Getting Started: totalmotivationMATHˆˇ˘ ˇ ˝˚ ˝ ˘ ˇ˝ ˘ ˇ ˜˚˛˝˙ˆˇ˛˘˜˚˛˝˙ˆ ˙˜ Unit mentorinminds.com totalmotivation EA 1 ILLEGAL O OPY 115 Getting Started:

ELA | LEVEL 1Teacher Edition Sample Page

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Getting Started: Unit 12 student edition pages 114–116

GSE Focus: ELAGSE1RI4

5 Unpacking the StandardMeanings of Words and Phrases – Students in Grade 1 are expected to use questioning strategies to determine meanings of words and phrases in a text.

Authors use words and phrases in informational texts to teach the reader ideas and concepts associated with the topics of the texts. The reader should ask and answer questions in order to determine definitions of words and phrases.

When teaching students to determine meanings of unknown words, model asking and answering questions such as the following: Do I know the meaning of this word? Have I seen this word in another text? What do I think the word means? Does my idea of the word’s meaning make sense in the sentence? Which print or digital source(s) can help me verify the meaning? Prompt students to ask and answer these questions when they encounter unknown words during independent reading.

6 Instructional Activities Use the following activities to provide instruction and practice for the GSE Focus Standard.

Ask and Answer – Display the passage-specific words. Have students answer the following questions about the words.

• What words do I know?• What words have word parts I know?• What words are similar in spelling?• What words are similar in meaning?• What words have I seen in other texts?• What words can I use correctly in sentences?Guide student responses to the questions as they determine the word meanings.

Sticky Words – Lead discussions with students about habits of skilled readers. Emphasize that skilled readers acknowledge when they encounter words they do not know during reading. Provide students with informational texts and sticky notes. As students read the texts, direct them to use the sticky notes to flag words with unknown meanings. Prompt students to ask and answer questions about the flagged words and the words around them. Allow students to debrief with partners to share what they learned about the words based on their questions and answers.

7 Formative Assessment Provide students with several sentences that contain passage-specific vocabulary words and instruct students to record questions and answers that would help them determine the meanings of words. Use student responses to clarify misconceptions and to plan further instruction or interventions.

MATH | LEVEL 6Teacher Edition Table of Contents

totalmotivationMATH™

TABLE OF CONTENTS

Unit 1 Understand Ratios and Use Ratio Language (MGSE6.RP.1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Unit 2 Understand Unit Rates and Use Rate Language (MGSE6.RP.2) . . . . . . . . . . . . . . . . . . . . . . . . . 9

Unit 3 Make and Use Tables of Equivalent Ratios (MGSE6.RP.3a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Unit 4 Solve Unit Rate Problems (MGSE6.RP.3b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Unit 5 Solve Percent Problems (MGSE6.RP.3c). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Unit 6 Convert Measurement Units (MGSE6.RP.3d) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

Unit 7 Solve Problems Involving Division of Fractions (MGSE6.NS.1) . . . . . . . . . . . . . . . . . . . . . . . . . . 49

Unit 8 Divide Multi-Digit Numbers (MGSE6.NS.2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

Unit 9 Perform Operations with Decimal Numbers (MGSE6.NS.3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

Unit 10 Find and Apply GCF and LCM (MGSE6.NS.4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

Unit 11 Understand Positive and Negative Numbers (MGSE6.NS.5) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

Unit 12 Recognize and Locate Opposite Numbers (MGSE6.NS.6a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

Unit 13 Understand Locations in the Coordinate Plane (MGSE6.NS.6b) . . . . . . . . . . . . . . . . . . . . . . . . 97

Unit 14 Locate Numbers on Number Lines and the Coordinate Plane (MGSE6.NS.6c) . . . . . . 105

Unit 15 Interpret Statements of Inequality (MGSE6.NS.7ab) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

Unit 16 Understand Absolute Value (MGSE6.NS.7cd) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

Unit 17 Graph Points on the Coordinate Plane (MGSE6.NS.8) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

Unit 18 Evaluate Expressions with Exponents (MGSE6.EE.1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

Unit 19 Write and Identify Parts of Expressions (MGSE6.EE.2ab) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

Unit 20 Evaluate Expressions at Specific Values (MGSE6.EE.2c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

Unit 21 Apply the Properties of Operations (MGSE6.EE.3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

Unit 22 Identify When Two Expressions Are Equivalent (MGSE6.EE.4) . . . . . . . . . . . . . . . . . . . . . . . . 169

Unit 23 Understand Solving an Equation or Inequality (MGSE6.EE.5) . . . . . . . . . . . . . . . . . . . . . . . . . 177

