Shelby County Schools Mathematics Instructional Maps Are Standards-Based Maps Driven By

Curriculum and Instruction – Mathematics Quarter 4 Grade 7 Introduction

In 2014, the Shelby County Schools Board of Education adopted a set of ambitious, yet attainable goals for school and student performance. The District is committed to these goals, as further described in our strategic plan, Destination 2025. By 2025,  80% of our students will graduate from high school college or career ready  90% of students will graduate on time  100% of our students who graduate college or career ready will enroll in a post-secondary opportunity

In order to achieve these ambitious goals, we must collectively work to provide our students with high quality, college and career ready aligned instruction. The Tennessee State Standards provide a common set of expectations for what students will know and be able to do at the end of a grade. College and career readiness is rooted in the knowledge and skills students need to succeed in post-secondary study or careers. The TN State Standards represent three fundamental shifts in mathematics instruction: focus, coherence and rigor.

Shelby County Schools 2016/2017 Revised 1/24/17 1 of 16 Curriculum and Instruction – Mathematics Quarter 4 Grade 7

The Standards for Mathematical Practice describe varieties of expertise, habits of minds and productive dispositions that mathematics educators at all levels should seek to develop in their students. These practices rest on important National Council of Teachers of Mathematics (NCTM) “processes and proficiencies” with longstanding importance in mathematics education. Throughout the year, students should continue to develop proficiency with the eight Standards for Mathematical Practice.

This curriculum map is designed to help teachers make effective decisions about what mathematical content to teach so that, ultimately our students, can reach Destination 2025. To reach our collective student achievement goals, we know that teachers must change their practice so that it is in alignment with the three mathematics instructional shifts.

Throughout this curriculum map, you will see resources as well as links to tasks that will support you in ensuring that students are able to reach the demands of the standards in your classroom. In addition to the resources embedded in the map, there are some high-leverage resources around the content standards and mathematical practice standards that teachers should consistently access:

The TN Mathematics Standards The Tennessee Mathematics Standards: Teachers can access the Tennessee State standards, which https://www.tn.gov/education/article/mathematics- are featured throughout this curriculum map and represent standards college and career ready learning at reach respective grade level. Standards for Mathematical Practice Mathematical Practice Standards Teachers can access the Mathematical Practice Standards, https://drive.google.com/file/d/0B926oAMrdzI4RUpMd1 which are featured throughout this curriculum map. This link 2 Curriculum and Instruction – Mathematics Quarter 4 Grade 7 pGdEJTYkE/view contains more a more detailed explanation of each practice along with implications for instructions.

Purpose of the Mathematics Curriculum Maps

This curriculum framework or map is meant to help teachers and their support providers (e.g., coaches, leaders) on their path to effective, college and career ready (CCR) aligned instruction and our pursuit of Destination 2025. It is a resource for organizing instruction around the TN State Standards, which define what to teach and what students need to learn at each grade level. The framework is designed to reinforce the grade/course-specific standards and content—the major work of the grade (scope)—and provides a suggested sequencing and pacing and time frames, aligned resources—including sample questions, tasks and other planning tools. Our hope is that by curating and organizing a variety of standards-aligned resources, teachers will be able to spend less time wondering what to teach and searching for quality materials (though they may both select from and/or supplement those included here) and have more time to plan, teach, assess, and reflect with colleagues to continuously improve practice and best meet the needs of their students.

The map is meant to support effective planning and instruction to rigorous standards; it is not meant to replace teacher planning or prescribe pacing or instructional practice. In fact, our goal is not to merely “cover the curriculum,” but rather to “uncover” it by developing students’ deep understanding of the content and mastery of the standards. Teachers who are knowledgeable about and intentionally align the learning target (standards and objectives), topic, task, and needs (and assessment) of the learners are best- positioned to make decisions about how to support student learning toward such mastery. Teachers are therefore expected--with the support of their colleagues, coaches, leaders, and other support providers--to exercise their professional judgement aligned to our shared vision of effective instruction, the Teacher Effectiveness Measure (TEM) and related best practices. However, while the framework allows for flexibility and encourages each teacher/teacher team to make it their own, our expectations for student learning are non-negotiable. We must ensure all of our children have access to rigor—high-quality teaching and learning to grade- Shelby County Schools 2016/2017 Revised 1/24/17 3 of 16 Curriculum and Instruction – Mathematics Quarter 4 Grade 7 level specific standards, including purposeful support of literacy and language learning across the content areas.

