shelby county schools’ mathematics instructional maps are … 6 2016_17 q3 re… · web...

Major Content Supporting Content Additional Content

Curriculum and Instruction – Mathematics Quarter 3 Grade 6

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

Shelby County Schools 2016/2017Revised 12/8/16

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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.


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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.


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Mathematical Practices

1. Make sense of problems and persevere in solving them

2. Reason abstractly and quatitatively

3. Construct viable arguments and

crituqe the reasoning of

others

4. Model with mathematics

5. Use appropriate tools strategically

6. Attend to precision

7. Look for and make use of

structure

8. Look for and express regularity

in repeated reasoning



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:


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The TN Mathematics StandardsThe Tennessee Mathematics Standards:https://www.tn.gov/education/article/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


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https://www.tn.gov/education/article/mathematics-standards



Mathematical Practice Standardshttps://drive.google.com/file/d/0B926oAMrdzI4RUpMd1pGdEJTYkE/view

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.


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https://drive.google.com/file/d/0B926oAMrdzI4RUpMd1pGdEJTYkE/view



Purpose of the Mathematics Curriculum Maps


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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.


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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 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.


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Additional Instructional SupportShelby 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.


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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 MapsShelby County Schools 2016/2017

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OverviewAn 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 StandardsThe 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


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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.

ContentTeachers 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”


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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 ResourcesDistrict 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.


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Topics Addressed in QuarterVariables and ExpressionsWriting Equations and InequalitiesSolving Equations and Inequalities

Independent and Dependent VariablesArea of Triangles, Special Quadrilaterals and PolygonsPolygons in Coordinate Plane


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Overview Students begin quarter 3 by reasoning about and solving one-variable inequalities and equations, using their knowledge of order of operations and the properties of equality for addition, subtraction, multiplication, and division. They will identify values for the variable in an equation and inequality that result in true number sentences (6.EE.5) and recognize that inequalities of the form x < c and x > c, where x is a variable and c is a fixed number have infinitely many solutions when the values of x come from a set of rational numbers (6.EE.5, 6.EE.8).


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Students learn the definition of solution in the context of placing a value into a variable to see if it makes the equation true (6.EE.7) and will later use this knowledge of simplifying expressions, order of operations and properties of equality to calculate the solution of multi-step equations and determine if their solution makes the equation true (6.EE.6). This work leads to analyzing equations in two variables to choose an independent variable and dependent variable.

Students determine whether or not the equation is solved for the second variable in terms of the first variable or vice versa and then use this information to determine which variable is independent and which is dependent. Students analyze an equation in two variables, choose an independent variable and a dependent variable, make a table using the variables and then graph the equation by plotting the points in the table (6.EE.9). Students will notice that for the graph, the independent variable is usually represented by the horizontal axis and the dependent variable is usually represented by the vertical axis. All of the


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concepts and skills lead to future work in reasoning with equations and inequalities (algebra 1), analyzing simultaneous equations (8.EE.8) and understanding that graphs of equations, in two variables, is the set of all its solutions plotted in a coordinate plane (algebra 1).

Near the end of the quarter students will use their knowledge of solving simple equations and graphing when they begin work in geometry. Students will solve problems that involve calculating the area of figures by decomposition and finding lengths of sides of polygons drawn in a coordinate plane (6.G.1 & 3).


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Year at a Glance DocumentGrade Level Standard Type of Rigor Foundational Standards Sample Assessment Items

6.EE.5 Conceptual Understanding, 5.OA.2, 5.OA.3, 6.EE.1 Learn Zillion: 6.EE.5-8


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https://learnzillion.com/lesson_plans/4330

https://drive.google.com/file/d/0B7EG2snqrtxHUFRRQnZZZVBJcm8/view?usp=sharing



Procedural Skill & Fluency 6.EE.6 Conceptual Understanding;

Application5.OA.2, 5.OA.3, 6.EE.1 Learn Zillion: 6.EE. 6 & 9

6.EE.7 Procedural & Application 5.NF.1, 5.NF.4, 6.NS.1 Illustrative Math: 6.EE6.EE.8 Conceptual Understanding &