Unit 24 Use Variables and Write Expressions (MGSE6.EE.6) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

Unit 25 Solve Problems by Writing and Solving Equations (MGSE6.EE.7) . . . . . . . . . . . . . . . . . . . . . 193

Unit 26 Write an Inequality to Represent a Problem (MGSE6.EE.8) . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

Unit 27 Analyze the Relationship Between Two Quantities (MGSE6.EE.9) . . . . . . . . . . . . . . . . . . . . 209

Unit 28 Find Area to Solve Problems (MGSE6.G.1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

Unit 29 Find Volume to Solve Problems (MGSE6.G.2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225

Unit 30 Use the Coordinate Plane to Solve Problems (MGSE6.G.3) . . . . . . . . . . . . . . . . . . . . . . . . . . 233


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Unit 31 Use Nets to Find Surface Area (MGSE6.G.4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241

Unit 32 Recognize a Statistical Question (MGSE6.SP.1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249

Unit 33 Understand Center, Spread, and Shape of Data (MGSE6.SP.2) . . . . . . . . . . . . . . . . . . . . . . . 257

Unit 34 Recognize Differences in Measures of Center and Variability (MGSE6.SP.3) . . . . . . . . 265

Unit 35 Display Data in Plots (MGSE6.SP.4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273

Unit 36 Summarize Numerical Data Sets (MGSE6.SP.5c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281

Unit 37 Relate the Choice of Measures to the Shape of Data (MGSE6.SP.5abd) . . . . . . . . . . . . . 289

Appendix A: Organization and Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297

Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299

Teacher and Student Edition Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300

Additional Teacher Edition Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306

Appendix B: Instructional Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309

Accommodations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .311

Standards for Mathematical Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312

Hess Cognitive Rigor Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315

Bloom’s Taxonomy/Revised Bloom’s Taxonomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316

Technology Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318

Appendix C: Answer Codings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321

Units 1–37 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323

Performance Tasks and Suggested Scoring Rubrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399

Appendix D: Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421

Image Bank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423

Comprehensive Literature List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455

Class Performance Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458

Chart Your Success . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460

Math Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467

Mathematics Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477


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MATH | LEVEL 6Teacher Edition Sample Page

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mentoringminds.com totalmotivationMATH™LEVEL 6 ILLEGAL TO COPY 209a

Analyze the Relationship Between Two Quantities

Unit 27 MGSE6.EE.9 student pages 209–216

Suggestions for Planning InstructionCareful planning and implementation of direct instruction in mathematics can yield huge benefits in terms of student performance. Total Motivation Math™ provides a wealth of tools for planning, including valuable resources for direct instruction, focused practice, and assessment of student learning. The following suggestions outline one way that Total Motivation Math can be used to plan effective lessons. The teacher should:

• review the teacher edition unit in either the print or online component, noting the standards for mathematical content and Standards for Mathematical Practice addressed by the unit.

• carefully read the unpacking of standards to clarify the standard. Note the identified vocabulary terms and the instructional activities that are aligned to the standard.

• review the pages in the corresponding unit of the Total Motivation Math™ Student Edition.

• assign the unit Assessment of Prerequisite Skills available in the online component. This pre-assessment indicates if there are any prerequisite skills for the unit that some students may need to review.

• note that the use of activities and practice pages in Total Motivation Math is designed to be flexible. For example, one or more pages in the student edition may be assigned as homework (depending on the school policy on homework), or selected pages may be reserved for use as part of a spiraled review. Teachers do not have to use all activities or assign all practice pages to deliver an effective lesson sequence.

• refer to answers to student edition questions on the corresponding teacher edition pages. Teachers should note that coding for Depth of Knowledge (DOK) and Revised Bloom’s Taxonomy (RBT) for each item may be found in Appendix C at the back of this book.

Georgia Standards of Excellence for Mathematical Content MGSE6.EE.9

Other Standards for Mathematical Content Addressed in this UnitMGSE6.NS.6c, MGSE6.EE.2a, MGSE6.EE.6

Standards for Mathematical Practice Addressed in this UnitSMP.1 Make sense of problems and persevere in solving them.

SMP.2 Reason abstractly and quantitatively.

SMP.3 Construct viable arguments and critique the reasoning of others.

SMP.4 Model with mathematics.

SMP.6 Attend to precision.

SMP.7 Look for and make use of structure.

SMP.8 Look for and express regularity in repeated reasoning.


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Unit 27 MGSE6.EE.9

Unpacking the StandardIn grade 6, students identify quantities in real-world situations as independent and dependent variables, where the dependent quantity changes relative to changes in the independent quantity. Students identify the independent and dependent quantities from tables, graphs, and equations. In addition, students write equations to show the relationships between the independent and dependent variables. Students use tables and graphs to analyze the relationship, using phrases such as the following, “As the independent quantity increases, the dependent quantity increases.”

