Shelby County Schools’ mathematics instructional maps ... 6 2016_17 Q3 10… · Web viewIn 2014, the Shelby County Schools Board of Education adopted a set of ambitious, yet attainable

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 9/27/16

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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 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-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 QuarterUse Positive & Negative Numbers to Represent Quantities in Real-World ContextRational Numbers and the Number LineRational Numbers and the Coordinate Plane

Ordering Rational NumbersGraphing PointsDraw Polygons in Coordinate Plane


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Absolute Value of Rational Numbers

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 & 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. They then use this information to determine which variable is independent and which is dependent and analyze an equation in two variables, choose an independent variable and a dependent variable, make a table and a graph for 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.


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Near the end of the quarter students will begin work on geometry by solving 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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Grade 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 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 TNCore Assessment Task: 6.EE.5-66.EE.8 Conceptual Understanding Achieve the Core: 6.EE


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

http://tncore.org/sites/www/Uploads/CRA_Tasks/PhaseIII/G6MowingtheLawnTaskAnchorSet.pdf

https://learnzillion.com/lesson_plans/4270




6.EE.9 Conceptual Understanding, Procedural Skill & Application

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

6.G.1 Procedural Skill & Fluency; Application

5.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

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



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.


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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 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/


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http://www.corestandards.org/

https://www.engageny.org/

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

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



http://www.nctm.org/ http://achievethecore.org/

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

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

model real-world situations.

Glencoe5-1B Variables and Expressions (pp. 274-278)5-1D Write Expressions (pp. 282-285)

Vocabulary: equations, equal sign, solve, solution, inequality, solution set, nonnegative rational number, substitution, algebraic


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http://achievethecore.org/

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



TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

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

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

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?

6-1A Equations (pp. 314-317)6-1D Solve and Write Addition Equations (pp. 322-326)6-2B Solve and Write Multiplication Equations (pp. 335-338)

Holt

expressions, variable, defining the variable

Writing in Math:Explain how to determine a solution for an equation or inequality.

Describe the method of substitution


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



TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESmakes an equation or inequality true.

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

How do expressions and equations apply to real life situations?

Objective(s): Students will explain what the solution

represents as it relates to an equation or inequality.

Students will determine whether a number

2-1 Variables and Expressions (pp. 50-53)2-4 Equations and their Solutions (pp. 66-69)2 – 5 Addition Equations (pp. 70-73)2 -7 Multiplication Equations (pp. 77-80)

when checking for a solution to an equation or inequality.


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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESpurpose at hand, any number in a specified set.

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

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

Students will solve whole number addition equations.

Students will solve whole number multiplication equations.

Building Conceptual Understanding:Math Shell Concept Development Lesson: Interpreting EquationsEngage NY: True and False Number SentencesEngage NY: Finding Solutions to Make Equations True


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https://www.engageny.org/resource/grade-6-mathematics-module-4-topic-g-lesson-25




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

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




TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESnonnegative 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 identify which substituted value(s) satisfy

Choose from the following resources and use them to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.

Additional Lesson(s):Shelby County Schools 2016/2017

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESthe 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 to determine your answer. Show that your

Better Lessons 6.EE.B.5Better Lesson: Reasoning About Inequality Solution SetsBetter Lesson: Writing Simple InequalitiesBetter Lesson: 6.EE.B.7

Task(s):You must establish a free account to


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http://betterlesson.com/lesson/544358/writing-and-solving-equations

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

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

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

http://betterlesson.com/common_core/browse/362/ccss-math-content-6-ee-b-5-understand-solving-an-equation-or-inequality-as-a-process-of-answering-a-question-which-values-from-a



TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESsolution 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.

access Edutoolbox.org resources.TN Task Ark: Exploring Expressions and EquationsIllustrative Math: Morning WalkIllustrative Math: Log Ride TaskIllustrative Math: Firefighter Allocation

Additional Resource(s):Shelby County Schools 2016/2017

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

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

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



TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES0.44(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 statement?

Learn Zillion: Justify multiple solutions to an inequality by substituting for an unknownLea 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


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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.

equations that involve multiplication

Correlated iReady Lesson(s): Solving Inequalities Solving Equations Using Equations to Solve Problems

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

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


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

6.E E . B .8: Write an inequality of the form x

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.

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

7-2B 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

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

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 represent inequality constraints on a number line.


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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES> 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.

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

between dependent and independent variables?

405)Holt

13-1 Tables and Functions (pp. 699-701)When covering this lesson remember that the standard are not ask students to solve equations.

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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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES 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 the dependent and independent variables

Objective(s): Students will solve inequalities. Students will write and graph inequalities Students will analyze the relationship

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

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

13 - 5 Inequalities (pp. 718-721)Shelby County Schools 2016/2017

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESusing 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 independent variable.

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

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

Choose from the following resources and use them to ensure that the intended


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Additional Information: Students can use many forms to represent

relationships between quantities. Multiple representations include describing the relationship using language, a table, an equation, or a graph. Translating between multiple representations helps students

outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.

Building Conceptual Understanding:EngageNY: Writing and Graphing Inequalities in Real-World Problems 6.EE.8Engage NY: Problems in Mathematical Terms


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https://www.engageny.org/resource/grade-6-mathematics-module-4-topic-h-lesson-31





TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESunderstand that each form represents the same relationship and provides a different perspective on the function.

Students will write inequalities to represent real world and mathematical situations. They should also recognize when to use an

6.EE.9

Additional Lesson(s):Engage NY: Multi-Step Problems in the Real World 6.EE.9Better Lesson: Recognize how an equation relates independent and dependent variables 6.EE.C.9


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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESopen or shaded circle when graphing inequalities.

Examples:1. Graph x ≤ 4.

Task(s):Illustrative Math: Fishing Adventures 6.EE.B.8Illustrative Math: Height Requirements 6.EE.B.8Illustrative Math: Chocolate Bar Sales 6.EE.C.9


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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 & RESOURCES2. 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∘ Fahrenheit. B. The value of a number substituted for x is greater than 4.

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

Correlated iReady Lesson(s): Applying a Function Rule to Complete a

Table Writing Function Rules


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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



TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESC. Marcus drinks more than 4 glasses of water every day. D.

E.

Relationships Between Variables I Equations


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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES3. 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 line.


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0 50 100

4. Less than $200.00 was spent by the Flores family on groceries last month. Write an inequality to represent this amount and graph this inequality on a number line.


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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESSolution: 200 > x

The purpose of standard 6.EE.9 is for


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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESstudents 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 variable that is affected by the change in the independent variable. Students


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


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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESx 1 2 3 4y 2.5 5 7.5 10

Solution:y = 2.5x


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Area of triangles, Special Quadrilaterals and Polygons in the Coordinate Plane(Allow approximately 3 weeks for instruction, review and assessment)

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

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

attributes, each of which can be measured

Glencoe9-1A Area of Parallelograms (pp. 522-527)9-1B Explore Area of Triangles (p. 528)

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


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6. G . A .1: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and

in many ways.

Essential Question(s): 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?

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

Holt

Writing in Math:Students will construct a Venn Diagram to contrast and compare one geometric figure to another.Students will work in pairs to create a list of figures that occur as a result of decomposing various polygons.


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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESmathematical problems.

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

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?

Objective(s): Students will decompose a rectangle into

triangles.

10-1 Area of Rectangles and Parallelograms (pp. 534-537)Companion 11-4A Polygons in the Coordinate Plane10-2 Area of Triangles and Trapezoids (page 540 -543)10-3 Area of Composite Figures (page 545-

Students will explain how to use coordinates of a figure, drawn on a coordinate plane, to calculate the lengths of the sides.

Graphic Organizers:Special Quadrilateral Foldable Instructions


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




TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESproblems.

6.NS.8 Solve real-world and mathematical 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

Students will find areas and missing dimensions of parallelograms.

Students will draw polygons in a coordinate plane.

Additional Information:Students should understand that area is the

547)

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

Choose from the following resources and

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://etorgerson.net/CMP_Covering.html

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

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



TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESthe same first coordinate or the same second coordinate. (This standard was introduced in quarter 2; however, it also supports 6.G.A.3 because both standards deal with finding the distance between points on a coordinate grid.)

number of squares needed to cover a plane figure. Students should understand why the area formulas for rectangles and triangles work.

Finding the area of triangles is introduced in relationship to the area of rectangles – a rectangle can be decomposed into two

use them to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.

Additional Lesson(s):Engage NY Lessons: 6.G.A.1Engage NY Lessons: 6.G.A.3


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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 & RESOURCEScongruent triangles. Therefore, the area of the triangle is half the area of the rectangle. The area of a rectangle can be found by multiplying base 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.

Better Lesson: 6.G.A.1Better Lesson: 6.G.A.3

Task(s)Illustrative Math: Finding Area of Polygons TaskIllustrative Math: Polygons in the Coordinate Plane Task


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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



TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESNCTM Illuminations: Discovering the Area Formula for a Triangle

Special quadrilaterals include rectangles, squares, 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 in

Illustrative Math: Same Base Height Variation 2 TaskIllustrative Math: Same Base and Height Variation 1 Task

Additional Resources: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


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

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

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



TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES2D or 3D

Illuminations: Isometric Drawing Tools

Students decompose shapes into rectangles and triangles to determine the area. For example, a trapezoid can be decomposed into triangles and rectangles (see figures below).

Shodor: Triangle Explorer ActivityKhan 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


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

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



TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESUsing the trapezoid’s dimensions, the area of the individual triangle(s) and rectangle can be found and then added together.

Correlated iReady Lesson(s): Concepts of Area and Perimeter Area of Parallelograms,

Quadrilaterals, and Polygons Polygons in a Coordinate Plane


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Example(s):Shelby County Schools 2016/2017

Revised 9/27/1660 of 79



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 TOOLBOXNWEA 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 TN Core/CCSSTNReady Math Standards

VideosKhan Academy


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http://www.khanacademy.org/

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

https://support.nwea.org/khanrit

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



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

TNCoreAchieve the CoreEdutoolbox

Watch Know LearnLearn ZillionVirtual NerdMath PlaygroundStudyJams

Calculator ActivitiesGreatest Common Factor CalculatorTI-73 Activities

Interactive ManipulativesNational Library of Virtual Manipulatives - NLVMNumber & Operations Virtual Manipulatives

Additional SitesPBSGCF Game


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http://www.oswego.org/ocsd-web/match/dragflip.asp?filename=slanegcf

http://www.learner.org/

http://nlvm.usu.edu/en/nav/topic_t_1.html

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://www.mathsisfun.com/greatest-common-factor-tool.html

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

http://www.mathplayground.com/

http://www.virtualnerd.com/

https://learnzillion.com/login

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

http://www.edutoolbox.org/

http://achievethecore.org/dashboard/300/search/1/2/0

http://www.tncore.org/

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

http://www.myhrw.com/



CASIO Activities Interactive Cartesian Plane Math Is Fun LCM GameGCF Game AAA MathFrayer 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.aaamath.com/g57g-grt-com-fac.html

http://jamit.com.au/htmlFolder/app1004.html

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

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




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Shelby County Schools’ mathematics instructional maps ... 6 2016_17 Q3 10… · Web viewIn 2014, the Shelby County Schools Board of Education adopted a set of ambitious, yet attainable