NYS COMMON CORE MATHEMATICS CURRICULUM Geometry Grade 7

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Session Agenda § Understand the

NYS COMMON CORE MATHEMATICS CURRICULUM What’s In a Module? Teacher Materials • Module Overview

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Types of Lessons 1. Problem

NYS COMMON CORE MATHEMATICS CURRICULUM What’s In a Lesson? Teacher Materials Lessons • Student

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

NYS COMMON CORE MATHEMATICS CURRICULUM © 2012 Common Core, Inc. All rights reserved. commoncore.

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Turn and Talk • What

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

NYS COMMON CORE MATHEMATICS CURRICULUM Highlight critical vocabulary in discussion © 2012 Common Core,

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

NYS COMMON CORE MATHEMATICS CURRICULUM Topic B: Constructing Triangles © 2012 Common Core, Inc.

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

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 Mid-Module Assessment • Progression Toward Mastery Rubric • Exemplary

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

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

NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 16 © 2012 Common Core, Inc. All rights

NYS COMMON CORE MATHEMATICS CURRICULUM Right Rectangular Pyramid Lesson 17 © 2012 Common Core,

NYS COMMON CORE MATHEMATICS CURRICULUM Slicing on an Angle Lesson 18 © 2012 Common

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

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

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 Area Problems with Circular Regions

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

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

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 Real-World Volume Problems Jim wants

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

NYS COMMON CORE MATHEMATICS CURRICULUM Biggest Takeaway Turn and Talk: • What questions were

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NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Session Agenda § Understand the mathematical concepts developed within Grade 7 Module 6. § Practice collecting evidence of effective instruction using transcripts of classroom instruction. § Discuss feedback strategies for supporting scaffolding and accommodation techniques for special populations. © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM What’s In a Module? Teacher Materials • Module Overview • Topic Overviews • Daily Lessons • Assessments Student Materials • Daily Lessons with Problem Sets Copy Ready Materials • Exit Tickets • Fluency Worksheets / Sprints • Assessments © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Types of Lessons 1. Problem Set Students and teachers work through examples and complete exercises to develop or reinforce a concept. 2. Socratic Teacher leads students in a conversation to develop a specific concept or proof. 3. Exploration Independent or small group work on a challenging problem followed by debrief to clarify, expand or develop math knowledge. 4. Modeling Students practice all or part of the modeling cycle with real-world or mathematical problems that are ill-defined. © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM What’s In a Lesson? Teacher Materials Lessons • Student Outcomes and Lesson Notes (in select lessons) • Classwork • General directions and guidance, including timing guidance • Bulleted discussion points with expected student responses • Student classwork with solutions (boxed) • Exit Ticket with Solutions • Problem Set with Solutions Student Materials • Classwork • Problem Set © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Turn and Talk • What difficulties would you anticipate with student understanding of the mathematics in this section? • What scaffolds would be effective for addressing those difficulties? © 2012 Common Core, Inc. All rights reserved. commoncore. org

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. © 2012 Common Core, Inc. All rights reserved. commoncore. org

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. © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM Correspondence A Story of Ratios ACTIVITY 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 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 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. 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. © 2012 Common Core, Inc. All rights reserved. commoncore. org

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 © 2012 Common Core, Inc. All rights reserved. commoncore. org

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 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 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 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 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 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 Student Responses © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios

NYS COMMON CORE MATHEMATICS CURRICULUM Biggest Takeaway Turn and Talk: • What questions were answered for you? • What new questions have surfaced? © 2012 Common Core, Inc. All rights reserved. commoncore. org A Story of Ratios