Quarter 4 Grade 5
Unit 1
Module
Aug. 10- Sept. 7 / Unit 2
Module
Sept.8-Nov. 3 / Unit 3
Module
Nov. 4-Dec. 8 / Unit 4
Module
Dec. 9- Feb. 10 / Unit 5
Module
Feb. 13- Mar. 24 / Unit 6
Module
Mar. 27- May 26
PlaceValueandDecimalFractions / Multi-Digit Whole Number and Decimal Fraction Operations / Additionand Subtraction of Fractions / Multiplication andDivision of Fractionsand Decimal Fractions / Additionand Multiplication withVolume and Area / Problem Solving withthe Coordinate Plane
5.NBT.A.1 / 5.OA.A.1 / 5.NF.A.1 / 5.OA.1 / 5.NF.B.4b / 5.OA.A.2
5.NBT.A.2 / 5.OA.A.2 / 5.NF.A.2 / 5.OA.2 / 5.NF.6 / 5.OA.B.3
5.NBT.A.3 / 5.NBT.A.1 / 5.NBT.B.7 / 5.MD.C.3 / 5.G.A.1
5.NBT.A.4 / 5.NBT.A.2 / 5.NF.B.3 / 5.MD.C.4 / 5.G.A.2
5.NBT.B.7 / 5.NBT.B.5 / 5.NF.B.4a / 5.MD.C.5
5.MD.A.1 / 5.NBT.B.6 / 5.NF.B.5 / 5.G.B.3
5.NBT.B.7 / 5.NF.B.6 / 5.G.B.4
5.MD.A.1 / 5.NF.7
5.MD.1
5.MD.2
Mathematics Grade 5
Year at a Glance 2016-2017
Key:
Major Clusters / Supporting Clusters / Additional ClustersNote: Please use the suggested pacing as a guide.
Use this guide as you prepare to teach a module for additional guidance in planning, pacing, and suggestions for omissions. Pacing and Preparation Guide (Omissions)
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, Destination2025. 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 readinessis 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.
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 StandardsThe Tennessee Mathematics Standards:
/ Teachers can access the Tennessee State standards, which are featured throughout this curriculum map and represent college and career ready learning at reach respective grade level.
Standards for Mathematical Practice
Standards for Mathematical Practice
/ Teachers can access the Mathematical Practice Standards, which are featured throughout this curriculum map. This link contains more a more detailed explanation of each practice along with implications for instructions.
Purpose of Mathematics Curriculum Maps
This 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 map is designed to reinforce the grade/course-specific standards and content—the major work of the grade (scope)—and provides suggested sequencing, pacing, time frames, and aligned resources. 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, 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, text(s), 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 judgment 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 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 K-5 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 alignmentto meet the expectations of the CCR standards and related instructional shifts while stillincorporating 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 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 specific examples of student work.
Tennessee State Standards
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 the 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 teachers' responsibility to examine the standards and skills needed in order to ensure student mastery of the indicated standard.
Content
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,performance in the major work of the grade) . 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 learning targets/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 Resources
District and web-based resources have been provided in the Instructional Resources column. At the end of each module 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.
Vocabulary and Fluency
The inclusion of vocabulary serves as a resource for teacher planning, and for building a common language across K-12 mathematics. One of the goals for CCSS is to create a common language, and the expectation is that teachers will embed this language throughout their daily lessons.
In order to aid your planning we have included a list of fluency activities for each lesson. It is expected that fluency practice will be a part of your daily instruction. (Note: Fluency practice is NOT intended to be speed drills, but rather an intentional sequence to support student automaticity. Conceptual understanding MUST underpin the work of fluency.)
Grade 5 Quarter 4 Overview
Module 5:Addition and Multiplication with Volume and Area (continued from Q3)
Module 6: Problem Solving with Coordinate Planes
Overview
In Quarter 4, module 3 will continue with the completion of Module 5. In Topic D, students draw two-dimensional shapes to analyze their attributes and use those attributes to classify them. Familiar figures, such as parallelograms, rhombuses, squares, trapezoids, etc., have all been defined in earlier grades and, in Grade 4, students have gained an understanding of shapes beyond the intuitive level. Grade 5 extends this understanding through an in-depth analysis of the properties and defining attributes of quadrilaterals. Grade 4’s work with the protractor is applied to construct various quadrilaterals. Using measurement tools illuminates the attributes used to define and recognize each quadrilateral (5.G.3). Students see, for example, that the same process they used to construct a parallelogram also produces a rectangle when all angles are constructed to measure . Students then analyze defining attributes and create a hierarchical classification of quadrilaterals (5.G.4).
Quarter 4 ends with the completion of Module 5. In this module, students develop an understanding of the coordinate system for the first quadrant of the coordinate plane and use it to solve problems. Students use the familiar number line as an introduction to the idea of a coordinate and construct two perpendicular number lines to create a coordinate system on the plane. They see that just as points on the line can be located by their distance from 0, the plane’s coordinate system can be used to locate and plot points using two coordinates. They then use the coordinate system to explore relationships between points, ordered pairs, patterns, lines and, more abstractly, the rules that generate them. This study culminates in an exploration of the coordinate plane in real world applications.
In Topic A, students come to realize that any line, regardless of orientation, can be made into a number line by first locating zero, choosing a unit length, and partitioning the length-unit into fractional lengths as desired. They are introduced to the concept of a coordinate as describing the distance of a point on the line from zero. As students construct these number lines in various orientations on a plane, they explore ways to describe the position of points not located on the lines. This discussion leads to the discovery that a second number line, perpendicular to the first, creates an efficient, precise way to describe the location of these points. Thus, points can be located using coordinate pairs, by starting at the origin, traveling a distance of units along the -axis, and units along a line parallel to the -axis. Students describe given points using coordinate pairs as well as use given coordinate pairs to plot points (5.G.1). The topic concludes with an investigation of patterns in coordinate pairs along lines parallel to the axes, which leads to the discovery that these lines consist of the set of points whose distance from the - or -axis is constant.
Students move in to plotting points and using them to draw lines in the plane in Topic B (5.G.1). They investigate patterns relating the - and -coordinates of the points on the line and reason about the patterns in the ordered pairs, laying important groundwork for Grade 6 proportional reasoning. Topic B continues as students use given rules (e.g., multiply by 2, then add 3) to generate coordinate pairs, plot points, and investigate relationships. Patterns in the resultant coordinate pairs are analyzed, leading students to discover that such rules produce collinear sets of points. Students next generate two number patterns from two given rules, plot the points, and analyze the relationships within the sequences of the ordered pairs (5.OA.3). Patterns continue to be the focus as students analyze the effect on the steepness of the line when the second coordinate is produced through an addition rule as opposed to a multiplication rule (5.OA.2, 5.OA.3). Students also create rules to generate number patterns, plot the points, connect those points with lines, and look for intersections.
Topic C finds students drawing figures in the coordinate plane by plotting points to create parallel, perpendicular, and intersecting lines. They reason about what points are needed to produce such lines and angles, and then investigate the resultant points and their relationships. Students also reason about the relationships among coordinate pairs that are symmetric about a line (5.G.1).
Problem solving in the coordinate plane is the focus of Topic D. Students draw symmetric figures using both angle size and distance from a given line of symmetry (5.G.2). Line graphs are also used to explore patterns and make predictions based on those patterns (5.G.2, 5.OA.3). To round out the topic, students use coordinate planes to solve real world problems.
Topic E provides an opportunity for students to encounter complex, multi-step problems requiring the application of concepts and skills mastered throughout the Grade 5 curriculum. They use all four operations with both whole numbers and fractions in varied contexts. The problems in Topic E are designed to be non-routine, requiring students to persevere in order to solve them. While wrestling with complexity is an important part of Topic E, the true strength of this topic is derived from the time allocated for students to construct arguments and critique the reasoning of their classmates. After students have been given adequate time to ponder and solve the problems, two lessons are devoted to sharing approaches and solutions. Students will partner to justify their conclusions, communicate them to others, and respond to the arguments of their peers.
In this final topic of Module 6, Topic F, and in fact, A Story of Units, students spend time producing a compendium of their learning. They not only reach back to recall learning from the very beginning of Grade 5, but they also expand their thinking by exploring such concepts as the Fibonacci sequence. Students solidify the year’s learning by creating and playing games, exploring patterns as they reflect back on their elementary years. All materials for the games and activities are then housed for summer use in boxes created in the final two lessons of the year.
Focus Grade Level Standard / Explicit Components of Rigor / Foundational Standards5.OA.A.2 / Conceptual Understanding / 5.OA.A.1
5.OA.B.3 / Conceptual Understanding / 4.OA.C.5, 3.OA.D.9
5.G.A.1 / Conceptual Understanding / 3.NF.A.2, 2.MD.B.6
5.G.A.2 / Conceptual Understanding, Procedural Skill and Fluency, Application / 3.NF.A.1, 2.MD.B.6
5.G.B.3 / Conceptual Understanding / 3.G.A.1, 4.G.A.2
5.G.B.4 / Conceptual Understanding / 5.G.B.3
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.
Fluency is designed to promote automaticity by engaging students in daily practice. Automaticity is critical so that students avoid using lower-level skills when they are addressing higher-level problems. The automaticity prepares students with the computational foundation to enable deep understanding in flexible ways. Therefore, it is recommended that students participate in fluency practice dailyusing the resources provided in the curriculum maps. Special care should be taken so that it is not seen as punitive for students that might need more time to master fluency.