Application6.NS.6, 6.NS.7 Achieve the Core: 6.EE

6.EE.9 Conceptual Understanding & 5.OA.3 NAEP Released Items: 6.EE.9 (pp. 11-15)


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https://www.educateiowa.gov/sites/files/ed/documents/NAEP%20-%20Grade%206%20Tasks%20-%20Expressions%20%26%20Equations.pdf

http://achievethecore.org/page/910/extending-previous-understandings-of-properties-mini-assessment

https://www.illustrativemathematics.org/content-standards/6/EE




Application 6.G.1 Procedural Skill & Fluency;

Application5.NF.4 Illustrative Math: 6.G.1;

6.G.3 Procedural Skill & Fluency; Application

5.G.2 NAEP Released Items: 6.G.1 & 3 (pp. 1-12)

engage ny Assessment: Select Grade 6


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https://www.engageny.org/resource/new-york-state-common-core-sample-questions

https://www.educateiowa.gov/sites/files/ed/documents/NAEP%20-%20Grade%206%20Tasks%20-%20Geometry.pdf

https://www.illustrativemathematics.org/content-standards/6/G/A/1/tasks/647




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Fluency Shelby County Schools 2016/2017

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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 6th grade listed below should be incorporated throughout your instruction over the course of the school year. Click engage ny Fluency


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https://www.engageny.org/resource/mathematics-fluency-support-grades-6-8/file/133021



Support to access exercises that can be used as a supplement in conjunction with building conceptual understanding.

6.NS.2 Fluently divide multi-digit numbers using standard algorithms 6.NS.3 Fluently add, subtract, multiply and divide multi-digit decimals

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


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http://www.nctm.org/Standards-and-Positions/Position-Statements/Procedural-Fluency-in-Mathematics/

http://www.corestandards.org/

https://www.engageny.org/

https://www.engageny.org/resource/mathematics-fluency-support-grades-6-8/file/133021



http://achievethecore.org/


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http://achievethecore.org/




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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESExpressions, Equations and Inequalities

(Allow approximately 6 weeks for instruction, review and assessment)Domain: Expressions and EquationsCluster: Reason about and solve one-variable equations and inequalities

6.E E . B .5: Understand solving an

Enduring Understanding(s): Equations and inequalities can be used to

model real-world situations.

Essential Question(s): Which values from a specified set, if any,

Glencoe5-1B Variables and Expressions (pp. 274-278)5-1D Write Expressions (pp. 282-285)6-1A Equations (pp. 314-317)6-1D Solve and Write Addition Equations (pp.

Vocabulary: equations, equal sign, solve, solution, inequality, solution set, nonnegative rational number, substitution, algebraic expressions, variable, defining the variable


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http://www.tn.gov/education/standards/math/std_math_gr_6.pdf



TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESequation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

make an equation or inequality true? In what ways can you reason and solve

one-variable equations and inequalities? How might an inequality describe a real-life

problem? How do expressions and equations apply

to real life situations?

322-326)6-2B Solve and Write Multiplication Equations (pp. 335-338)

Holt2-1 Variables and Expressions (pp. 50-53)

Writing in Math:Write a real-world problem that could be represented by the following equation:d – 32 = 64


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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES 6.EE.B.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

Objective(s): Students will explain what the solution

represents as it relates to an equation or inequality.

Students will determine whether a number is a solution of an equation or if a number from a specified set makes an inequality true.

2-4 Equations and their Solutions (pp. 66-69)2 – 5 Addition Equations (pp. 70-73)2 -7 Multiplication Equations (pp. 77-80)

Building Conceptual Understanding:Math Shell Concept Development Lesson:


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http://map.mathshell.org/lessons.php?unit=6215&collection=8&redir=1




TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

6.E E . B .7: Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

Additional Information: Students explore equations as

expressions being set equal to a specific value. The solution is the value of the variable that will make the equation or inequality true.

Students will use various processes to

Interpreting Equationsengage ny : True and False Number Sentences Lesson 23engage ny : True and False Number Sentences

Choose from the following resources and use them to deepen students' conceptual understanding of mathematical content and


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https://www.engageny.org/resource/grade-6-mathematics-module-4-topic-g-lesson-24



http://map.mathshell.org/lessons.php?unit=6215&collection=8&redir=1




TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESidentify which substituted value(s) satisfy the equation or inequality.

Examples:The equation 0.44s = 11 where s represents the number of stamps in a booklet. The booklet of stamps costs 11 dollars and each stamp costs 44 cents. How many stamps are in the booklet? Explain the strategies you used

develop their ability to apply that knowledge to non-routine problems.

Suggested Additional Lesson(s):engage n y: Finding Solutions to Make Equations TrueBetter Lesson: Reasoning About Inequality Solution Sets


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http://betterlesson.com/lesson/544180/reasoning-about-inequality-solution-sets

http://betterlesson.com/lesson/544180/reasoning-about-inequality-solution-sets





TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESto determine your answer. Show that your solution is correct using substitution.

Solution: There are 25 stamps in the booklet. I got my answer by dividing 11 by 0.44 to determine how many groups of 0.44 were in 11. By substituting 25 in for s and then multiplying, I get 11.

Better Lesson: Writing Simple InequalitiesBetter Lesson: Equations to Represent Real-world Scenarios

Suggested Task(s):You must establish a free account to access Edutoolbox.org resources.TN Task Ark: Exploring Expressions and


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http://www.edutoolbox.org/system/files/rasp_file/6_EE_5thru8ArcFINAL.pdf

http://betterlesson.com/lesson/543969/writing-algebraic-equations-to-represent-real-world-scenarios-one-step

http://betterlesson.com/lesson/543969/writing-algebraic-equations-to-represent-real-world-scenarios-one-step

http://betterlesson.com/lesson/544181/writing-simple-inequalities




0.44(25) = 11. 11 = 11 ✓

Twelve is less than 3 times another number can be shown by the inequality 12 < 3n. What numbers could possibly make this a true

EquationsIllustrative Math: Morning WalkIllustrative Math: Log Ride TaskIllustrative Math: Firefighter Allocation

Suggested Additional Resource(s):Learn Zillion: Justify multiple solutions to an inequality by substituting for an unknown


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https://www.illustrativemathematics.org/content-standards/6/EE/B/6/tasks/425




TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESstatement?

Solution: Since 3 x 4 is equal to 12, the value must be greater than 4. Therefore, any value greater than 4 will make the inequality true.

Lea r n Z i l l i on E v a l u a t i ng Expre s s i o ns w i t h Subs t it u t i on Lea r n Z i l l i on S o l v i ng A dd iti o n / Su b t r ac t i on

Equa t i ons Learn Zillion: Write and solve single-step equations that involve multiplication


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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESCorrelated iReady Lesson(s): The iReady program includes a variety of resources that can be used to support teacher-led instruction in Tier 1 and guided small-group Tier 1, 2 or 3 instruction.

Solving Inequalities Solving Equations Using Equations to Solve Problems


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Domain: Expressions and EquationsCluster: Reason about and solve one-variable equations and inequalities; Represent and analyze quantitative relationships between dependent and independent variables.

Enduring Understanding(s): Variables and inequality symbols can be

used to represent two quantities in a real-world problem that change in relationship to one another.

The relationship between two variables begins with the distinction between dependent and independent variables.

Glencoe7-2B Inequalities (p. 396-399) Only cover the following from this lesson because they directly address the standard.Concept Summary, Real-World Example 4, Practice & Problem Solving #14-15; H.O.T Problem #18; Test Practice # 19-20

Vocabulary: inequality, solution of an inequality, constraint, dependent variable, independent variable

Writing in Math:Have students to explain why some inequalities have an infinite number of solutions. Also have them to describe how to


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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES 6.E E . B .8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

Essential Question(s): How might an inequality describe a real-life

situation? How can a numerical constraint be

represented algebraically? How can you show that inequalities can

have infinitely many solutions? In what ways can you show the relationship

7-2D Write and Graph Inequalities (pp 402-405)

Holt13-1 Tables and Functions (pp. 699-701)When covering this lesson remember that

represent inequality constraints on a number line.Have students think of and write about real-world situations in which a function is used to find the relationship between two quantities. Have them write the equation for the function and find the y-values for any three x-values.


