N YS CO MMO N COR E MAT H E MAT I C S C U RR I C U LU M Geometry Grade 7 Module 6 2012 Common Core, Inc. All rights reserved. commoncore.org A Story of Ratios N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M

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 N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M Whats 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 N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M 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 N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M Whats 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 N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M A Story of Ratios Curriculum Overview of A Story of Ratios

2012 Common Core, Inc. All rights reserved. commoncore.org N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M 2012 Common Core, Inc. All rights reserved. commoncore.org A Story of Ratios N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M

2012 Common Core, Inc. All rights reserved. commoncore.org A Story of Ratios N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M 2012 Common Core, Inc. All rights reserved. commoncore.org A Story of Ratios

N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M 2012 Common Core, Inc. All rights reserved. commoncore.org A Story of Ratios N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M 2012 Common Core, Inc. All rights reserved. commoncore.org

A Story of Ratios N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M 2012 Common Core, Inc. All rights reserved. commoncore.org A Story of Ratios N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M

2012 Common Core, Inc. All rights reserved. commoncore.org A Story of Ratios N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M 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 N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M 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

N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M 2012 Common Core, Inc. All rights reserved. commoncore.org A Story of Ratios N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M 2012 Common Core, Inc. All rights reserved. commoncore.org

A Story of Ratios GRAP HIC O RGAN I ZER N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M

2012 Common Core, Inc. All rights reserved. commoncore.org A Story of Ratios N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M A Story of Ratios CREATING

MODELS 2012 Common Core, Inc. All rights reserved. commoncore.org N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M Highlight critical vocabulary in discussion 2012 Common Core, Inc. All rights reserved. commoncore.org

A Story of Ratios N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M 2012 Common Core, Inc. All rights reserved. commoncore.org A Story of Ratios N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M

2012 Common Core, Inc. All rights reserved. commoncore.org A Story of Ratios N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M 2012 Common Core, Inc. All rights reserved. commoncore.org A Story of Ratios

N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M 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 N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M Topic B: Constructing Triangles 2012 Common Core, Inc. All rights reserved. commoncore.org A Story of Ratios

N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M 2012 Common Core, Inc. All rights reserved. commoncore.org A Story of Ratios N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M 2012 Common Core, Inc. All rights reserved. commoncore.org

A Story of Ratios EXPLICITLY TEACH VOCABULARY N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M 2012 Common Core, Inc. All rights reserved. commoncore.org A Story of Ratios

A Story of Ratios N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M Correspondence 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 N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M 2012 Common Core, Inc. All rights reserved. commoncore.org A Story of Ratios

N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M 2012 Common Core, Inc. All rights reserved. commoncore.org A Story of Ratios N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M 2012 Common Core, Inc. All rights reserved. commoncore.org

A Story of Ratios N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M 2012 Common Core, Inc. All rights reserved. commoncore.org A Story of Ratios N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M

2012 Common Core, Inc. All rights reserved. commoncore.org A Story of Ratios N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M 2012 Common Core, Inc. All rights reserved. commoncore.org A Story of Ratios

N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M 2012 Common Core, Inc. All rights reserved. commoncore.org A Story of Ratios N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M 2012 Common Core, Inc. All rights reserved. commoncore.org

A Story of Ratios N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M 2012 Common Core, Inc. All rights reserved. commoncore.org A Story of Ratios N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M

2012 Common Core, Inc. All rights reserved. commoncore.org A Story of Ratios N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M A Story of Ratios LESSON TRANSCRIPT ACTIVITY

2012 Common Core, Inc. All rights reserved. commoncore.org N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M 2012 Common Core, Inc. All rights reserved. commoncore.org A Story of Ratios N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M

2012 Common Core, Inc. All rights reserved. commoncore.org A Story of Ratios N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M 2012 Common Core, Inc. All rights reserved. commoncore.org A Story of Ratios

N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M 2012 Common Core, Inc. All rights reserved. commoncore.org A Story of Ratios N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M 2012 Common Core, Inc. All rights reserved. commoncore.org

A Story of Ratios N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M Checking for Identical Triangles Lesson 14 / Examples 1-2 2012 Common Core, Inc. All rights reserved. commoncore.org

A Story of Ratios N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M A Story of Ratios Using Unique Triangles to Solve Real World and Mathematical Problems Quadrilateral is a model of a kite. Diagonals and represent the sticks that help keep the kite rigid.

Lesson 15 / Exercise 2 2012 Common Core, Inc. All rights reserved. commoncore.org N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M Mid-Module Assessment

Assessment Progression Toward Mastery Rubric Exemplary Student Responses

2012 Common Core, Inc. All rights reserved. commoncore.org A Story of Ratios N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M 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 N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M A Story of Ratios Slicing a Right Rectangular Prism with a Plane

Lesson 16 2012 Common Core, Inc. All rights reserved. commoncore.org N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M Lesson 16 2012 Common Core, Inc. All rights reserved. commoncore.org

A Story of Ratios N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M Right Rectangular Pyramid Lesson 17 2012 Common Core, Inc. All rights reserved. commoncore.org

A Story of Ratios N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M Slicing on an Angle Lesson 18 2012 Common Core, Inc. All rights reserved. commoncore.org

A Story of Ratios N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M 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 N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M 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

N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M A Story of Ratios Real World Area Problems Ten targets are being painted as shown in the following figure. The radius of the smallest circle is , and each successive, larger circle is more in radius than the circle before it. A tester can of red and of white paint is purchased to paint the target. Each can of paint covers . Is there enough paint of each color to create all ten targets?

Lesson 20 / Example 2 2012 Common Core, Inc. All rights reserved. commoncore.org N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M 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 N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M

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

N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M A Story of Ratios Area Problems with Circular Regions The diameters of four half circles are sides of a square with side lengths of Find the exact area of the shaded region. Lesson 22 / Problem Set #4

2012 Common Core, Inc. All rights reserved. commoncore.org N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M 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 N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M 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 N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M A Story of Ratios Volume of Right Prisms Two containers are shaped like right triangular prisms, each with the same

height. The base area of the larger container is more than the base area of the smaller container. How many times must the smaller container be filled with water and poured into the larger container in order to fill the larger container? Lesson 25 / Example 3 2012 Common Core, Inc. All rights reserved. commoncore.org N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M

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

N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M 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 N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M End-of-Module Assessment

Assessment Progression Toward Mastery Rubric Exemplary Student Responses 2012 Common Core, Inc. All rights reserved. commoncore.org A Story of Ratios N YS C O M M O N C O R E M AT H E M AT I C S C U R R I C U L U M

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