prove geometric SE/TE: theorems algebraically. TE: 418A-418B 2 Prove the slope criteria for parallel and perpendicular lines and use them to solve problems. SE/TE: , , , TE: 196A-196B, 204A-204B, 458A-458B, 467A-467B 3 Find the point on a directed line segment between two given points that partitions the segment in a given ratio. SE/TE: 20-23, TE: 26A-26B, 56A-56B 4 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles. SE/TE: 50-53, , , CB 667 TE: 56A-56B, 405A-405B, 622A-622B Geometric Measurement and Dimension A Explain volume formulas and use them to solve problems. 1 Give an informal argument for the SE/TE: CB 659, , CB 725 formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid and cone. TE: 724A-724B 2 Use volume formulas for cylinders, pyramids, cones, spheres and composite figures to solve problems. SE/TE: , , , TE: 641A-641B, 724A-724B, 732A-732B, 740A-740B
7 A Correlation of Common Core 2015 To the Grade-Level Expectations B Visualize relationships between two-dimensional and three-dimensional objects. 1 Identify the shapes of two-dimensional SE/TE: cross-sections of three-dimensional objects. TE: 695A-695B 2 Identify three-dimensional objects SE/TE: generated by transformations of two-dimensional objects. TE: 811A-811B Modeling with A Apply geometric concepts in modeling situations. 1 Use geometric shapes, their measures and their properties to describe objects. SE/TE: , , , , , , , , , TE: 513A-513B, 622A-622B, 628A-628B, 634A- 634B, 707A-707B, 715A-715B, 724A-724B, 732A- 732B, 740A-740B, 749A-749B 2 Apply concepts of density based on area and volume in modeling situations. SE/TE: CB 741, TE: 749A-749B 3 Apply geometric methods to solve design mathematical modeling problems. SE/TE: TE: 169A-169B Conditional Probability and Rules of Probability A Understand independence and conditional probability and use them to interpret data. 1 Describe events as subsets of a sample SE/TE: space using characteristics of the outcomes, or as unions, intersections or complements of other TE: 829A-829B events. 2 Understand the definition of independent events and use it to solve problems. SE/TE: TE: 861A-861B 3 Calculate conditional probabilities of events. SE/TE: TE: 861A-861B
8 A Correlation of Common Core 2015 To the Grade-Level Expectations 4 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. 5 Recognize and explain the concepts of conditional probability and independence in a context. 6 Apply and interpret the Addition Rule for calculating probabilities. 7 Apply and Interpret the general Multiplication Rule in a uniform probability model. 8 Use permutations and combinations to solve problems. SE/TE: , , TE: 829A-829B, 835A-835B, 855A-855B SE/TE: , TE: 835A-835B, 861A-861B SE/TE: TE: 849A-849B SE/TE: TE: 849A-849B SE/TE: TE: 842A-842B
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