Getting tated: motivationmath - Mentoring Minds...mentoringminds .com ™ttal motivation ELA EE 1...

ELA | LEVEL 1Teacher Edition Sample Page

mentoringminds.com

Unit 1

2

mentoringminds.com totalmotivationELA™LEVEL 1 ILLEGAL TO COPY 115

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 7Teacher Edition Table of Contents

Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Student Edition Unit Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Teacher Edition Unit Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Instructional Technology Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Instructional Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

The 5E Model of Instruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Instruction Checklist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Mathematical Process Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Hess Cognitive Rigor Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Bloom’s Taxonomy (Original/Revised) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

English Language Proficiency Standards (ELPS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

Unit 1 Describe relationships between sets of rational numbers 7.2(A) – S . . . . . . . . . . . . . . . . . 39

Unit 2 Fluently add, subtract, multiply, and divide rational numbers to solve problems 7.3(A) – S, 7.3(B) – R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

Unit 3 Represent constant rates of change in mathematical and real-world problems 7.4(A) – R . . 59

Unit 4 Calculate unit rates from rates in mathematical and real-world problems 7.4(B) – S . . . . . 69

Unit 5 Determine the constant of proportionality 7.4(C) – S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

Unit 6 Solve problems involving ratios, rates, and percents 7.4(D) – R . . . . . . . . . . . . . . . . . . . . . 89

Unit 7 Convert between measurement systems 7.4(E) – S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

Unit 8 Generalize the critical attributes of similarity 7.5(A) – S . . . . . . . . . . . . . . . . . . . . . . . . . . 109

Unit 9 Describe π as the ratio of the circumference of a circle to its diameter 7.5(B) – S . . . . . . 119

Unit 10 Solve problems involving similar shape and scale drawings 7.5(C) – R . . . . . . . . . . . . . . 129

Unit 11 Represent sample spaces for simple and compound events using lists and tree diagrams 7.6(A) – S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

Unit 12 Select and use different simulations to represent simple and compound events 7.6(B) . 149

Unit 13 Make predictions and determine solutions using experimental data and theoretical probability 7.6(C) – S, 7.6(D) – S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

Unit 14 Find probabilities of a simple event and its complement and describe the relationship between the two 7.6(E) – S . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

Unit 15 Use data from a random sample to make inferences about a population 7.6(F) . . . . . . . 179

Unit 16 Solve problems using data represented in bar graphs, dot plots, and circle graphs 7.6(G) – R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

Unit 17 Solve problems using qualitative and quantitative predictions and comparisons from simple experiments 7.6(H) – R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199

motivationmath™

Table of Contents

18271.indb 4 5/12/17 3:34 PM


mentoringminds.com

Unit 1

2













Unit 18 Determine experimental and theoretical probabilities related to simple and compound events 7.6(I) – R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

Unit 19 Represent linear relationships using verbal descriptions, tables, graphs, and equations 7.7(A) – R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

Unit 20 Model the relationship between the volume of a rectangular prism and a rectangular pyramid 7.8(A) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231

Unit 21 Explain the relationship between the volume of a triangular prism and a triangular pyramid 7.8(B). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241

Unit 22 Use models to determine the approximate formulas for the circumference and area of a circle 7.8(C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251

Unit 23 Solve problems involving the volume of rectangular and triangular prisms and pyramids 7.9(A) – R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263

Unit 24 Determine the circumference and area of circles 7.9(B) – R . . . . . . . . . . . . . . . . . . . . . . . 273

Unit 25 Determine the area of composite figures 7.9(C) – R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283

Unit 26 Solve problems involving the lateral and total surface area of rectangular and triangular prisms and pyramids using nets 7.9(D) – S . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293

Unit 27 Write one-variable, two-step equations and inequalities, and represent solutions using a number line 7.10(A) – S, 7.10(B) – S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303

Unit 28 Write a corresponding real-world problem given a one-variable, two-step equation or inequality 7.10(C) – S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313

Unit 29 Model and solve one-variable, two-step equations and inequalities 7.11(A) – R . . . . . . . . 323

Unit 30 Determine if the given value(s) make(s) one-variable, two-step equations or inequalities true 7.11(B) – S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333

Unit 31 Write and solve equations using geometric concepts 7.11(C) – S . . . . . . . . . . . . . . . . . . . 343

Unit 32 Compare two groups of numeric data using comparative dot plots or box plots 7.12(A) – R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355

Unit 33 Use data from a random sample to make inferences about a population 7.12(B) – S . . . 365

Unit 34 Compare two populations based on data in random samples from these populations 7.12(C) – S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375

Unit 35 Calculate the sales tax for a given purchase and calculate income tax for earned wages 7.13(A) – S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385

Unit 36 Identify the components of a personal budget; create and organize a financial assets and liabilities record and construct a net worth statement; use a family budget estimator to determine the minimum budget and wage needed to meet basic needs 7.13(B) – S, 7.13(C) – S, 7.13(D) – S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395

motivationmath™

Table of Contents

18271.indb 5 5/12/17 3:34 PM


mentoringminds.com

Unit 1

2













Unit 37 Calculate and compare simple and compound interest; analyze and compare monetary incentives 7.13(E) – S, 7.13(F) – S . . . . . . . . . . . . . . . . . . . . . . . . . . . 405

Performance Assessments: Teacher Information and Answer Keys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415

Math Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429

Chart Your Success . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441

Class Performance Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446

Grade 7 Mathematics Reference Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449

motivationmath™

Table of Contents

18271.indb 6 5/12/17 3:34 PM

MATH | LEVEL 6Teacher Edition Sample Page

mentoringminds.com

Unit 33

TEKS 6.11(A) – Readiness

mentoringminds.com motivationmath™LEVEL 6 ILLEGAL TO COPY 361

Graph points in all four quadrants

Vocabulary FocusThe following are essential vocabulary terms for this unit.

axis/axes horizontal quadrant x-coordinate

coordinate plane ordered pair vertical y-axis

coordinates origin x-axis y-coordinate

Vocabulary ActivitySwat the Term

The teacher reads The Fly on the Ceiling by Dr. Julie Glass. The teacher displays an unlabeled, large coordinate plane (with all four quadrants). The large coordinate plane can be a poster, a wall-mounted dry erase or chalkboard, a coordinate plane that is projected, or a coordinate plane created using painter’s tape. Students form two teams. The first player from each team receives a fly swatter from the teacher. The teacher calls a vocabulary term, and the players swat a corresponding location on the grid (e.g., terms include the following: origin, x-axis, y-axis, Quadrant I, Quadrant II, Quadrant III, Quadrant IV, horizontal axis, vertical axis). The player who first swats a correct location wins a point for his/her team. The players are then replaced with the next player from each team, and play continues. The activity can be expanded to include instructions such as the following.