Re�ection Notes:What materials/activities were effective?

What were the most common errors/misconceptions?

What concepts should be emphasized in instruction?

Partners Individual

Key for Recommended Grouping

Groups Whole Class


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mentoringminds.com totalmotivationMATH™LEVEL 6 ILLEGAL TO COPY 209

Analyze the Relationship Between Two Quantities

Introduction: Unit 27 MGSE6.EE.9 student page 209

Start Here

1 Assessment of Prerequisite Skills The teacher may assign the Assessment of Prerequisite Skills for Unit 27 as an online assignment. Students log in to Total Motivation Math™ and complete this pre-assessment. The teacher may access the Reports area to review student performance and use the information to plan additional instruction to help students develop an understanding of the concepts in this unit.

2 Introduction Activity (DOK: 2, RBT: Apply)The teacher and class discuss what it means for a person to be independent or dependent (e.g., An independent person is not controlled by others. A dependent person is controlled by someone else.). Students brainstorm situations in which they are independent (e.g., spending one’s own money at the store) and dependent (e.g., waiting for a sibling to finish tutorials before leaving school).

To illustrate the difference between an independent person and a dependent person, the teacher provides a rope to each student pair and assigns one student to be “independent” and the other to be “dependent.” Each student holds one end of the rope. The “independent” student walks a random path around the classroom, while the “dependent” student follows because he or she is holding the other end of the rope. Then the students switch roles and repeat the activity. Afterward, the teacher displays a table of values. (NOTE: Table is available in Appendix D: Resources/Image Bank.) The teacher and class discuss the two types of quantities shown in the table (number of chores completed and number of dollars earned). Students state opinions as to which quantity is independent and which is dependent. The teacher and students discuss that the number of chores completed is an independent quantity because Matthew determines that number himself. The number of dollars earned is a dependent quantity because the earnings depend on the number of chores completed. The teacher and class then generate an equation based on the pattern in the table (d = 2c).

3 Formative Assessment (DOK: 2, RBT: Apply)The teacher displays a table such as the following. (NOTE: Table is available in Appendix D: Resources/Image Bank.)

Class Pizza PartyNumber of Pizzas Ordered (p) 4 5 6 7

Number of Slices (s) 32 40 48 56

The teacher directs students to raise their right hands if the number of pizzas ordered is the independent quantity or their left hands if the number of pizzas ordered is the dependent quantity. The teacher provides opportunities for questions so that students understand that the number of pizzas ordered is the independent quantity and the number of slices is the dependent quantity. Using individual response boards, students write an equation to describe the relationship between the number of pizzas ordered and the number of slices of pizza (s = 8p). Through observation and student responses, the teacher determines each student’s level of comprehension.

4 Connecting to the Student Edition: IntroductionThe teacher may wish to work with the students as a whole group or in small groups to complete the Introduction page in the student edition. If desired, this page can be projected from the online component for whole group instruction.

5 Answers1. the amount Alex earns 2. independent variable

dependent variable; Explanations will vary.3. x; y4. y = 2x 5. cost 6. number of tickets 7. c = 5.75t


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Vocabulary/Journal: Unit 27 MGSE6.EE.9 student page 210

1 Vocabulary FocusThe teacher introduces the essential vocabulary terms for this unit.

continuous data discrete data quantity x-axis

coordinate plane equation variable y-axis

dependent variable independent variable

2 Vocabulary Activity (DOK: 2, RBT: Understand)The teacher displays a class chart with columns labeled “Independent Quantity” and “Dependent Quantity.” Students copy the chart in math journals, and each student pair records a real-world example of one independent quantity and a corresponding dependent quantity. The teacher assigns half of the pairs to record their independent quantity examples in the class chart and the other half to record their dependent quantity examples in the chart.

Independent Quantity Dependent Quantity

the number of hours a person works on a job

the number of miles the car can travel before it runs out of gas

the number of DVDs purchased

the total number of wheels on the cars in the parking lot

3 Vocabulary Formative Assessment (DOK: 2, RBT: Understand)In math journals, pairs record the examples listed in the class chart from the Vocabulary Activity. Then, students fill in the missing example for each quantity. The teacher and class discuss possible responses. During the activity, the teacher offers feedback as needed.

Independent Quantity Dependent Quantity

the number of hours a person works on a job

the amount of the paycheck

the number of gallons of gas in a car

the number of miles the car can travel before it runs out of gas

the number of DVDs purchased

the total cost of the purchase

the total number of cars in the parking lot

the total number of wheels on the cars in the parking lot

4 Connecting to the Student Edition: Vocabulary/JournalAt this point, the teacher may wish to assign the Vocabulary Activity and/or the Journal prompt in the student edition. The Journal prompt may also be reserved as a reflection/closure activity.

