Nys Common Core Mathematics Curriculum Lesson 24 Geometry Answers

NYS COMMON CORE MATHEMATICS CURRICULUM Session Agenda • Module Overview • Focus on Topics

NYS COMMON CORE MATHEMATICS CURRICULUM Session Agenda • Module Overview • Focus on Topics and Lessons • Module in Review • Implementation Discussions © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Session Objectives • Gain an

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Session Objectives • Gain an understanding of the content enveloped in Module 6. • Understand what was, what is, and why the change. • See how geometry concepts from here forward are starting to take shape. • Gain the knowledge necessary to implement with fidelity. © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Curriculum Overview of A Story

NYS COMMON CORE MATHEMATICS CURRICULUM Grade 7 Module 6 Overview Let's look at: •

NYS COMMON CORE MATHEMATICS CURRICULUM Grade 7 Module 6 Overview Let's look at: • Foundational Standards (p. 5) • Focus Standards (p. 4) • Mathematical Practice Standards (p. 5 -6) • Table of Contents and Narrative © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Topic A: Unknown Angles 7.

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Topic A: Unknown Angles 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. • Prerequisites: G 4 M 4 and G 7 M 3 • Goal is to build fluency in these difficult problems • Build recognition and use of structure MP. 7 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Complementary and Supplementary Angles Lesson

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Solving for Unknown Angles Using

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Topic B: Constructing Triangles 7.

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Topic B: Constructing Triangles 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. New Terminology New Tools New Approach © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Correspondence Two identical triangles are

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Correspondence Two identical triangles are shown below. Give a correspondence that matches equal sides and equal angles. Lesson 5 / Example 2 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM Drawing Geometric Shapes Lesson 6 / Exploratory Challenge ©

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Drawing Geometric Shapes Use a

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Drawing Geometric Shapes Use a ruler, protractor, and compass to complete the following: Lesson 6 / Exploratory Challenge © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Drawing Geometric Shapes Use a

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Three Sides Condition Two Sides

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Three Sides Condition Two Sides and the Included Angle Condition Lesson 9 / Exploratory Challenge 4 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM Two Angles and a Given Side Lesson 10 /

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Conditions on Measurements that Determine

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Conditions on Measurements that Determine a Triangle Are there conditions on the lengths of the sides of a triangle? Are there conditions on the measures of the angles in a triangle? Lesson 11 / Exploratory Challenge 1&2 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Conditions on Measurements that Determine

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Conditions on Measurements that Determine a Triangle Is there a "Three Angles" condition for unique triangle? Lesson 11 / Exploratory Challenge 2 d © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Two Sides and a Non-Included

NYS COMMON CORE MATHEMATICS CURRICULUM Checking for Identical Triangles Lesson 14 / Examples 1

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Using Unique Triangles to Solve

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Using Unique Triangles to Solve Real World and Mathematical Problems Lesson 15 / Exercise 2 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM Mid-Module Assessment • Progression Toward Mastery Rubric • Exemplary

NYS COMMON CORE MATHEMATICS CURRICULUM Mid-Module Assessment • Progression Toward Mastery Rubric • Exemplary Student Responses © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Topic C: Slicing Solids 7.

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Topic C: Slicing Solids 7. G. A. 3 Describe the two-dimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Slicing 3 -Dimensional figures by a plane and the resulting 2 -Dimensional slices. © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Slicing a Right Rectangular Prism

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Slicing a Right Rectangular Pyramid

NYS COMMON CORE MATHEMATICS CURRICULUM Slicing on an Angle Lesson 18 / Example 1

NYS COMMON CORE MATHEMATICS CURRICULUM Slicing on an Angle Lesson 18 / Example 3

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Understanding 3 -Dimensional Figures If

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Understanding 3 -Dimensional Figures If slices parallel to the tabletop are taken of this figure, then what would each slice look like? Given the level slices that you determined, how many unit cubes are in the figure? Lesson 19 / Exercise 2 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Topic D: Problems Involving Area

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Topic D: Problems Involving Area and Surface Area 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. © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM Real World Area Problems Lesson 20 / Example 2

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Mathematical Area Problems Examine the

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Mathematical Area Problems Examine the change in dimension and area of squares as the lengths and widths are increased by the given amount. Lesson 21 / Example 1 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Area Problems with Circular Regions

NYS COMMON CORE MATHEMATICS CURRICULUM Surface Area Determine the surface area of the right

NYS COMMON CORE MATHEMATICS CURRICULUM Surface Area Determine the surface area of the right prism. Lesson 23 / Exercise 4 © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Topic E: Problems Involving Volume

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Topic E: Problems Involving Volume 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. © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM Volume of Right Prisms Lesson 25 / Example 3

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Volume of Composite 3 -Dimensional

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Volume of Composite 3 -Dimensional Objects Find the volume of the right prism shown whose base is the region between two right triangles. Use two different strategies. Lesson 26 / Example 2 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Real-World Volume Problems Jim wants

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Real-World Volume Problems Jim wants to know how much his family spends on water for showers. Water costs $1. 50 per 1000 gallons. His family averages 4 showers per day (total). The average length of a shower is 10 minutes. He places a bucket in his shower and turns on the water. After one-minute, the bucket has 2. 5 gallons of water in it. About how much money does his family spend on water for showers in a month (30 days)? Lesson 27 / Exit Ticket © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM End-of-Module Assessment • Progression Toward Mastery Rubric • Exemplary

NYS COMMON CORE MATHEMATICS CURRICULUM End-of-Module Assessment • Progression Toward Mastery Rubric • Exemplary Student Responses © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Module 6 in Review Take

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Module 6 in Review Take a few moments to discuss, with those around you, the major highlights of the Module. • Likes • What was and what is • Concerns • Major Takeaways © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Key Points • • Student

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Key Points • • Student transitioning to more complex levels of geometry Using algebra to solve unknown angle problems Explore the structure of triangles Determine the conditions that determine unique triangles Identify identical triangles and use their relationship to solve problems Describe the slices of three-dimensional figures Apply strategies for area, surface area, and volume in solving real world and mathematical problems © 2012 Common Core, Inc. All rights reserved. commoncore. org