Additional Instructional Support Shelby County Schools adopted our current math textbooks for grades 6-8 in 2010-2011. The textbook adoption process at that time followed the requirements set forth by the Tennessee Department of Education and took into consideration all texts approved by the TDOE as appropriate. We now have new standards; therefore, the textbook(s) have been vetted using the Instructional Materials Evaluation Tool (IMET). This tool was developed in partnership with Achieve, the Council of Chief State Officers (CCSSO) and the Council of Great City Schools. The review revealed some gaps in the content, scope, sequencing, and rigor (including the balance of conceptual knowledge development and application of these concepts), of our current materials.

The additional materials purposefully address the identified gaps in alignment to meet the expectations of the CCR standards and related instructional shifts while still incorporating the current materials to which schools have access. Materials selected for inclusion in the Curriculum Maps, both those from the textbooks and external/supplemental resources (e.g., engageny), have been evaluated by district staff to ensure that they meet the IMET criteria.

How to Use the Mathematics Curriculum Maps

Overview An overview is provided for each quarter. The information given is intended to aid teachers, coaches and administrators develop an understanding of the content the students will learn in the quarter, how the content addresses prior knowledge and future learning, and may provide some non-summative assessment items.

Tennessee State Standards The TN State Standards are located in the left column. Each content standard is identified as the following: Major Work, Supporting Content or Additional Content.; a key can be found at the bottom of the map. The major work of the grade should comprise 65-85% of your instructional time. Supporting Content are standards that supports student’s learning of the major work. Therefore, you will see supporting and additional standards taught in conjunction with major work. It is the teacher’s responsibility to examine the standards and skills needed in order to ensure student mastery of the indicated standard.

Content 4 Curriculum and Instruction – Mathematics Quarter 4 Grade 7 Teachers are expected to carefully craft weekly and daily learning objectives/ based on their knowledge of TEM Teach 1. In addition, teachers should include related best practices based upon the TN State Standards, related shifts, and knowledge of students from a variety of sources (e.g., student work samples, MAP, etc.). Support for the development of these lesson objectives can be found under the column titled ‘Content’. The enduring understandings will help clarify the “big picture” of the standard. The essential questions break that picture down into smaller questions and the objectives provide specific outcomes for that standard(s). Best practices tell us that clearly communicating and making objectives measureable leads to greater student mastery.

Instructional Support and Resources District and web-based resources have been provided in the Instructional Resources column. Throughout the map you will find instructional/performance tasks, i-Ready lessons and additional resources that align with the standards in that module. The additional resources provided are supplementary and should be used as needed for content support and differentiation.

Shelby County Schools 2016/2017 Revised 1/24/17 5 of 16 Curriculum and Instruction – Mathematics Quarter 4 Grade 7 Topics Addressed in Quarter

Area and Circumference of a Circle Area, Volume & Surface Area of 2- and 3-D Objects Supplementary, Complementary, Vertical & Adjacent Angles

Overview In quarter 4 students continue their study of geometry topics they have been developing over the years, such as area, surface area, and volume. Students will explore the two-dimensional figures that result from taking slices of right rectangular prisms and right rectangular pyramids parallel to the base, parallel to a lateral face, and slices that are not parallel to the base nor lateral face, but are skewed slices (7.G.A.3).

Mid quarter students will discover the angle relationships formed by intersecting lines and use this information to calculate unknown angle measures in various figures (7.G.5). Later in the quarter students will expand their knowledge of the volume of right rectangular prisms (6.G.2) to discover the formula for volume (7.G.6) and use their knowledge of composing and decomposing two-dimensional shapes to calculate area (6.G.1) to extend that concept to volume.