5 AnswersVocabulary Activity Responses will vary.

Journal Explanations will vary, but students should include the idea that independent quantities represent the input and dependent quantities represent the output.Explanations will vary, but students should include that independent quantities are graphed on the x-axis and dependent quantities are graphed on the y-axis.


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Partner Practice: Unit 27 MGSE6.EE.9 student page 211

1 Instructional Activities (Select from the following activities.) 1. The teacher displays the following scenario.

The choir at Emerson Middle School sells chocolate bars to raise money for an upcoming trip to a competition. The bars are sold for $1.50 each, and one box contains 20 chocolate bars.

The teacher prepares sets of cards printed with the labels boxes of chocolate bars or cost ($), one label per card. The teacher includes sets of values representing the labels. An example matching pair is shown.

boxes ofchocolate bars

cost ($)

0.75 1.25 2 2.5 22.5 37.5 60 75

The teacher distributes one card to each student. Students study their cards. On the teacher’s signal, students move to find a partner holding a card with a related quantity and data set based on the information in the problem. Pairs discuss the quantities and determine which quantity represents the independent variable and which represents the dependent variable. Students then use the values for the quantities to create graphs, labeled to represent the data on the cards. Finally, on the back of the original card, each pair records an equation showing the relationship between the independent and dependent variables. Pairs take turns sharing their work with the class, and the teacher offers feedback as needed. (DOK: 2, RBT: Apply)

2. The teacher displays a variety of tables and graphs printed on poster paper. Groups of 2–3 students are assigned to each poster. Groups discuss the posters and the relationships reflected in the tables and graphs. In math journals, students answer the following questions.

• What is the independent quantity represented in the table/graph?• What is the dependent quantity represented in the table/graph?• As the independent quantity increases, what happens to the dependent quantity?• What is the relationship between the independent and dependent quantities? Represent the

relationship using an equation.

Groups take turns sharing the information in the tables or graphs and their responses to the questions. The teacher offers feedback and asks additional questions to determine the need for additional instruction or intervention. (DOK: 1, RBT: Analyze)

2 Formative Assessment (DOK: 2, RBT: Analyze)Students complete Critical Thinking problem 1 on page 215 of the student edition. The teacher reviews responses and plans additional instruction.

3 Connecting to the Student Edition: Partner PracticeAt this point in the lesson, the teacher may wish to have students work with partners to complete the Partner Practice page in the student edition, in print or online. If desired, this page can be projected from the online component as student pairs debrief the completed work and the class discusses the results of the practice.

4 Answers1. D2. B3. A, C, D, and F


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Independent Practice: Unit 27 MGSE6.EE.9 student page 212

1 Instructional Activity (DOK: 2, RBT: Apply)The teacher distributes a sheet of graph paper, a ruler, and sticky dots to groups of 3–4 students. The teacher displays the following problem.

Each weekend, Travis plays in a basketball league at the local community center. After the games, many of the players go to the nearby café for burgers. Each burger costs $2.75. Create a table, construct a graph, and write an equation that can be used to determine the cost of purchasing burgers each weekend for any number of players.

Groups read the problem and create a table of values to represent the situation. Next, students use the paired values to create a graph using the graph paper and sticky dots. Students label the axes of the graph appropriately. Beneath the graph, students record statements describing the graph, identifying the independent and dependent variables. Students also write an equation to show the relationship between the independent and dependent variables. Groups display their work, and the class conducts a gallery walk to review. The teacher and class discuss any discrepancies in the representations, and the teacher provides clarification as needed.

2 Formative Assessment (DOK: 2, RBT: Apply)On half sheets of paper, the teacher prints either a table or a graph showing a relationship. Each student receives a half sheet of paper as an exit ticket. Students record an equation to represent the relationship shown, identify the independent and dependent quantities in the table or graph, and write a complete sentence describing the relationship between the quantities (e.g., As the __________ increases, the __________ decreases.). The teacher reviews student responses and plans additional instruction or intervention.

3 Connecting to the Student Edition: Independent PracticeAt this point, the teacher may wish to assign the Independent Practice page to be completed independently in the student edition using either the print or online component. If the online component is used, student work is graded automatically and results may be viewed in the Reports area.

4 Answers1. B2. C and D3. C


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Assessment: Unit 27 MGSE6.EE.9 student page 213

1 Reflection/Closure Activity (DOK: 2, RBT: Apply)At the conclusion of instruction, it is recommended that the teacher engage students in an activity that allows them to reflect upon their learning and summarize main concepts.