• Swat the quadrant in which the x- and y-coordinates are both positive. (Quadrant I)• Swat the quadrant in which the x- and y-coordinates are both negative. (Quadrant III)• Swat the quadrant in which the x-coordinate is positive and the y-coordinate is negative. (Quadrant IV)• Swat the quadrant in which the x-coordinate is negative and the y-coordinate is positive. (Quadrant II)• Swat the quadrant that contains the ordered pair (-3, -4). (Quadrant III)• Swat the quadrant that contains the ordered pair (2, -6). (Quadrant IV)• Swat the quadrant that contains the ordered pair (- 1 __

2 , 2). (Quadrant II)

• Swat the quadrant that contains the ordered pair (2, 3.5). (Quadrant I)

(DOK: 1, Bloom’s/RBT: Comprehension/Understand, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.C, (c)2.E, (c)2.I, (c)3.E)

6 ILLEGAL TO COPY totalmotivationMATH™LEVEL 7 mentoringminds.com

7.2(A) Unit 1 Describe Relationships Between Sets of Rational Numbers

Prepare for the Unit Student Pages 7–14

Review the following information to clarify the TEKS before planning instruction.

Reporting Category 1 – Probability and Numerical Representations

The student will demonstrate an understanding of how to represent probabilities and numbers.

Domain – Number and Operations

TEKS 7.2 – The student applies mathematical process standards to represent and use rational numbers in a variety of forms.

Supporting Standard – 7.2(A)Extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of rational numbers.

Mathematical Process TEKS Addressed in This Unit7.1(B), 7.1(E), 7.1(F), 7.1(G)

Unpacking the TEKS

Grade 6Students worked with whole numbers, integers, and rational numbers and were first introduced to negative values. Sixth-grade students created and used graphic organizers to classify and categorize numbers, determining whether a given number belonged to the set of rational numbers, the set of integers, the set of whole numbers, or to multiple sets.

Grade 7In grade 7, students extend the classification of numbers to include the set of counting (natural) numbers as a category. With the exception of activities in which students create a model to show the relationship between number sets, a model should be available for student reference throughout this unit. Irrational numbers are excluded at this level. Although Venn diagrams are used most frequently to show the relationship between number sets, other representations may be used as well, provided the representation makes clear the idea that number sets are nested and not overlapping. Note: A rational number that simplifies to an integer or counting number should be classified in the most descriptive set possible. For example, 15 ___ 3 simplifies to 5 and is classified as a counting number.

7


mentoringminds.com

Unit 33


362 ILLEGAL TO COPY motivationmath™LEVEL 6 mentoringminds.com


Suggested Formative Vocabulary AssessmentOn a sheet of paper, each student draws two perpendicular lines to represent the x- and y-axes, dividing the paper into fourths. The student labels the x-axis, the y-axis, the origin, and each of the four quadrants. In each quadrant, the student records three facts (using complete sentences) about that quadrant. The teacher reviews student work to assess student learning and plans additional instruction as needed.(DOK: 2, Bloom’s/RBT: Comprehension/Understand, ELPS: (c)1.C, (c)1.E, (c)5.B, (c)5.G)

Suggested Instructional Activities

1. In pairs, students play Coordinate Plane Battleship. Provide a handout of a coordinate plane for each student. Players mark four points on their planes without showing their partners. In turn, players try to guess the locations of the points by naming coordinates until they have scored four “hits” by guessing the four points marked on the partner’s coordinate plane.(DOK: 2, Bloom’s/RBT: Comprehension/Understand, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.C, (c)2.E, (c)2.I, (c)3.E)

2. Students work with partners and play a modified version of Connect Four using a coordinate grid and different colors of pencils or markers. In turn, each player names an ordered pair and points to the location to claim a point on the coordinate grid. If the ordered pair is correct, the player records the point in his/her designated color. The first player to correctly name and locate four coordinates in a horizontal, vertical, or diagonal row is the winner. A variation of this game can be played using a coordinate grid marked in fractional units.(DOK: 2, Bloom’s/RBT: Comprehension/Understand, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.E, (c)3.D, (c)3.F)

3. Students complete the Get the Picture? Motivation Station activity on page 269 in the student edition. Then students use a full-page coordinate grid to create their own dot-to-dot picture, listing the coordinates in order. Students trade their coordinate lists and complete one another’s dot-to-dot pictures. The teacher displays student creations.(DOK: 3, Bloom’s/RBT: Synthesis/Create, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.C, (c)2.E, (c)2.I, (c)3.D, (c)3.E)

4. Students work in groups of three to create a flow chart describing how to graph an ordered pair in a four-quadrant coordinate plane. Each group records their work on a large poster or sheet of butcher paper and presents the flow chart to the class. For each flow chart, the teacher displays an ordered pair, and the students follow the directions on the flow chart to graph the point.(DOK: 2, Bloom’s/RBT: Application/Apply, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.C, (c)2.E, (c)2.I, (c)3.D, (c)3.E, (c)5.B)

mentoringminds.com totalmotivationMATH™LEVEL 7 ILLEGAL TO COPY 7

Describe Relationships Between Sets of Rational Numbers Unit 1 7.2(A)Introduction

Activity: (10–15 minutes)

The teacher displays a large nested Venn diagram.

All Students

7th-Grade Students

7th-Grade Boys

7th-GradeBoys withGlasses

The teacher gives sticky notes to several students and instructs them to write their names on the notes. Each student places his/her sticky note in the most appropriate circle of the Venn diagram. The teacher asks students to give their observations about the locations of the sticky notes. Possible responses include: Students in the 7th-grade Boys with Glasses circle are included in all of the circles; No girls are located in the two innermost circles; No notes were placed in the All Students circle (unless the class is mixed-level.) The teacher then asks the students to record definitions in math journals for the terms rational numbers, integers, and whole numbers. Student pairs share their definitions, clarifying and recording one final definition.