The geometry standards covered in this quarter are part of the additional standards that engage students in content that is related to some of the focus standards. These standards are from the number system, expressions/equations and proportional relationships domains and are incorporated where appropriate. The inclusion of these standards should help students see the connection between these major work standards and the geometry standards and how they can be applied to real-world situations. Including these focus standards should also provide additional opportunities for students to engage with them prior to the state assessment. During the weeks after the assessment students will continue working with some of the remaining focus standards through use of performance tasks and lessons that reinforce grade-level standards and that provide opportunities for students to apply their knowledge to mathematical and real-world problems. Moreover, engaging students in meaningful work around these focus standards will serve as a bridge to success in learning 8th grade math content.

Year at a Glance Document

Grade Level Type of Rigor Foundational Standards Sample Assessment Items

6 Curriculum and Instruction – Mathematics Quarter 4 Grade 7 Standard 7.G.3 Conceptual Understanding Orglib.com: 7.g.3 Practice Test 7.G.4 Conceptual Understanding 6.G.1, 6.G.4 Math Shell: Octagon Tiles 7.G.4-6 & Procedural 7.G.5 Conceptual Understanding Learnzillion: 7.G.2 & 7.G.5 & Procedural 7.G.6 Application & Procedural 6.G.1, 6.G.2, 6.G.4 Learnzillion: 7.G.3 & 7.G.6 7.EE.4a (previously Conceptual Understanding, 6.EE.6, 6.EE.7, 6.EE.8 Smarter Balance Test Items: #9, covered) Procedural Skill, 12, 30 & 31 Application 7.NS.3 (previously Procedural Skill, 6.NS.3 Math Shell: Lottery covered) Application 7.RP.3 (previously Procedural Skill, 6.RP.3 Inside Mathematics Performance covered) Application Task: Which is Bigger?

Shelby County Schools 2016/2017 Revised 1/24/17 7 of 16 Curriculum and Instruction – Mathematics Quarter 4 Grade 7 Fluency

NCTM Position

Procedural fluency is a critical component of mathematical proficiency. Procedural fluency is the ability to apply procedures accurately, efficiently, and flexibly; to transfer procedures to different problems and contexts; to build or modify procedures from other procedures; and to recognize when one strategy or procedure is more appropriate to apply than another. To develop procedural fluency, students need experience in integrating concepts and procedures and building on familiar procedures as they create their own informal strategies and procedures. Students need opportunities to justify both informal strategies and commonly used procedures mathematically, to support and justify their choices of appropriate procedures, and to strengthen their understanding and skill through distributed practice.

The fluency standards for 7th grade listed below should be incorporated throughout your instruction over the course of the school year. Click engage ny Fluency Support to access exercises that can be used as a supplement in conjunction with building conceptual understanding.

 7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers.  7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.  7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form.  7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

References:  https://www.engageny.org/  http://www.corestandards.org/  http://www.nctm.org/  http://achievethecore.org/