The teacher uses a four-corners model to provide two different relationships for each student. One relationship is represented by a verbal description of the independent and dependent variables, and the other is represented by a graph. Students complete each of the remaining three corners for the relationship.

Verbal DescriptionBefore the storm, the temperature was 40ºF. For every hour the storm continues, the temperature drops one degree.

Independent: ______________Dependent: _______________

Equation Equation

GraphGraphTable Table y

x 2 4 6 8 10

10

8

6

4

2

Laps

Min

ute

s

Verbal Description

Independent: ______________Dependent: _______________

2 Formative Assessment (DOK: 1, RBT: Analyze)The teacher collects one model from each student from the Reflection/Closure Activity. The pages are taped facedown on the classroom wall. Each student selects a model from the wall. Students review the selected models and mark any errors and record comments. The teacher returns each model to the creator. The teacher collects models and uses student work to determine the need for additional instructional activities or interventions.

3 Connecting to the Student Edition: Assessment At this point, the teacher may choose to assign the Assessment pages in the print or online component. Note that if the online component is used, the first page of the Assessment uses a selected-response format and will be scored by the computer. The second page of the Assessment will be teacher graded. After students complete the Assessment, the teacher may access the Reports area to review students’ results. Following the completion of the Assessment pages, the teacher uses the information to plan additional instruction and/or interventions.

4 Answers1. C2. B and C3. D4. A

5 Interventions (DOK: 1, RBT: Apply)After students complete the Assessment pages, the teacher determines which students are in need of further instruction and selects one or more of the Intervention activities for individual students or small groups of students.

The teacher creates sets of cards, each with a description that explains the relationship between independent and dependent variables. The teacher prepares corresponding cards printed with either tables or graphs. Students place all cards faceup on their desks. Each student selects a card with a table or graph and locates the matching description card. The group discusses the independent and dependent quantities for each matched set of cards.


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Unit

27


Assessment: Unit 27 MGSE6.EE.9 student page 214

1 Connecting to the Student Edition: Assessment The second Assessment page utilizes an open-response format. Students may complete this page in either the print or online component. This page is teacher graded but allows students to communicate their thinking.

2 Answers5. Shoe Sizes; Explanations will vary.

Student Ages; Explanations will vary.

6. s = 2 __ 3 r (or equivalent)

Independent: regular price or r Dependent: sale price or s

3 Interventions (Select from the following activities.) 1. The teacher displays a sentence that describes the relationship between an independent variable and a

dependent variable. Some example sentences are shown.

• For each additional coin, the total amount of money increases by $0.05.• A rock-climber climbs at a rate of 25 meters per hour.• Maria uses 2 1 __ 4 cups of blueberries for each dozen blueberry muffins she makes.

Using individual response boards, students write “depends” sentences (e.g., The total amount of money depends on the number of coins.) and then use the sentences to identify the independent and dependent variables. The teacher checks responses and clarifies misconceptions. The process is repeated with other sentences. (DOK: 1, RBT: Apply)

2. The teacher gives each pair of students a different sentence from Intervention activity 1 on page 214. Working independently, one student creates a table, and the other student creates a graph showing the relationship between a pair of independent and dependent variables. Each pair displays their sentence, table, and graph for the class. The class discusses the relationships represented in the tables and graphs and determines an equation to represent the relationship. The teacher records the equations and clarifies misconceptions as needed. (DOK: 2, RBT: Apply)

4 Formative Assessment (DOK: 2, RBT: Apply)The teacher conferences with each student, providing the student with either a graph or table of values. Students identify the independent and dependent variables, describe the relationship between the variables, and give an equation to represent the relationship. The teacher checks each student’s level of understanding and determines the need for additional intervention.


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Unit 2

7


Critical Thinking: Unit 27 MGSE6.EE.9 student page 215

1 Connecting to the Student Edition: Critical ThinkingThe teacher determines if students will complete the Critical Thinking questions in the print or online version and assigns one or both questions. Students may work individually, with partners, or in small groups to solve one or both problems. The teacher may also choose to solve the problems as a whole group activity, projecting the Critical Thinking page from the online component. In addition, the teacher may elect to assign the Critical Thinking questions over more than one class period.

2 Answers1. x-axis: Ramp Height (in); y-axis: Distance Traveled (ft)

ramp height, increases, distance the car travels, increases

2. y

x 1 2 3 4 5 6 7 8 9 10

50

40

30

20

10

Hours Worked Amount Earned

1

3

5

7

9

$ 5

$15

$25

$35

$45

Equation: y = 5x

Hours Worked

Am

ou

nt

Ea

rned

($)

The amount earned (dependent) will be affected. The dependent quantities in the table will increase. The line in the graph will become steeper. The equation will change to y = 6.5x.