The teacher creates a nested Venn diagram to represent the relationship between the sets of numbers, including the set of counting numbers. The teacher asks students to give examples of numbers that would be located in the Counting Numbers section of the diagram. The teacher records correct responses in the diagram, and incorrect responses are written outside the diagram as a group. The teacher asks students to study the group of numbers not recorded in the diagram and compare the numbers to those recorded in the diagram. Working with an elbow partner, students write a definition for counting numbers based on their observations. The teacher asks student pairs to share their definitions, recording key information on the board. The teacher and students work together to write a clear definition for the set of counting numbers using the information recorded. Students record the definition in math journals. Students sketch diagrams similar to the one shown and record at least two numbers in each section, if possible. The teacher asks students the following question: What number(s) belong in the Whole Numbers section of the diagram? (Zero is the only number that fits in the Whole Numbers section since Counting Numbers are included.) (DOK: 2, RBT: Analyze, ELPS: (c)1.A, (c)1.C, (c)1.E, (c)1.H, (c)2.C, (c)3.D, (c)3.E, (c)4.F, (c)5.B)

Formative Assessment (5–10 minutes) Each student is given a blank Venn diagram composed of four nested circ les labeled Rational Numbers, Integers, Whole Numbers, and Counting Numbers. The teacher lists ten numbers (e.g., - 5 __ 7 , 0, 3.

_ 3 , 2 __ 3 , -8, 3, 18 ___ 6 , 1.5, - 24 ___ 3 , -3.25)

on the board, and students record the numbers on their diagrams. The teacher asks the class probing questions such as the following.

• Why did you classify 1.5 as a rational number instead of an integer? • If a number fits into all four categories, where is it placed? Why?

Through examination of student Venn diagrams and answers, the teacher makes plans to provide clarifications in future instructional activities. (DOK: 2, RBT: Analyze, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.C, (c)3.D, (c)3.H)

Connect to the Student Edition: Introduction, page 7

7


mentoringminds.com

Unit 33




Suggested Formative AssessmentThe teacher reads statements such as those shown below. Students give a thumbs-up if the statement is true and a thumbs-down if the statement is false. The teacher notes areas of misunderstanding and plans additional instruction and/or intervention activities as needed.

• On a coordinate plane, the x-axis is horizontal. (true)• On a coordinate plane, the y-axis is diagonal. (false)• The x- and y-axes are perpendicular. (true)• When plotting a point, always begin at the origin. (true)• When plotting the point (-2, -4), move down 2 spaces and then move left 4 spaces. (false)• When plotting the point (2, -4), move right 2 spaces and then move down 4 spaces. (true)• The ordered pairs (2, -2) and (-2, 2) name the same location on a coordinate plane. (false)• The ordered pair (0, 3) names a point on the y-axis. (true)• The ordered pair (3, 0) names a point on the x-axis. (true)(DOK: 1, Bloom’s/RBT: Comprehension/Understand, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.C, (c)2.E, (c)2.I)

Suggested Reflection/Closure Activity

Students reflect on the concepts addressed in the lesson and, in turn, each student shares one new fact or idea learned.(DOK: 1, Bloom’s/RBT: Comprehension/Understand, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.C, (c)2.D, (c)3.D, (c)3.E, (c)3.F)

Suggested Formative AssessmentStudents complete the following information as an exit ticket. The teacher provides each student with a slip of paper like the one shown below. Students complete the ticket and give it to the teacher as they leave. The teacher reviews the answers and determines if additional instruction or interventions are needed.

Name ______________________ Exit Ticket

-2 -1 1 2

2

1

-1

-2A

B C

D

1. Label the x-axis and the y-axis.

2. Draw point O at the origin.

3. Label each quadrant with I, II, III, or IV.

4. Record the ordered pairs for these points.

A __________ C __________

B __________ D __________

(DOK: 1, Bloom’s/RBT: Comprehension/Understand, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)4.G)



Vocabulary FocusThe following are essential vocabulary terms for this unit.

counting numbers negative number repeating decimal terminating decimalexclusive positive number set Venn diagraminclusive rational number subset whole numbersintegers

Vocabulary Activities

Activity: Stake Your Claim (10–15 minutes)

The teacher creates cards labeled counting numbers, whole numbers, integers, and rational numbers, divides the class into four groups, and randomly assigns one card per group. The students select one member to represent the group, and he/she holds the card. The teacher calls numbers, including positive and negative integers, fractions, and decimals. The group representative claims the number called if it best fits in the classification assigned to the group. The group earns a point for each correct claim, and the card is passed to another group member. The groups exchange cards after every five numbers are called until each group has represented each classification. (DOK: 1, RBT: Understand, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.C, (c)2.E, (c)3.E)

Formative Assessment (5–10 minutes) On a sheet of paper, each student writes the terms counting numbers, whole numbers, integers, and rational numbers. Next to each term, the student writes a brief definition of the classification and an example of a number that fits that classification. The teacher examines student output to assess student learning and plans additional review of the vocabulary as needed. (DOK: 1, RBT: Understand, ELPS: (c)1.C, (c)1.E, (c)5.B, (c)5.G)

Connect to the Student Edition: Vocabulary Activity, page 12

Instructional Activities

Activity 1: (20–30 minutes) The teacher displays a set of numbers on the board. The teacher names a number classification. Students hold their thumbs up if they agree the classification fits the numbers in the set or down if they do not agree that the classification fits the numbers in the set. After naming all possible classifications, the class discusses the most descriptive classification for the set. Some examples of sets and their classifications are shown below.

• { 12 ___ 3 , 5, 6.0} (thumbs-up for all classifications; counting)

• {0, -4 __ -2 , 3} (thumbs-up for all classifications except counting; whole)

• {-2, 4, 8 __ -1 } (thumbs-up for integers and rational numbers; integers)

• {7 , - 1 __ 2 , 4.2} (thumbs-up for rational numbers; rational numbers)

(DOK: 2, RBT: Analyze, ELPS: (c)1.C, (c)1.D, (c)1.E, (c)1.H, (c)2.E, (c)2.G, (c)3.G, (c)4.G)

7


mentoringminds.com

Unit 33




Interventions

1. The teacher creates a coordinate plane on the floor, marking the x- and y-axes with painter’s tape. The teacher writes ordered pairs of integers on index cards, one ordered pair per card, and gives one card to each student. In turn, each student must walk from the origin to the point designated by the ordered pair on his/her card, explaining the move (e.g., “I am starting at the origin. I am moving 3 spaces to the right and 2 spaces up.”). When a student arrives at the designated point, he/she reads the ordered pair. The teacher continues the activity using ordered pairs of rational numbers.(DOK: 2, Bloom’s/RBT: Comprehension/Understand, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.C, (c)2.D, (c)2.E, (c)2.I, (c)3.D, (c)3.E, (c)3.F, (c)3.H)

2. Each student writes his/her initials in large block letters on a coordinate plane. Students place points and label the ordered pairs at significant locations (e.g., the vertices of the angles of a letter) so that the ordered pairs of the points can be used to recreate the points and trace the letters. (DOK: 2, Bloom’s/RBT: Application/Apply, ELPS: (c)1.C, (c)1.H, (c)2.I)

3. Students play a game in groups of four. Each group uses two dice (red and white) and a 1–4 spinner. Each player in the group receives a blank coordinate grid. In turn, each player rolls the dice to determine an ordered pair. (The red die indicates the x-coordinate, and the white die indicates the y-coordinate.) Then the player spins the spinner to determine the quadrant and resulting signs for the ordered pair. The player locates, marks, and labels the correct point on the coordinate grid. Other players must confirm correct placement before play passes to the next player. The object of the game is to be the first player to correctly plot an ordered pair in all four quadrants of his/her coordinate plane.(DOK: 1, Bloom’s/RBT: Comprehension/Understand, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.D, (c)2.E, (c)2.I, (c)3.E)

4. Students use interactive online sources to play games that involve locating ordered pairs on a coordinate plane.(DOK: 1, Bloom’s/RBT: Comprehension/Understand, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)4.F)

Suggested Formative AssessmentThe teacher individually interviews each student in the intervention group. The teacher gives the student a coordinate plane and displays an ordered pair. The student explains how to plot the point. The teacher repeats this several times so the student plots points in all four quadrants. Based on student responses, the teacher modifies instruction and/or plans additional interventions.(DOK: 1, Bloom’s/RBT: Comprehension/Understand, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.D, (c)2.E, (c)2.I)


Describe Relationships Between Sets of Rational Numbers Unit 1 7.2(A)Activity 2: (20–30 minutes)

The teacher records the following statements on index cards, one statement per card.

• All counting numbers are integers. • Some rational numbers are whole numbers. • Some integers are positive numbers.

The teacher prints two or more cards with each statement, so that there are enough statements for each pair of students in the class. Student pairs work to create a model, including three numbers in each section, to justify the statement is true. Each pair locates another pair in the class that has the same statement to compare models. (DOK: 2, RBT: Analyze, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.C, (c)2.E, (c)2.I, (c)3.D, (c)3.E)

Activity 3: (20–30 minutes)

The teacher assigns a specific positive or negative number written in the form a __ b to student pairs. Students determine whether the assigned number is a repeating decimal or a terminating decimal. Then the partners classify the number as a counting number, whole number, integer, and/or rational number. Student pairs present the classifications to the class and explain their reasoning. (DOK: 2, RBT: Apply, ELPS: (c)1.C, (c)1.E, (c)2.C, (c)3.D, (c)3.E, (c)3.F)


The teacher randomly assigns a classification, counting numbers, whole numbers, integers, or rational numbers, to each student. The student lists three numbers in the range from -10 to 10 that fit into his/her assigned classification. At least one number should be written as a fraction or decimal. The teacher selects students to share the assigned classifications and the three written numbers. The class discusses any numbers classified incorrectly. (DOK: 2, RBT: Apply, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.C, (c)2.E, (c)2.I, (c)3.D)

Formative Assessment (5–10 minutes)

The teacher creates a large, rectangular Venn diagram using tape on the floor of the classroom or outside with string and stakes. A label is secured in the top corner of each section.

Rational Numbers

Integers

Whole Numbers

Counting Numbers

Each student is given a card printed with a number, including number(s) that fit into each classification on the diagram. Students move to the section of the diagram that best represents the given number. Once each student has chosen a location, the teacher asks students to justify their locations. Students may choose to move to another section of the diagram if they have made a mistake. When all students agree on the placements, the students step out of the diagram, and the process is repeated with a new set of numbers. (DOK: 2, RBT: Analyze, ELPS: (c)1.C, (c)1.E, (c)2.E, (c)3.D, (c)3.E)

Connect to the Student Edition: Guided Practice, page 8, Independent Practice, page 9

7


mentoringminds.com

Unit 33




Extending Student Thinking

Students use grade-appropriate Internet and library resources to research the life and accomplishments of René Descartes, the mathematician credited with the development of the Cartesian plane. Students prepare a presentation for the class by organizing information and graphics on a tri-fold board or by developing a dramatic monologue in which a student poses as Descartes and tells about his life.(DOK: 4, Bloom’s/RBT: Synthesis/Create, ELPS: (c)1.E, (c)4.G, (c)5.G)



Interventions


The teacher displays a nested Venn diagram. The teacher places 12 to 15 numbers, including positive and negative decimals, fractions, whole numbers, and zero, on sticky notes in the Rational Numbers section of the diagram. Students work as a group to move the sticky notes to the Integers, Whole Numbers, or Counting Numbers sections of the diagram, as appropriate. As students move the notes, the teacher asks questions to check for student understanding.

• Why do you think the (Integers, Whole Numbers, Counting Numbers) section is the best placement for that number? • Why did you choose to leave (number) in the Rational Numbers section? • Why can (number) not be placed in the (Rational Numbers, Integers, Whole Numbers, Counting Numbers) section? (DOK: 2, RBT: Analyze, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.C, (c)2.D, (c)3.D, (c)3.E)

Activity 2: (15–20 minutes) The teacher displays a diagram showing the relationship between number sets, with ample room for students to stand in front of the diagram. The teacher divides students into two groups. The groups form two lines, and the first person in each line receives a flyswatter. The teacher calls out or displays a number. The first student in each line runs to the diagram and swats the most specific section of the diagram to show the number’s classification. The first student to swat the correct section earns a point for his/her team. The students pass the flyswatter to the next student in line, and the process is repeated until all students have a turn or until the teacher calls time. The team with more points wins. (DOK: 2, RBT: Analyze, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.I)

Activity 3: (15–20 minutes) Each group of four students is given a set of cards with diff erent numbers written on each card. Each student selects a role: counting number, whole number, integer, or rational number. The students take turns turning over one card at a time and raise their hands if the number fits their selected role. All students in the group must agree on the classification before the next player’s turn. (DOK: 2, RBT: Analyze, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.C, (c)2.D, (c)3.D, (c)3.E, (c)3.F)