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6.E E . C .9: Use variables to represent twoquantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between

between dependent and independent variables?

Objective(s): Students will write inequalities that

represent a specific condition in a real-world math problem.

Students will analyze the relationship

the standards are not asking students to solve equations.

13-2 Graphing FunctionsOnly cover the following from this lesson because they directly address the standard. p. 702 Warm-up; p. 703 Ex. 3; p. 705 # 30


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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESthe dependent and independent variables using graphs and tables, and relate these to the equation.

between the dependent and independent variables using graphs and tables, and relate these to the equation.

Students will explain the difference between the independent variable and the dependent variable

Students will write an equation to express the quantity in terms of the dependent and

13 - 5 Inequalities (pp. 718-721)Only cover the following from this lesson because they directly address the standard.p.718; p. 720 #1-6, 19-24, 37-39, 41-42, p. 721 #49-55


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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESindependent variable.

Students will relate the dependent and independent variables to the equation.

Additional Information: Students can use many forms to represent

relationships between quantities. Multiple representations include describing the

Choose from the following resources and use them to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.

Building Conceptual Understanding:engage NY : Writing and Graphing Inequalities in


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https://www.engageny.org/resource/grade-6-mathematics-module-4-topic-h-lesson-34



TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESrelationship using language, a table, an equation, or a graph. Translating between multiple representations helps students understand that each form represents the same relationship and provides a different perspective on the function.

Real-World Problems 6.EE.8engage ny : Problems in Mathematical Terms 6.EE.9

Suggested Additional Lesson(s):engage ny : Multi-Step Problems in the Real World 6.EE.9


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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES Students will write inequalities to represent

real world and mathematical situations. They should also recognize when to use an open or shaded circle when graphing inequalities.

Examples:1. Graph x ≤ 4.

Learn Zillion: Recognize how an equation relates independent and dependent variables 6.EE.C.9

Suggested Task(s):TN Task Ark: Exploring Expressions and Equations (6.EE.8 tasks) Illustrative Math: Fishing Adventures 6.EE.B.8


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2. An inequality is shown: x > 4 Select the statement(s) and number line(s) that can be represented by the inequality. Circle all that apply. A. The temperature increased by 4∘

Illustrative Math: Height Requirements 6.EE.B.8Illustrative Math: Chocolate Bar Sales 6.EE.C.9

Suggested Additional Resources:Station Activities pp. 51 & 82Learn Zillion: 6.EE.B.8 Lessons 11, 12 & 14


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https://learnzillion.com/search?utf8=%E2%9C%93&query=6.ee.b.8&page=1&sort=Relevance&models%5B%5D=LessonPlan&models%5B%5D=Resource

https://drive.google.com/file/d/0B83r9RBkwHBQWDV1cWxNenVCSFU/edit

https://www.illustrativemathematics.org/content-standards/6/EE/C/9/tasks/806

https://www.illustrativemathematics.org/content-standards/6/EE/C/9/tasks/806





TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESFahrenheit. B. The value of a number substituted for x is greater than 4. C. Marcus drinks more than 4 glasses of water every day. D.

Correlated iReady Lesson(s): The iReady program includes a variety of resources that can be used to support teacher-led instruction in Tier 1 and guided small-group Tier 1, 2 or 3 instruction. Applying a Function Rule to Complete a

Table


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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESE.

3. Jonas spent more than $50 at an amusement park. Write an inequality to represent the amount of money Jonas spent. What are some possible amounts of money Jonas could have spent? Represent the situation on a number

Writing Function Rules Relationships Between Variables I

Equations


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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESline.

0 50 100

4. Less than $200.00 was spent by the Flores family on groceries last month. Write an inequality to represent this


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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESamount and graph this inequality on a number line.

Solution: 200 > x


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The purpose of standard 6.EE.9 is for students to understand the relationship between two variables, which begins with the distinction between dependent and independent variables. The independent variable is the variable that can be changed; the dependent variable is the


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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESvariable that is affected by the change in the independent variable. Students recognize that the independent variable is graphed on the x-axis; the dependent variable is graphed on the y-axis.

Example:What is the relationship between the two


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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESvariables? Write an expression that illustrates the relationship.

x 1 2 3 4y 2.5 5 7.5 10

Solution:y = 2.5x

Area of triangles, Special Quadrilaterals and Polygons in the Coordinate PlaneShelby County Schools 2016/2017

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES(Allow approximately 3 weeks for instruction, review and assessment)

Domain: GeometryCluster: Solve real-world and mathematical problems involving area, surface area and volume.

6. G . A .1: Find the area of right triangles, other triangles, special quadrilaterals, and

Enduring Understanding(s): Everyday objects have a variety of

attributes, each of which can be measured in many ways.

Essential Question(s):

Glencoe9-1A Area of Parallelograms (pp. 522-527)9-1B Explore Area of Triangles (p. 528)9-1C Area of Triangle (pp. 529-534)9-1D Area of Trapezoids (pp. 535-539)9-3C Area of Composite Figures (pp. 561-565)

Vocabulary: right triangle, quadrilateral, polygon, vertex, edge, area, decompose, base, height

Writing in Math:Describe the relationship that exists between the area of one triangle and the area of the


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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESpolygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

6. G . A .3: Draw polygons in the coordinate plane given coordinates for the vertices;

How can you find the area of composite figure?

How can my understanding of finding areas of rectangles and triangles help find the area of another shape?

How can the coordinate plane be used as a strategy to find the length of a side of a figure and the area of a figure?

Additional Lesson 7: Polygons on the Coordinate Plane (pp. 801-806)

Holt10-1 Area of Rectangles and Parallelograms (pp. 534-537)Companion 11-4A Polygons in the Coordinate

parallelogram.

Find an example of a map that uses longitude and latitude in a magazine or on the Internet. Write a real-world problem in which you can find the approximate area of a location on the map.


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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESuse coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

6.NS.8 Solve real-world and

Objective(s): Students will decompose a rectangle into

triangles. Students will find areas and missing

dimensions of parallelograms. Students will draw polygons in a coordinate

Plane10-2 Area of Triangles and Trapezoids (page 540 -543)10-3 Area of Composite Figures (page 545-547)

Building Conceptual Understanding:

Graphic Organizers:Special Quadrilateral Foldable Instructions Properties of Parallelogram Foldable Area Formulas for Triangles/Rectangles/Other Shapes


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http://www.mathnstuff.com/math/spoken/here/2class/150/area.htm

http://www.mathnstuff.com/math/spoken/here/2class/150/area.htm

https://pamjwilson.wordpress.com/2012/10/15/made4math-monday-parallelogram-foldable/

http://www.authorstream.com/Presentation/Brainy007-5146-Foldable-Quadrilaterals-Designed-foldable-for-quadrilaterals-ppt-powerpoint/

http://tn.gov/education/article/mathematics-standards



TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESmathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. (This standard was introduced in quarter

plane.

Additional Information:Students should understand that area is the number of squares needed to cover a plane figure. Students should understand why the area formulas for rectangles and triangles

Connected Math Lesson: Investigations 1-4Covering & Surrounding Additional Resources

Choose from the following resources and use them to deepen students' conceptual understanding of mathematical content and develop their ability to apply that


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http://etorgerson.net/CMP_Covering.html

http://www.ridleysd.k12.pa.us/cms/lib2/PA01001042/Centricity/Domain/572/Covering%20Textbook.pdf



TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES2; however, it also supports 6.G.A.3 because both standards deal with finding the distance between points on a coordinate grid.)

work.

Finding the area of triangles is introduced in relationship to the area of rectangles – a rectangle can be decomposed into two congruent triangles. Therefore, the area of the triangle is half the area of the rectangle. The area of a rectangle can be found by multiplying

knowledge to non-routine problems.

Suggested Additional Lesson(s):engage ny Lessons: 6.G.A.1 engage ny Lessons: 6.G.A.3 Better Lesson: 6.G.A.1Better Lesson: 6.G.A.3


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http://betterlesson.com/search?common_core_id=372&from=autocomplete_option

http://betterlesson.com/common_core/browse/370/ccss-math-content-6-g-a-1-find-area-of-right-triangles-other-triangles-special-quadrilaterals-and-polygons-by-composing-into-rec

https://www.engageny.org/resource/grade-6-mathematics-module-5-topic-b-overview

https://www.engageny.org/resource/grade-6-mathematics-module-5-topic-overview



TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESbase x height; therefore, the area of the triangle is 1/2bh or (b x h)/2. The following site helps students to discover the area formula of triangles.

NCTM Illuminations: Discovering the Area Formula for a Triangle

Special quadrilaterals include rectangles,

Suggested Task(s)Illustrative Math: Finding Area of Polygons TaskIllustrative Math: Polygons in the Coordinate Plane TaskIllustrative Math: Same Base Height Variation 2 Task


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http://illuminations.nctm.org/Lesson.aspx?id=1874

http://illuminations.nctm.org/Lesson.aspx?id=1874



TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESsquares, parallelograms, trapezoids, rhombi, and kites. Students can use tools such as the Isometric Drawing Tool on NCTM’s Illuminations site to shift, rotate, color, decompose and view figures in2D or 3D

Illuminations: Isometric Drawing Tools

Illustrative Math: Same Base and Height Variation 1 Task

Suggested Additional Resources:NCTM ARC: Discovering Area RelationshipsShodor: Build Your Own Polygon in a Plane O n li ne M a t h L e a r n i ng A r ea of T r i an g l e s Shodor: Triangle Explorer Activity


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http://www.shodor.org/interactivate/activities/TriangleExplorer/

http://www.shodor.org/interactivate/textbooks/section/280/

http://www.nctm.org/Classroom-Resources/ARCs/Discovering-Area-Relationships/

http://illuminations.nctm.org/Activity.aspx?id=4182



TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESStudents decompose shapes into rectangles and triangles to determine the area. For example, a trapezoid can be decomposed into triangles and rectangles (see figures below). Using the trapezoid’s dimensions, the area of the individual triangle(s) and rectangle can be found and then added together.

Khan Academy: Area of a ParallelogramsLea r n Z i l l i on P o l yg ons i n C oo r d i na t e P l ane A r ea o f C o m pos it e Fi g u r es A dd i t i on a l Pr a c ti c e I n t e r ac t i v e Area o f C o m pos it e S hap e s

Correlated iReady Lesson(s): The iReady


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Example(s):

program includes a variety of resources that can be used to support teacher-led instruction in Tier 1 and guided small-group Tier 1, 2 or 3 instruction.

Concepts of Area and Perimeter Area of Parallelograms,

Quadrilaterals, and Polygons Polygons in a Coordinate Plane


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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESFind the area of the trapezoid shown below using the formulas for rectanglesand triangles


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Students should be able to draw a figure on the coordinate plane given the coordinates.


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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESStudents should recognize the conditions under which a vertical line or horizontal line will be created.

Example(s): If the points on the coordinate plane below

are the three vertices of a rectangle, what are the coordinates of the fourth vertex?


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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESHow do you know? What are the length and width of the rectangle? Find the area and the perimeter of the rectangle.


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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESSolution:To determine the distance along the x-axis between the point (-4, 2) and (2, 2) a student must recognize that -4 is |-4| or 4 units to the left of 0 and 2 is |2| or 2 units to the right of zero, so the two points are total of 6 units apart along the x-axis. Students should represent this on the coordinate grid and numerically


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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESwith an absolute value expression, |-4| + |2|. The length is 6 and the width is 5.The fourth vertex would be (2, -3).The area would be 5 x 6 or 30 units2.The perimeter would be 5 + 5 + 6 + 6 or 22 units.

On a map, the library is located at (-2, 2),


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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESthe city hall building is located at (0, 2), and the high school is located at (0, 0). Represent the locations as points on a coordinate grid with a unit of 1 mile. What is the distance from the library to the city hall building? What is the distance from the city hall building to the high school? How do you know?


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What shape is formed by connecting the three locations? The city council is planning to place a city park in this area. How large is the area of the planned park?

The area of the rectangular school garden is 24 square units. The length of


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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESthe garden is 8 units. What is the length of the fence needed to enclose the entire garden?

The sixth grade class at Hernandez School is building a giant wooden H for their school. The “H” will be 10 feet tall and 10 feet wide and the thickness of the block letter will be


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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES2.5 feet.

1. How large will the H be if measured in square feet?2. The truck that will be used to bring the wood from the lumberyard to the school can only hold a piece of wood that is 60 inches by 60 inches. What pieces of wood (how many and which dimensions) will need to be bought to


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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCEScomplete the project?

Solution:1. One solution is to recognize that, if filled in, the area would be 10 feet tall and 10 feet wide or 100 ft2. The size of one piece removed is 5


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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESfeet by 3.75 feet or 18.75 ft2. There are two of these pieces. The area of the “H” would be 100 ft2 – 18.75 ft2 – 18.75 ft2, which is 62.5ft2.A second solution would be to decompose the “H” into two tall rectangles measuring 10 ft by 2.5 ft and one smaller rectangle measuring 2.5 ft by 5 ft. The area of each tall rectangle would be 25 ft2 and the area of the smaller rectangle


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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESwould be 12.5 ft2. Therefore the area of the “H” would be 25 ft2 + 25 ft2 + 12.5 ft2 or 62.5ft2.2. Sixty-inches is equal to 5 feet, so the dimensions of each piece of wood are 5ft by 5ft. Cut two pieces of wood in half to create four pieces 5 ft. by 2.5 ft. These pieces will make the two taller rectangles. A third piece would be cut to measure 5ft. by 2.5 ft. to


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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCEScreate the middle piece.


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RESOURCE TOOLBOXThe Resource Toolbox provides additional support for comprehension and mastery of grade-level skills and concepts. While some of these resources are imbedded in the map,

the use of these categorized materials can assist educators with maximizing their instructional practices to meet the needs of all students.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


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https://support.nwea.org/khanrit

https://teach.mapnwea.org/assist/help_map/ApplicationHelp.htm#UsingTestResults/MAPReportsFinder.htm



www.myhrw.comwww.connected.mcgraw-hill.com

TNReady Math StandardsAchieve the CoreEdutoolbox

Khan AcademyWatch Know LearnLearn ZillionVirtual NerdMath PlaygroundStudy Jams

Calculator ActivitiesTI-73 Activities

Interactive ManipulativesNational Library of Virtual Manipulatives - NLVM

Additional SitesPBS: Grades 6-8 Lesson Plans


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http://www.learner.org/resources/lessonplanbrowse.html?g%5B%5D=6-8&d%5B%5D=MATH

http://nlvm.usu.edu/en/nav/category_g_3_t_2.html

http://education.ti.com/en/us/activity/search/subject?d=E6BF78EF098644A8A458D8D1B4AA1A44&s=B843CE852FC5447C8DD88F6D1020EC61&sa=3702C4C225D647AD888ECE38B4EB90A2

http://studyjams.scholastic.com/studyjams/jams/math/index.htm

http://www.mathplayground.com/

http://www.virtualnerd.com/

https://learnzillion.com/login

http://ccss6.watchknowlearn.org/Category.aspx?CategoryID=15865

http://www.khanacademy.org/

http://www.edutoolbox.org/

http://achievethecore.org/category/854/mathematics-lessons

http://tn.gov/education/article/mathematics-standards

http://www.connected.mcgraw-hill.com/

http://www.myhrw.com/



CASIO ActivitiesTI-Inspire for Middle Grades

Interactive Cartesian Plane Math Is Fun AAA Math: EquationsFrayer Model TemplateGrade 6 Flip Book (This book contains valuable resources that help develop the intent, the understanding and the implementation of the state standards.)


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http://community.ksde.org/LinkClick.aspx?fileticket=5-B58NkWJIs%3D&tabid=5646&mid=13290

http://wvde.state.wv.us/strategybank/FrayerModel.html

http://www.aaastudy.com/equ.htm

http://www.mathsisfun.com/data/cartesian-coordinates-interactive.html

http://education.ti.com/en/timathnspired/us/middle-grades-math

http://www.casioeducation.com/educators/activities

shelby county schools’ mathematics instructional maps are … 6 2016_17 q3 re… · web...

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