3 Extending Student Thinking (DOK: 3, RBT: Apply)Extending Student Thinking offers suggestions for differentiated instruction for students in need of an additional challenge.

Using grade-level appropriate Internet resources, students research a relationship between two quantities in which the distinction between the independent and dependent quantities is either difficult to determine or might be considered situational (i.e., In one setting, the quantities might be related in one way while in another the roles are reversed.). Students write a brief synopsis about the situation researched, including explanations and examples of the quantities.

4 Formative Assessment (DOK: 2, RBT: Understand)Students present the results of their research to the class. The teacher and students provide constructive feedback to the presenters and ask questions as needed.


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Unit

27


Motivation Station: Unit 27 MGSE6.EE.9 student page 216

1 Connecting to the Student Edition: Motivation Station (DOK: 2, RBT: Apply)The teacher may choose to have students play the Motivation Station game.

Students play “Dependent on What?” with partners. Each pair needs a game board, one number cube, and a paper clip to use with the spinner. Each player needs a pencil. Player 1 rolls the number cube and spins the spinner. The player matches the number rolled to the table with the same number. He or she then completes the section in the chart that matches the space on the spinner, using the information from the numbered table. If answered correctly, the player initials his or her work, and play passes to the next player. If incorrect, the player loses a turn, and play passes to the next player. If the section has already been initialed, the player spins and rolls again. The game ends when all sections of the chart are complete. The winner is the player with more sections initialed.

2 Answers

1 2 3 4 5 6

Independent Quantity x cups of sugar

miles drivennumber of

weeksnumber of

slicesnumber of

weeks

Dependent Quantity y dozens of cookies

gallons usedgrowth (inches)

total cost($)

weight (pounds)

Equation y = 3x c = 4s g = m ____ 23.3 g = 0.5w c = 1.75s p = 2 __ 3 w

3 ConnectionsThe teacher reviews the Connections and encourages students to complete these activities at home, individually or with a parent or guardian.

4 Additional ResourcesLiterature ConnectionsThe following title provides additional connections to unit concepts. This book may be used as an introduction or extension to unit concepts presented during classroom instruction. The book may also be placed in the classroom library or in a math center for easy student access.

Mystery Math: A First Book of Algebra – David A. Adler

Vocabulary CardsConsult the Motivation Math™ Word Play Activities with Teacher Guide that accompanies the Motivation Math™ Vocabulary Card Set (available as a separate purchase) for additional activities to use with content vocabulary terms that have not yet been mastered. Activities include word wall activities as well as additional activities designed for whole group, small group, partners, or individual students.

MATH | LEVEL 6Student Edition Sample Page

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Name __________________________________________

Standard MGSE6.EE.9

Use the information to answer questions 1–4.

Nicky completes chores, and his younger brother Alex helps. Their parents pay the brothers for completed chores. They pay Alex first and then pay Nicky twice the amount Alex earns. The graph shows the relationship between the amounts Alex and Nicky earn.

y

x 1 2 3 4 5 6 7 8 9 10

14

12

10

8

6

4

2

Alex’s Earnings ($)

Nic

ky’

s E

arn

ing

s ($

)

Earnings

1. The amount of money Nicky earns is dependent on —

_________________________________________.

2. Based on the graph, do Alex’s earnings represent the independent variable or the dependent variable?

Based on the graph, do Nicky’s earnings represent the independent variable or the dependent variable? Explain your answer.

_________________________________________

_________________________________________

_________________________________________

3. Fill in the blanks.

The independent quantities are graphed

along the _____-axis.

The dependent quantities are graphed along

the _____-axis.

4. Write an equation to show the relationship between Alex and Nicky’s earnings.

Use the table to answer questions 5–7.

The table shows the cost for student admission at Lincoln Cinema.

Student Movie TicketsNumber of Tickets (t) Cost (c)

1 $ 5.75

2 $11.50

3

4

$17.25

$23.00

5. What label describes the dependent variable?

6. What label describes the independent variable?

7. Write an equation to describe the relationship between the independent and dependent variables.

Unit 27 Introduction


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210 ILLEGAL TO COPY totalmotivationMATH™LEVEL 6 mentoringmindsonline.com

Name __________________________________________

Standard MGSE6.EE.9

Explain how to determine whether a set of values in a table is independent or dependent.

______________________________________________________________________________

________________________________________________________________________________________

Explain how to determine whether a set of values on a graph is independent or dependent.