Activity 4: (15–20 minutes) Each student creates a set of four nested boxes using index cards or card stock. Students label the boxes with number classifications as shown. The teacher calls a number. Each student records the number on a slip of paper and places the slip in the box labeled with the most descriptive classification. The student then nests the box that contains the slip inside larger boxes, if possible, and records all appropriate classifications of the number in a math journal. The teacher and students repeat the process with other numbers. (DOK: 2, RBT: Analyze, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.I)

CountingNumbers

WholeNumbers

Integers

RationalNumbers

Formative Assessment (5–10 minutes) Individual students are given a blank Venn diagram. Working with each student individually, the teacher displays several numbers, and the student explains where on the Venn diagram each number is placed. The teacher displays as many numbers as necessary for the student to demonstrate an understanding of classifying rational numbers. Based on student responses, the teacher plans additional interventions. (DOK: 2, RBT: Understand, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.D, (c)2.E, (c)2.I, (c)3.D, (c)3.H)

7


mentoringminds.com

Unit 33




Answer Codings (Student pages 263–267)

Page Question Answer Process TEKS

Bloom’s Original/ Revised

DOK Level ELPS

263

1 H, J Comprehension/Understand 1 (c)1.C, (c)1.E, (c)1.H, (c)4.G

2 B Comprehension/Understand 1 (c)1.C, (c)1.E, (c)1.H, (c)4.G

3 (-1 2 _ 3 , -5 1 _

3 ) Comprehension/Understand 1 (c)1.C, (c)1.E, (c)1.H, (c)4.G

4 A, F, L Comprehension/Understand 2 (c)1.C, (c)1.E, (c)1.H, (c)4.G

5 A, E Comprehension/Understand 1 (c)1.C, (c)1.E, (c)1.H, (c)4.G

6 F, G Comprehension/Understand 2 (c)1.C, (c)1.E, (c)1.H, (c)4.G

7 (0, 0) Comprehension/Understand 2 (c)1.C, (c)1.E, (c)1.H, (c)4.G

8 C, D Comprehension/Understand 1 (c)1.C, (c)1.E, (c)1.H, (c)4.G

9Answers will vary but may include: ( 1 _

3 , 5 1 _

3 ), ( 2 _

3 , 5), (2, 3 2 _

3 ).

Comprehension/Understand 1 (c)1.C, (c)1.E, (c)1.H, (c)4.G

264

1 C Comprehension/Understand 2 (c)1.C, (c)1.E, (c)1.H, (c)4.G

2 G Comprehension/Understand 2 (c)1.C, (c)1.E, (c)1.H, (c)4.G

3 D Comprehension/Understand 2 (c)1.C, (c)1.E, (c)1.H, (c)4.G

4 G 6.1(A) Comprehension/Understand 2 (c)1.C, (c)1.E, (c)1.H, (c)4.G

5 A 6.1(A) Application/Apply 2 (c)1.C, (c)1.E, (c)1.H, (c)4.G

265


2 H Comprehension/Understand 2 (c)1.C, (c)1.E, (c)1.H, (c)4.G

3 D 6.1(F) Application/Apply 2 (c)1.C, (c)1.E, (c)1.H, (c)4.G


5 A Comprehension/Understand 2 (c)1.C, (c)1.E, (c)1.H, (c)4.G

266


2 F Comprehension/Understand 2 (c)1.C, (c)1.E, (c)1.H, (c)4.G


4 J Comprehension/Understand 2 (c)1.C, (c)1.E, (c)1.H, (c)4.G



267

1 Answers will vary. 6.1(F) Analysis/Analyze 2 (c)1.C, (c)1.E, (c)1.H, (c)4.G

2III and IVAnswers will vary.The point will move to Quadrant II.

6.1(F) Analysis/Analyze 2 (c)1.C, (c)1.E, (c)1.H, (c)4.G


Describe Relationships Between Sets of Rational Numbers Unit 1 7.2(A)Extending Student ThinkingActivity: (complete outside of regular class time)

Working in groups of 2–4, students use grade-appropriate Internet and library resources to research the history of rational and irrational numbers, including the Egyptians’ Kahun Papyrus, Euclid’s works, and the disagreement between Hippasus and Pythagoras over the existence of irrational numbers. Students present the information in a creative format. Students might deliver a “postgame report” of an imaginary debate between Hippasus and Pythagoras or act out a dramatic interpretation of an off icial presentation of the Kahun Papyrus. (DOK: 4, RBT: Evaluate, ELPS: (c)1.E, (c)2.C, (c)2.I, (c)3.D, (c)4.G, (c)5.G)

Connect to the Student Edition: Critical Thinking, page 11

Reflection/Closure Activity

Activity: (10–15 minutes) Students divide a sheet of paper into five columns labeled Number, Counting Number, Whole Number, Integer, and Rational Number. The teacher reads a list of numbers, and students record each number in the Number column. In the columns to the right, students record checks for each classification that applies. An example is shown below. (DOK: 2, RBT: Analyze, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)4.G)

Number Counting Number Whole Number Integer Rational Number

14 ✓ ✓ ✓ ✓

-45 ✓ ✓

9 __ 3 ✓ ✓ ✓ ✓

0 ✓ ✓ ✓

Connect to the Student Edition: Journal, page 12, Assessment, page 10, Motivation Station, page 13, Homework, page 14

Critical Thinking TraitsStudents may demonstrate multiple critical thinking traits as they participate in the instructional activities for this unit. For example, on the Critical Thinking page, students should experience the following critical thinking traits: Problem 1—Examine, Reflect, Adapt; Problem 2—Communicate, Examine, Link.

On the Motivation Station page, students should experience the following critical thinking traits: Examine, Link. (See Critical Thinking Traits information in Teacher Resources.)

PartnersIndividual

Key for Recommended Groupings

Groups Whole Class

7

MATH | LEVEL 6Student Edition Sample Page

mentoringminds.com


Name __________________________________________

Unit 33 IntroductionStandard 6.11(A) – Readiness

1 Which points are located in Quadrant IV?

2 Which point is located at (–4, 0)?

3 What are the coordinates for point D?

4 Which points have a y-value greater than 4?

5 Which points are located in Quadrant II?

6 Which points have an x-value of 0?

7 What is the ordered pair that is located 2 whole units to the right and 3 whole units down from point E?

8 Which points have negative values for both x and y?

9 If points F and I are connected to form a line segment, name another ordered pair on the line segment.

Use the coordinate grid to answer questions 1–9.

x

y

A

E

B

C

D

G

I

L

K

H

J

–6 –5 –4 –3 –2 –1 1 2 3 4 5 6

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

F


Name __________________________________________

Unit 1 IntroductionStandard 7.2(A) – Supporting

1 Complete the diagram to show the relationship between the following sets of numbers: Counting Numbers, Integers, Rational Numbers, and Whole Numbers.