8 Curriculum and Instruction – Mathematics Quarter 4 Grade 7 TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES Geometry: Draw and Describe Geometric Figures (Allow approximately 4.5 weeks for instruction, review and assessment) Domain: Geometry Enduring Understandings: Use the Real-World Examples, Vocabulary: parallelogram, Cluster(s): Draw, construct and  Geometric attributes, such as Problem Solving and H.O.T. rectangle, square, rhombus, describe geometrical figures and shapes, lines, angles, and figures exercises from the following book trapezoid, polygon, equilateral, describe the relationships between provide descriptive information lessons. equiangular, regular polygon them. about an object’s properties and support visualization and problem Glencoe Writing in Math: solving. 12-1D p. 688 (Key Concept Chart); p. Joseph drew a regular polygon and 7.G.A.3 Describe the two- 691 #24-32 measured one of its interior angles. dimensional figures that result Essential Questions: 12-1E Polygons and Angles Explain why it is impossible for his angle measure to be 145°. from slicing three-dimensional  What 2-D figure results from slicing Holt (Sample Response: Regular decagons figures, as in plane sections of 3-D figures? right rectangular prisms and right 8-7 Classifying Quadrilaterals have equal angles measuring 144° 10-1 Lesson Extension Cross Sections and regular 11-sided polygons have rectangular pyramids. Objectives: angles measuring 147.27°.)  Students will describe rectangular Additional Recommended regions that result from slicing a Resources: Graphic Organizer: right rectangular prism by a plane engage ny : Slicing a Right Rectangular Cross Sections perpendicular to one of the faces. Prism Illustrative Math: Cube Ninjas 7.G.3 Additional Information: (7.G.2) Students draw geometric shapes with engage ny : Lessons 16-19 (7.G.3) given parameters. Parameters could Math Shell: Describing and Defining include parallel lines, angles, Quadrilaterals perpendicular lines, line segments, etc. Choose from the following resources and use them to Example(s): deepen students' conceptual Is it possible to draw a triangle with understanding of mathematical a 90˚ angle and one leg that is 4 content and develop their ability inches long and one leg that is 3 to apply that knowledge to non- inches long? If so, draw one. Is there routine problems. more than one such triangle? Optional Resources: Draw a triangle with angles that are 60 degrees. Is this a unique Better Lesson: 7.G.3 Shelby County Schools 2016/2017 Revised 1/24/17 9 of 16 Curriculum and Instruction – Mathematics Quarter 4 Grade 7 TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES triangle? Why or why not? Khan Academy: Cross Sections 7.G.3 Learnzillion: Draw Geometric Shapes Draw an isosceles triangle with only Learn Zillion: Construct a Triangle one 80 degree angle. Is this the only Cross Sections 7.G.3 possibility or can you draw another Lesson: Any Way You Slice It 7.G.3 triangle that will also meet these Learn zillion: Cross Section of a conditions? Rectangular Prism Math Station Activities: pp. 95, 102 & 110

Through exploration, students Correlated iReady Lesson(s): The recognize that the sum of the angles iReady program includes a variety of of any triangle will be 180. resources that can be used to support teacher-led instruction in Tier 1 and Additional Information: (7.G.3) guided small-group Tier 1, 2 or 3 Students need to describe the instruction. resulting face shape from cuts made parallel and perpendicular to the  Cross-sections of Prisms and bases of right rectangular prisms and Pyramids pyramids. Cuts made parallel will take the shape of the base; cuts made perpendicular will take the shape of the lateral (side) face. Cuts made at an angle through the right rectangular prism will produce a parallelogram;

Geometry: Angle Measures, Area, Surface Area and Volume Domain: Geometry Enduring Understanding(s): Focus on Real-World Examples, Vocabulary: area, circumference, Cluster: Solve real-life and  Formulas for calculating key aspects Problem Solving and H.O.T. supplementary, complementary, mathematical problems involving of geometric figures can be Exercises of the following book vertical, and adjacent angles, surface angle measure, area, surface area developed by using existing lessons. area, volume, 2D figure, 3D figure, and volume. knowledge of the shapes. polygon, quadrilateral, right prism, 10 Curriculum and Instruction – Mathematics Quarter 4 Grade 7 TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES  Intersecting lines can form various Glencoe cube, lateral face, lateral area, 7.G.B.4 Know the formulas for types of angles. Ch. 10 All Lessons (Exclude 1D, 1F, internal face the area and circumference of a 2C & 2F) circle and use them to solve Essential Question(s): Writing in Math: Holt Describe how to calculate the area of problems; give an informal  How do you find the surface area 8-3 Line and Angle Relationships a circle when given only the derivation of the relationship and volume of a 3D figure? 9-2 Circumference (Examples 3, 4 & circumference of the circle. between the circumference and  What is the total number of degrees area of a circle. #17-27) in supplementary and 9-5 Area of Circles Explain what conditions make angles complementary angles?  7.NS.3 Solve real-world and 10-1 Intro to 3D Figures complimentary, supplementary, mathematical problems  What is the relationship between 10-2 Hands-on Lab vertical and adjacent. involving the four vertical and adjacent angles? 10-2 Volume of Prisms and Cylinders ( operations with rational Prisms only) Have students discuss their own numbers. Objective(s): 10-3 Volume of Pyramids (Cones are definitions for volume and surface  7.EE.4 Solve word  Students will derive the formulas not part of the standard) area. Have them share some problems leading to for the area and circumference of a 10-4 Surface Area of Prisms examples of common objects that equations of the form px circle. (Cylinders are not part of the have volume and surface area. standard) + q = r and p(x + q) = r,  Students will apply understanding 10-5 Hands –on Lab where p, q, and r are Suppose the height of a square of area and circumference of 10-5 Surface Area of Pyramids (Cones specific rational numbers. pyramid is doubled. Explain what circles to solve real-world and are not part of the standard) Solve equations of these mathematical problems. happens to the volume of the forms fluently. Compare  Students will determine the pyramid. Support your reasoning an algebraic solution to an Additional Recommended relationships between angles with an example. arithmetic solution, Resources: formed by intersecting lines and identifying the sequence Math Shell Lesson: Finding Areas of use that information to solve for Graphic Organizers: of the operations used in Circles unknown angles in a figure. each approach. Illustrative Math: Eight Circles 7.G.4 Printable Nets for 3-D Figures (These standards Illustrative Math: Illustrate the Area of Geometry Formula Sheet Additional Information: (7.G.B.4) correlate with 7.G.4 a Circle 7.G.4 Students understand the relationship because they involve Illustrative Math: Sand Under the between radius and diameter. solving equations, Swing Set 7.G.6 & 7.RP.3 Students also understand the ratio of involving rational Currently Illustrative Math does circumference to diameter can be numbers, in the form of not have tasks for 7.G.5 expressed as pi. Building on these the area and understandings, students generate circumference formula for Choose from the following the formulas for circumference and a circle.) resources and use them to area. Shelby County Schools 2016/2017 Revised 1/24/17 11 of 16 Curriculum and Instruction – Mathematics Quarter 4 Grade 7 TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES  7.G.B.5 Use facts about deepen students' conceptual supplementary, complementary, The illustration below shows the understanding of mathematical vertical, and adjacent angles in a relationship between the content and develop their ability multi-step problem to write and circumference and area. If a circle is to apply that knowledge to non- solve simple equations for an cut into wedges and laid out as routine problems. unknown angle in a figure. shown, a parallelogram results. Half of an end wedge can be moved to the Optional Resources:  7.G.B.6 Solve real-world and other end and a rectangle results. Learnzillion: Area and Circumference mathematical problems involving The height of the rectangle is the of a Circle 7.G.B.4 area, volume and surface area of same as the radius of the circle. The Learnzillion: Various Types of Angles two- and three-dimensional base length is the circumference 7.G.B.5 objects composed of triangles, (2πr). The area of the rectangle (and Math Shell Lesson: Designing a 3D quadrilaterals, polygons, cubes, therefore the circle) is found by the Product in 2D- A Sports Bag and right prisms. following calculations: Math Station Activities  7.RP.A.3 Use proportional relationships to solve Correlated iReady Lesson: The multi-step ratio and iReady program includes a variety of percent problems. (Some resources that can be used to support volume, area and surface teacher-led instruction in Tier 1 and area contextual problems guided small-group Tier 1, 2 or 3 may require the use of instruction. scale factors or unit rates to solve.)  Area and Circumference of a Circle Area = Base x Height  Problem Solving with Angles Area=(2πr)(r)  Surface Area of Composed Area = (πr)(r) Figures 2 Area = πr  Volume of Composed Figures http://mathworld.wolfram.com/Circle.  Area of Composed Figures html

Example: The center of the circle is at (5, -5). What is the area of the circle? Solution:

12 Curriculum and Instruction – Mathematics Quarter 4 Grade 7 TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES The radius of the circle is 4. Using the formula, Area = Πr2, the area of the circle is approximately 50.24 units2.

Additional Information: (7.G.5) Students use understandings of angles and deductive reasoning to write and solve equations Example: Write and solve an equation to find the measure of angle x.

Solution: Find the measure of the missing angle inside the triangle (180 – 90 – 40), or 50°. The measure of angle x is supplementary to 50°, so subtract 50 from 180 to get a measure of 130° for x.

Additional Information: (7.G.6) Students do not need to memorize formulas. They must have an understanding of why the formula works and how the formula relates to the measure (area and volume) and the figure. This understanding should be for all students.

Shelby County Schools 2016/2017 Revised 1/24/17 13 of 16 Curriculum and Instruction – Mathematics Quarter 4 Grade 7 TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES Example(s): A triangle has an area of 6 square feet. The height is four feet. What is the length of the base? Solution: One possible solution is to use the formula for the area of a triangle and substitute in the known values, then solve for the missing dimension. The length of the base would be 3 feet.

The surface area of a cube is 96 in2. What is the volume of the cube? Solution: The area of each face of the cube is equal. Dividing 96 by 6 gives the area of 16 in2 for each face. Because each face is a square, the length of the edge would be 4 in. The volume could then be found by multiplying 4 x 4 x 4 or 64 in3.

Rational Numbers, proportional relationships, Expressions and Equations (Allow approximately 4 weeks for instruction, review and assessment) 7.RP.A Analyze proportional Correlation to Grade 8 Focus Lesson Plans 7.RP.1 and 7.RP.2 relationships and use them to solve Standards Scroll to HCPSS Lessons and real-world and mathematical Tasks problems. 8.EE.B Understand the connections between proportional relationships, Lessons for Learning Lesson Plans lines and linear equations. (pp. 28-30 & 36-40).

Online Math Learning: Scroll to 7.RP section

7.NS.A Apply and extend previous Correlation to Grade 8 Focus Online Math Learning: Scroll to 7.NS understandings of operations with Standards section fractions to add, subtract, multiply 14 Curriculum and Instruction – Mathematics Quarter 4 Grade 7 TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES and divide rational numbers. Lessons for Learning Lesson Plans 8.EE.A Work with radicals and integer (pp. 5-11) exponents. Lesson Plans: 7.NS.1 Scroll to HCPSS Lessons and Tasks

Lesson Plans: 7.NS Scroll to HCPSS Lessons and Tasks 7.EE.A Use properties of operations to Correlation to Grade 8 Focus Online Math Learning: Scroll to 7.EE generate equivalent expressions. Standards section

8.EE.C Analyze and solve linear Lesson Plans: 7.EE.A Scroll to HCPSS equations and pairs of simultaneous Lessons and Tasks linear equations. Lessons for Learning Lesson Plans (pp. 12-27) 7.EE.B Solve real-life and Correlation to Grade 8 Focus Online Math Learning: Scroll to 7.EE mathematical problems using Standards section numerical and algebraic expressions and equations. 8.EE.A Work with radicals and integer Lesson Plans 7.EE.B.4 exponents. Lessons for Learning Lesson Plans 8.EE.C Analyze and solve linear (pp. 12-27) equations and pairs of simultaneous linear equations.

Shelby County Schools 2016/2017 Revised 1/24/17 15 of 16 Curriculum and Instruction – Mathematics Quarter 4 Grade 7 RESOURCE TOOLBOX NWEA MAP Resources: https://teach.mapnwea.org/assist/help_map/ApplicationHelp.htm#UsingTestResults/MAPReportsFinder.htm - Sign in and Click the Learning Continuum Tab – this resources will help as you plan for intervention, and differentiating small group instruction on the skill you are currently teaching. (Four Ways to Impact Teaching with the Learning Continuum) https://support.nwea.org/khanrit - These Khan Academy lessons are aligned to RIT scores.

Textbook Resources Standards Support Videos www.myhrw.com TNReady Math Standards Khan Academy www.connected.mcgraw-hill.com Achieve the Core Watch Know Learn Edutoolbox Learn Zillion Virtual Nerd Math Playground StudyJams

Calculator Interactive Manipulatives: Additional Sites: Texas Instruments Education National Library of Virtual PBS: Grades 6-8 Lesson Plans CASIO Activities Manipulatives TI-73 Activities Glencoe Virtual Manipulatives Frayer Model Template TI-Inspire for Middle Grades http://www.betterlessons.com http://www.insidemathematics.org Foldables Vocabulary Math Cards Middle School Mathematics Vocabulary Word Wall Cards Grade 7 Flip Book (This book contains valuable resources that help develop the intent, the understanding and the implementation of the state standards.)