________________________________________________________________________________________

________________________________________________________________________________________

Journal

Comprehension

Understand

continuous data dependent variable equation quantity x-axis

coordinate plane discrete data independent variable variable y-axis

Words for the Wise

A cinquain poem has five lines and does not have to rhyme. Write two cinquain poems using the following pattern for the words “independent” and “dependent.”

Independent

____________ ____________

______________ ______________ ______________

____________ ____________ ____________ ____________

_______________

Dependent

____________ ____________

______________ ______________ ______________

____________ ____________ ____________ ____________

_______________

Line 1: one word (given)

Line 2: two words

Line 3: three words

Line 4: four words

Line 5: one word

Vocabulary Activity

Unit 27 Vocabulary/Journal


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Name __________________________________________

Standard MGSE6.EE.9

1. The Chic Boutique has a sale on school spirit clothing. The table shows the regular price, r, and the amount of discount, d.

Spirit Clothing SaleRegular Price Amount of Discount

$12.00 $3.60

$15.00 $4.50

$22.00 $6.60

$30.00 $9.00

Which equation BEST represents the relationship between r and d?

A d = r ___ 0.3

B r = 0.3 ___ d

C r = 0.3d

D d = 0.3r

2. A string of lights has 3 bulbs for every foot of cord. The relationship between the number of bulbs, b, and the number of feet of cord, c, is represented by the equation b = 3c. Which table correctly shows this relationship?

A b 1 2 3 4

c 3 4 5 6

B b 3 6 9 12

c 1 2 3 4

C b 3 9 27 81

c 1 2 3 4

D b 1 2 3 4

c 3 6 9 12

3. Luis has a lawn mowing business. The graph shows the relationship between the number of lawns mowed, m, and the amount of money earned, d.

d

m 1 2 3 4 5 6 7 8 9 10

200180160140120100

80604020

Number of Lawns Mowed

Lawn MowingBusiness

Am

ou

nt

Ear

ned

($)

Select the FOUR statements that are true.

A The number of lawns Luis mows represents the independent variable.

B The number of lawns Luis mows depends on the amount of money he earns.

C The amount of money Luis earns is dependent on the number of lawns he mows.

D As the number of lawns Luis mows increases, the amount of money he earns increases.

E The equation m = 25d can be used to describe the relationship between the independent and dependent variables.

F The equation d = 25m can be used to describe the relationship between the independent and dependent variables.

Unit 27 Partner Practice


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Name __________________________________________

Standard MGSE6.EE.9

Use the graph to answer questions 1 and 2.

For a community service project, the sixth-grade classes paint mini-murals around town. The relationship between the number of mini-murals painted and the number of hours spent on the project is shown.

y

x 2 4 6 8 10

10

8

6

4

2

Number of Hours

Community ServiceProject

Min

i-M

ura

ls P

ain

ted

1. Which equation BEST represents the relationship between the independent and dependent variables shown in the graph?

A y = 3x C y = x + 3

B y = 1 __ 3 x D y = x + 1 __ 3

2. Select the TWO statements that are true.

A For every hour spent working on the project, 3 mini-murals are painted.

B The independent values are represented by the number of mini-murals painted.

C As the number of hours increases, the number of mini-murals painted increases.

D The number of mini-murals painted depends on the number of hours spent working on the project.

3. An ice cream shop sells ice cream cones for $2 each. The relationship between the number of ice cream cones sold and the amount of money collected is represented by the equation y = 2x. Which graph BEST shows this relationship?

A

y

x 2 4 6 8 10

10

8

6

4

2

B

y

x 2 4 6 8 10

10

8

6

4

2

C

y

x 2 4 6 8 10

10

8

6

4

2

D

y

x 2 4 6 8 10

10

8

6

4

2

Unit 27 Independent Practice


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Name __________________________________________

Standard MGSE6.EE.9

Use the table to answer questions 1 and 2.

Brianna uses the table to calculate the cost for her babysitting services.

Number of Hours (h) Cost (c)

2 $17.00

3 $25.50

4 $34.00

5 $42.50

1. Which equation BEST represents the relationship between the independent and dependent quantities?

A c = h + 8.5

B h = 8.5c

C c = 8.5h

D h = 8.5 ___ c

2. Select the TWO statements that are true.

A The values for h represent the dependent variable.

B The values for c represent the dependent variable.

C The cost for babysitting depends on the number of hours Brianna babysits.

D The number of hours Brianna babysits depends on the cost for babysitting.

3. A snow cone stand determines that more snow cones are sold as temperatures rise. Which statement is NOT true?

A The temperature does not depend on the number of snow cones sold.

B The temperature is the independent variable in the scenario.

C The number of snow cones sold depends on the temperature.

D The number of snow cones sold is graphed on the x-axis.