____________________

____________________

________________

________

2 Use the completed diagram above to determine the set or sets to which each number belongs.

– 2 _ 5 ___________________________

0 ___________________________

– 13 ___________________________

5 ___________________________

0. __ 3 ___________________________

– 4 __ 2 ___________________________

3 List three numbers that belong to each of the following number sets.

Counting numbers _____________________

Integers _____________________________

Rational numbers _____________________

Whole numbers _______________________

4 Label each statement as true or false. Rewrite each false statement so that it is true.

The set of integers is a subset of the set of whole numbers.

___________________________________

___________________________________

All counting (natural) numbers are whole numbers.

___________________________________

___________________________________

If a number is an element of the set of rational numbers, it is also an element of the set of integers.

___________________________________

___________________________________

Not every whole number is an integer.

___________________________________

___________________________________

5 List the set of numbers that matches each description.

a. Natural numbers less than 6

________________________________

b. Integers between – 6 and 3, exclusive

________________________________

c. Whole numbers that do not belong to the subset of natural numbers

________________________________

d. Rational numbers with a denominator of 10 that lie between – 1 _ 2 and 0, inclusive

________________________________

7


mentoringminds.com

264 ILLEGAL TO COPY motivationmath™LEVEL 6 mentoringmindsonline.com

Name __________________________________________

Standard 6.11(A) – ReadinessUnit 33 Guided Practice

Use the polygon shown on the coordinate grid to answer questions 1–3.

y

x

2

1

–1

–2

–2 –1 1 2

1 Which ordered pair does NOT represent a vertex of the polygon?

A (– 3 _ 4 , – 1 _ 2 )

B ( 1 _ 4 , 2 1 _ 2 )

C (–1 1 _ 2 , 1 3 __ 4 )

D (1, – 3 _ 4 )

2 Which ordered pair lies inside the polygon and is located in Quadrant IV?

F (– 1 _ 2 , – 3 _ 4 )

G ( 3 _ 4 , – 1 _ 2 )

H (– 1 _ 4 , – 1 _ 2 )

J ( 1 _ 2 , – 3 _ 4 )

3 Which point is located on the perimeter of the polygon?

A (– 1 _ 2 , 2 1 _ 4 )

B (1, – 1 _ 2 )

C ( 3 _ 4 , 2 1 _ 4 )

D (1 1 _ 2 , 3 _ 4 )

Use the map to answer questions 4 and 5.

The routes Tia takes from her house to different places are represented on the grid below.

y

x

Tia’shouse

Store

School

Park

8

6

4

2

–2

–4

–6

–8

–8 –6 –4 –2 2 4 6 8

4 Which ordered pair best represents a point on Tia’s route to the store?

F (–5, 6)

G (–2.5, 0)

H (–2, 5)

J (–3.5, –3)

5 Each unit on the grid represents 1 mile. For Tia to travel from the park to the library, she must go 3 miles south and 5 miles west. Which represents the coordinates of the library?

A (0, –8)

B (10, –8)

C (–8, 0)

D (–8, 10)


Name __________________________________________

Standard 7.2(A) – SupportingUnit 1 Guided Practice

1 Which representation best shows the relationship between whole numbers and counting numbers?

A Whole Numbers

Counting Numbers

B

Whole Numbers

Counting Numbers

C Whole Numbers

Counting Numbers

D

Counting

Numbers

WholeNumbers

2 Which of the following statements is NOT true?

F All whole numbers are rational numbers.

G All integers are rational numbers.

H All integers are whole numbers.

J All counting numbers are whole numbers.

3 To which of the following sets of numbers does 7 _ 8 belong?

I. Natural numbers II. Whole numbers III. Integers IV. Rational numbers

A I and II only C I, II, and IV only

B I and IV only D IV only

4 Which diagram best demonstrates the relationship between sets of numbers?

F

Rational Numbers

Counting Numbers Whole Numbers Integers

G

Counting Numbers

Whole Numbers

Rational Numbers

Integers

H

Rational Numbers Integers

Counting Numbers Whole Numbers

J

Counting Numbers

Whole Numbers

Integers

Rational Numbers

7


mentoringminds.com


Name __________________________________________

Unit 33 Independent PracticeStandard 6.11(A) – Readiness

Use the grid to answer questions 1–3.

y

x

Q

TV

U

W

X

S

n

m

54321

–1–2–3–4–5

–5 –4 –3 –2 –1 1 2 3 4 5

l

1 Which of the following are NOT coordinates located on line n?

A (4 1 _ 2 , 1 1 _ 2 )

B (1, –1 1 _ 2 )

C (0, –3)

D (–1 1 _ 2 , –4 1 _ 2 )

2 For which point(s) do the x- and y-coordinates have the same value?

F Point S only

G Points S and W only

H Points S, W, and X only

J Points S, W, X, and V only

3 Points T, S, and U represent 3 vertices of a parallelogram. Which best represents point Y, the fourth vertex of the parallelogram?

A (2, –3 1 _ 2 )

B (1, –3 1 _ 2 )

C ( 1 _ 2 , –3 1 _ 2 )

D (0, –3 1 _ 2 )

Use the grid to answer questions 4 and 5.

y

x

2

1

–1

–2

–2 –1 1 2

4 Which ordered pair represents a point located inside the quadrilateral but outside the pentagon?

F (–0.5, –1.25)

G (–0.25, 0.75)

H (–0.75, –0.5)

J (–1.5, –0.75)

5 Which of the following represents a point in Quadrant III that is located on the perimeter of the pentagon?

A (–1.5, –0.25)

B (–0.75, 0.25)

C (0.75, –1.5)

D (–1.25, –1.25)


Name __________________________________________

Unit 1 Independent PracticeStandard 7.2(A) – Supporting

1 The Venn diagram represents the relationship between integers and whole numbers.

Whole Numbers

Integers

Which number would be an element of the set of Integers but not an element of the set of Whole Numbers?

A 0

B – 3

C 5

D – 1 _ 2

2 Set A = {0, 3, 8}. Set A is NOT a subset of which set of numbers?

F Rational numbers

G Integers

H Whole numbers

J Counting numbers

3 Which of the following sets contains an element that CANNOT be classified as rational?

A { 1 _ 2 , 5.5, 13 3 _ 4 , – 4.5}

B {0, 0. _ 9 , 43 __ 3 , – 2}

C {– 13.76, – 5 _ 2 , 9 _ 0 , 95}

D {2 1 _ 2 , – 7, 0.2323, 0 _ 3 }

4 If a number is a member of the set of integers, then it must also be a member of which other set?

F Rational numbers

G Counting numbers

H Whole numbers

J Not here

5 Which lists the correct labels for the diagram shown?

d.

c.b.

a.

A a. Rational Numbers b. Integers c. Whole Numbers d. Natural Numbers

B a. Natural Numbers b. Whole Numbers c. Integers d. Rational Numbers

C a. Natural Numbers b. Integers c. Whole Numbers d. Rational Numbers

D a. Rational Numbers b. Integers c. Natural Numbers d. Whole Numbers

7


mentoringminds.com


Name __________________________________________

Standard 6.11(A) – ReadinessUnit 33 Assessment

Use the grid to answer questions 1–6.

y

x

A

F G

HJ

C

B 2

1

–1

–2

–2 –1 1 2

1 Which ordered pair represents a point inside both the triangle and the rectangle?

A (0.2, 1)

B (0.8, 0.4)

C (–0.6, 1.2)

D (–0.4, –1.4)

2 Which of the following represents a point in Quadrant IV that is located at a vertex of one of the figures?

F (1.2, –1.2)

G (–2.4, –1.2)

H (2.2, –1.6)

J (–0.6, 1.6)

3 Which best describes the signs of all coordinates located in Quadrant II?

A (–x, –y)

B (–x, y)

C (x, –y)

D (x, y)

4 A right triangle is formed using points C and H as two of the vertices. Which point best represents the coordinates for point X, the third vertex of the triangle?

F (1.2, –1.8)

G (1.8, –2.6)

H (2.2, –1)

J (2.2, –1.2)

5 Which ordered pair represents an intersection of two line segments?

A (0, –1.6)

B (–1.2, 1)

C (–1, –1.2)

D (0.8, –1.2)

6 Which ordered pair represents a point located inside the triangle but outside the rectangle?

F (–0.2, 1.4)

G (–1.2, –0.2)

H (–0.4, –1.4)

J (0.4, –0.8)


Name __________________________________________

Standard 7.2(A) – SupportingUnit 1 Assessment

1 In which section of the diagram does the number – 6 _ 3 belong?

Rational Numbers

Whole Numbers

Integers

Counting Numbers

A Rational Numbers

B Integers

C Whole Numbers

D Counting Numbers

2 Which best describes all possible classifications for the following set of numbers?

{0, 4, 25, 32}

I. Counting numbers II. Integers III. Rational numbers IV. Whole numbers

F IV only

G I and IV only

H II, III, and IV only

J I, II, III, and IV

3 Which of the following statements is always true?

A All integers are counting numbers.

B All rational numbers are integers.

C All integers are whole numbers.

D All counting numbers are whole numbers.

4 Aldine uses the diagram below to explain the relationship between integers and rational numbers.

Integers

Rational Numbers

Which of the following rational numbers does NOT belong to the subset of integers?

F 6 _ 2

G – 4.0

H – 15 __ 3

J 7.5

5 Given the set of numbers {– 2, 0, 12 __ 2 , 8, 10} , which elements belong to the set of natural numbers?

A 12 __ 2 , 8, and 10 only

B 8 and 10 only

C 0, 8, and 10 only

D 0, 12 __ 2 , 8, and 10 only

7


mentoringminds.com


Name __________________________________________

Standard 6.11(A) – Readiness Unit 33 Critical Thinking

Use the grid to answer the questions that follow.

x

y

10

8

6

4

2

–2

–4

–6

–8

–10

–10 –8 –6 –4 –2 2 4 6 8 10

1 An ordered pair is located in Quadrant III. The x-coordinate is greater than the y-coordinate. List 3 possible ordered pairs that meet this criteria.

__________ __________ __________

2 Draw a line segment on the coordinate plane above using the following criteria:

• One endpoint must be located in Quadrant IV.

• The line segment must intersect the y-axis but must NOT intersect the x-axis.

In which quadrant or quadrants does the line segment lie? ________________________

What are the endpoints of the line segment? ____________________________________

If the x- and y-coordinates of the endpoint located in Quadrant IV are reversed, describe what happens to the point’s location.

________________________________________________________________________

Analysis

Analyze


Name __________________________________________

Standard 7.2(A) – Supporting Unit 1 Critical Thinking

1 Create a set of numbers, Set A, using the guidelines below.

• Must contain a minimum of 5 members

• Exactly 1 member must be a natural number

• Exactly 2 members must be whole numbers

• At least 1 member must be a rational number only

Set A = ____________________________________________________________________

Justify Set A is correct using a visual representation.

2 Callen draws the diagram below to represent the relationship between sets of numbers.

Based on what has been studied in this unit, is Callen’s diagram an accurate representation of the relationship between sets of numbers? Justify your answer using words and creating your own diagram above, if appropriate.

___________________________________________________________________________

___________________________________________________________________________

Analysis

Analyze

Application

Apply

Rational Numbers

Integers

Negative Numbers

Positive Numbers

WholeNumbers

7


mentoringminds.com


Name __________________________________________

Standard 6.11(A) – ReadinessUnit 33 Journal/Vocabulary Activity

Explain to a younger student what happens when an ordered pair is not plotted in the correct order.

___________________________________________________________________________

___________________________________________________________________________

Is there ever a time when the order of the coordinates does not matter? Explain.

____________________________________________________________________________

____________________________________________________________________________

Use the terms in the box to correctly label the picture shown. Each term is used only once.

x-coordinate Quadrant III coordinate plane x-axis

y-axis origin Quadrant I point Quadrant IV

y-coordinate Quadrant II ordered pair

(–3, –4) (1, –4.5)

1.

2.

3.

4.

5.

6.

11.

12.

8.

10.

9.

7.

Vocabulary Activity

Analysis

Analyze

Journal


Name __________________________________________

Standard 7.2(A) – SupportingUnit 1 Journal/Vocabulary Activity

Consider the classifications of each number below.

7 _ 3 : Rational number – 15 __ 5 : Rational number, integer

Explain the similarities and differences between the two numbers, specifically why they are classified differently.

___________________________________________________________________________

___________________________________________________________________________

Create a concept web for the following vocabulary terms: rational numbers, integers, whole numbers, and counting numbers. Provide at least two examples for each term.

Relationship between sets of numbers

term term term term

examples examples examples examples

Vocabulary Activity

Analysis

Analyze

Journal

7


mentoringminds.com


Name __________________________________________

Unit 33 Motivation StationStandard 6.11(A) – Readiness

Get the Picture?

Complete Get the Picture? individually. Plot the ordered pairs listed below, and then connect them in the order they are shown to reveal a picture.

Ordered Pairs

1. (3 2 __ 3 , 2 1 __ 3 ) 9. ( 2 __ 3 , –2 2 __ 3 ) 17. (–1 1 __ 3 , –2 2 __ 3 ) 25. (–3, –1 2 __ 3 )

2. (3, 2) 10. (0, –2 2 __ 3 ) 18. (–2, –2 2 __ 3 ) 26. (–2 1 __ 3 , – 1 __ 3 )

3. (2 1 __ 3 , 1 __ 3 ) 11. ( 1 __ 3 , –1 2 __ 3 ) 19. (–1 1 __ 3 , –1 1 __ 3 ) 27. (–1, 1 __ 3 )

4. (2, –1 1 __ 3 ) 12. ( 1 __ 3 , –1 1 __ 3 ) 20. (–2, –1 1 __ 3 ) 28. (1 1 __ 3 , 1 __ 3 )

5. (2, –2 2 __ 3 ) 13. (– 1 __ 3 , –1 1 __ 3 ) 21. (–2 2 __ 3 , –2) 29. (2 2 __ 3 , 2 1 __ 3 )

6. (1 1 __ 3 , –2 2 __ 3 ) 14. (– 1 __ 3 , –2 2 __ 3 ) 22. (–3 1 __ 3 , –2 1 __ 3 ) 30. (3 1 __ 3 , 2 2 __ 3 )

7. (1 1 __ 3 , –1 1 __ 3 ) 15. (–1, –2 2 __ 3 ) 23. (–4, –2 2 __ 3 ) 31. (3 2 __ 3 , 2 2 __ 3 )

8. (1, –1 2 __ 3 ) 16. (–1, –2) 24. (–3 2 __ 3 , –2 1 __ 3 )

x

y

Start/End

–3 –2 –1 1 2 3

3

2

1

–1

–2

–3


Name __________________________________________

Unit 1 Motivation StationStandard 7.2(A) – Supporting

It’s Written in the NumbersPlay It’s Written in the Numbers with a partner. Each pair of players needs a game board and a paper clip to use with the spinner. Each player needs a different color pen or pencil. Player 1 begins by spinning to determine a number set and then records a number in the appropriate location on the diagram. If recorded correctly, player 1 earns points for the set rolled according to the chart. He or she then records the number, number set, and points earned in the table, and play passes to player 2, who repeats the process. If a player incorrectly records a number in the diagram, he or she loses a turn. The game ends when each player has recorded 9 numbers in the diagram. The player with more points wins.

Points Earned

Rational Number 5 points

Integer 4 points

Whole Number 3 points

Counting Number 2 points

Rational Numbers

Whole Numbers

Integers

Counting Numbers

CountingNumbers

IntegersRationalNumbers

WholeNumbers

Player 1 Player 2

Number Number Set Points Number Number Set Points

7


mentoringminds.com


Name __________________________________________

Standard 6.11(A) – ReadinessUnit 33 Homework

1. Research jobs that use the coordinate plane. Select 2 different jobs and write one paragraph about each, explaining how the coordinate plane is used and why it is important to that job. Share with the class.

2. Use string and stakes to create a coordinate plane in the yard. Take turns with friends and family tossing a beanbag, or a similar object, onto the grid. Give the coordinates of the location where the object lands. If correct, the person earns a point. The winner is the person with the most points.

1 Plot a point that lies on AB, and label it Q.

2 What are the coordinates for point Q?

3 List the ordered pairs for each labeled point that lies in Quadrant II.

4 List one ordered pair that lies on the circle and inside the rectangle.

5 List one ordered pair that lies inside the circle and that is located in Quadrant IV.

6 Plot a point that could be used to complete a rectangle that is twice the area of triangle MNP. Label the point R. What are the coordinates for point R?

7 Plot point (x, y) where x < 0 and x · y > 0. Label the point S. Explain how you determined where to plot point S.

___________________________________

___________________________________

8 In which quadrant does point S lie?

9 In which quadrant does point J lie? Explain. ___________________________________

___________________________________

Connections

Use the coordinate grid to answer questions 1–9.

y

x

A

B

F C

E D

J

M

N P

4

3

2

1

–1

–2

–3

–4

–4 –3 –2 –1 1 2 3 4


Name __________________________________________

Standard 7.2(A) – SupportingUnit 1 Homework

1. Research the origin of the term rational number. Write a brief paragraph detailing the origin of the term, including who first used the term to describe numbers, in what country the term originated, and the approximate year of origin.

2. Write a rap or a poem to aid you in remembering the sets of numbers and their relationships. Share your creation with your family or friends.

1 Record the numbers described in the diagram.

Two numbers belonging only to the Rational Numbers section

Three numbers that best belong in the Integers section

One number that best belongs in the Whole Numbers section

Four numbers that best belong in the Natural Numbers section

2 Write a number set for each description given.

a. The counting numbers between 20 and 30, exclusive

________________________________

b. The rational numbers with a denominator of 3 that lie between – 1 and 1, inclusive

________________________________

c. The integers that are multiples of 4, and are greater than 0 but less than 20

________________________________

d. The whole numbers greater than or equal to 0 and less than 8

________________________________

3 Record the numbers from the diagram below that are incorrectly located. For each number recorded, give the correct location.

Rational Numbers

Integers

Counting Numbers

16

–5

–20.45

– 3 __ 4

– 24 __ 6

___________________________________

___________________________________

___________________________________

___________________________________

Connections

Refer to the diagram to answer the following questions.

Rational Numbers

Integers

Whole Numbers

Counting Numbers

7

Getting tated: motivationmath - Mentoring Minds...mentoringminds .com ™ttal motivation ELA EE 1...

Documents

Transcript of Getting tated: motivationmath - Mentoring Minds...mentoringminds .com ™ttal motivation ELA EE 1...