4. The graph shows the relationship between Santiago’s age, s, and Veronica’s age, v.

v

s 2 4 6 8 10 12 14

201816141210

8642

Which equation BEST represents the relationship between the independent and dependent variables?

A v = s + 4

B s = v + 4

C v = 2s

D s = v __ 2

Unit 27 Assessment


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Name __________________________________________

Standard MGSE6.EE.9

5. For the day’s math lesson, students in Mr. Carson’s class were asked to list their ages and shoe sizes in a chart. Mr. Carson created the following graph using the data from the chart.

y

x 2 4 6 8 10 12 14

10

8

6

4

2

Student Agesvs. Shoe Sizes

What label should be written on the axis representing the dependent variable? Explain your answer.

What label should be written on the axis representing the independent variable? Explain your answer.

6. The table shows the relationship between regular prices and sale prices in a clothing shop.

Clothing Shop PricesRegular Price (r) Sale Price (s)

$18 $12

$24 $16

$27 $18

$36 $24

Write an equation to represent the sale price given the regular price.

Identify the independent and dependent variables.

Independent: ___________________________ Dependent: _________________________

Unit 27 Assessment


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Name __________________________________________

Standard MGSE6.EE.9 Unit 27 Critical Thinking

1. In Mr. Taylor’s math class, students build ramps to race toy cars. They test the hypothesis that the steepness of the ramp affects the distance (in feet) the car travels. Each group in the class is assigned a different height (in inches) to build their ramp. The data collected during the tests is shown in the graph. Based on the given information, label the x- and y-axes.

20

16

12

8

4

1 2 3 4 5 6x

y

Complete the statement to show the relationship between the independent and dependent quantities by filling in the blanks and circling the correct terms.

As the ______________________________ (increases/decreases), the ______________________________ (increases/decreases).

Analysis

Analyze

2. Jennifer babysits on the weekends to earn spending money. She charges $5 per hour for each child. Create a table to show the amount of money Jennifer earns for one child in relation to the number of hours she works. Then graph the data, labeling the axes, and write an equation to show the relationship.

y

x 1 2 3 4 5 6 7 8 9 10

50

40

30

20

10

Hours Worked Amount Earned

1

3

5

7

9

Equation: _______________

If Jennifer increases her rate to $6.50 per hour, which quantities will be affected? Discuss how the change will be represented in the different representations.

_________________________________________________________________________________________

_________________________________________________________________________________________

Analysis

Analyze


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Name __________________________________________

Standard MGSE6.EE.9Unit 27 Motivation Station

Dependent on What?

Play “Dependent on What?” with a partner. Each pair needs a game board, one number cube, and a paper clip to use with the spinner. Each player needs a pencil. Player 1 rolls the number cube and spins the spinner. The player matches the number rolled to the table with the same number. He or she then completes the section in the chart that matches the space on the spinner, using the information from the numbered table. If answered correctly, the player initials his or her work, and play passes to the next player. If incorrect, the player loses a turn, and play passes to the next player. If the section has already been initialed, the player spins and rolls again. The game ends when all sections of the chart are complete. The winner is the player with more sections initialed.

DependentQuantity

IndependentQuantity

IndependentQuantity

DependentQuantity

EquationEquation

1 2 3 4 5 6

Independent Quantity

Dependent Quantity

Equation

1x 0.5 1 1.5 2

y 1.5 3 4.5 6

2Cups of Sugar, s 3 __ 4 1 1 __ 2 2 1 __ 4 3

Dozens of Cookies, c 3 6 9 12

3Gallons Used, g 5 7 9 11

Miles Driven, m 116.5 163.1 209.7 256.3

4Number of Weeks, w 1 2 3 4

Growth (inches), g 0.5 1 1.5 2

5Number of Slices, s 2 4 6 8

Total Cost ($), c 3.50 7 10.50 14

6Number of Weeks, w 0 1 2 3

Weight (pounds), p 0 2 __ 3 1 1 __ 3 2

1. Interview your science teacher about independent and dependent variables and how they are used in science. Write a paragraph describing the similarities and differences of the terms “independent” and “dependent” as used in math and science.

2. Find two tables and two graphs in a newspaper. Cut out the examples and attach them to a sheet of paper. Under each example, identify the independent quantities and the dependent quantities.

Connections

Documents

Getting Started: totalmotivationMATHˆˇ˘ ˇ ˝˚ ˝ ˘ ˇ˝ ˘ ˇ ˜˚˛˝˙ˆˇ˛˘˜˚˛˝˙ˆ ˙˜ Unit mentorinminds.com totalmotivation EA 1 ILLEGAL O OPY 115 Getting Started: