Getting tated: motivationmath - Mentoring MindsUnit 20 Use models and diagrams to explain the...

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 8Teacher 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 real numbers 8.2(A) – S . . . . . . . . . . . . . . . . . . . . 39

Unit 2 Approximate the value of an irrational number and locate the value on a number line 8.2(B) – S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

Unit 3 Convert between standard decimal and scientific notations 8.2(C) – S . . . . . . . . . . . . . . . . 61

Unit 4 Order sets of real numbers 8.2(D) – R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

Unit 5 Generalize that ratios of corresponding sides of similar shapes are proportional 8.3(A) – S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

Unit 6 Compare and contrast attributes of a shape and its dilation 8.3(B) – S . . . . . . . . . . . . . . . 89

Unit 7 Use an algebraic representation to explain the effect of a scale factor applied to two-dimensional figures 8.3(C) – R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

Unit 8 Use similar right triangles to develop an understanding of slope 8.4(A) – S . . . . . . . . . . . 109

Unit 9 Graph proportional relationships 8.4(B) – R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

Unit 10 Use data from a table or graph to determine the rate of change or slope and y-intercept 8.4(C) – R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

Unit 11 Represent linear proportional and non-proportional situations with tables, graphs, and equations 8.5(A) – S, 8.5(B) – S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

Unit 12 Contrast bivariate sets of data that suggest a linear relationship with sets that do not 8.5(C) – S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

Unit 13 Use a trend line to make predictions 8.5(D) – R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

Unit 14 Solve problems involving direct variation 8.5(E) – S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

Unit 15 Distinguish between and identify examples of proportional and non-proportional situations 8.5(F) – S, 8.5(H) – S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

Unit 16 Identify functions 8.5(G) – R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

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Unit 17 Write an equation in the form y = mx + b to model a linear relationship between two quantities 8.5(I) – R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199

Unit 18 Describe the volume formula of a cylinder in terms of its base area and height 8.6(A) – S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

Unit 19 Model the relationship between the volume of a cylinder and a cone 8.6(B) . . . . . . . . . . 219

Unit 20 Use models and diagrams to explain the Pythagorean Theorem 8.6(C) – S . . . . . . . . . . 227

Unit 21 Solve problems involving the volume of cylinders, cones, and spheres 8.7(A) – R . . . . . 237

Unit 22 Determine solutions for lateral and total surface area problems involving rectangular prisms, triangular prisms, and cylinders 8.7(B) – R . . . . . . . . . . . . . . . . . . . . 247

Unit 23 Use the Pythagorean Theorem and its converse to solve problems 8.7(C) – R . . . . . . . . 257

Unit 24 Determine the distance between two points on a coordinate plane using the Pythagorean Theorem 8.7(D) – S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265

Unit 25 Write one-variable equations or inequalities that represent problems and write real-world problems given one-variable equations or inequalities 8.8(A) – S, 8.8(B) – S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273

Unit 26 Model and solve one-variable equations with variables on both sides of the equal sign 8.8(C) – R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283

Unit 27 Use informal arguments to establish facts about angle relationships 8.8(D) – S . . . . . . . 293

Unit 28 Identify and verify values of x and y that simultaneously satisfy two linear equations 8.9(A) – S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305

Unit 29 Generalize properties of orientation and congruence of transformations and differentiate between transformations that preserve congruence and those that do not 8.10(A) – S, 8.10(B) – S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313

Unit 30 Explain the effect of transformations on a coordinate plane using an algebraic representation 8.10(C) – R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325

Unit 31 Model the effect of dilations on linear and area measurements 8.10(D) – S . . . . . . . . . . . 335

Unit 32 Construct a scatterplot and describe the association between bivariate data 8.11(A) – S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343

Unit 33 Determine the mean absolute deviation using a data set of no more than 10 data points 8.11(B) – S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353

Unit 34 Simulate generating random samples to develop the notion of a random sample being representative of the population 8.11(C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363

Unit 35 Solve problems comparing how interest rate and loan length affect cost of credit; calculate total cost of repaying a loan using online calculators; identify and explain advantages and disadvantages of different payment methods 8.12(A) – S, 8.12(B), 8.12(E) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373

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Unit 36 Explain how regular investments grow over time; calculate and compare simple and compound interest 8.12(C) – S, 8.12(D) – R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383

Unit 37 Analyze and determine if a situation is financially responsible and identify the benefits of financial responsibility and the costs of financial irresponsibility 8.12(F) . . . . . . . . . . . 393

Unit 38 Estimate the cost of college education and devise a periodic savings plan 8.12(G) – S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403

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

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

Chart Your Success . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445

Class Performance Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450

Grade 8 Mathematics Reference Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453

motivationmath™

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MATH | LEVEL 6Teacher Edition Sample Page

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Unit 33

TEKS 6.11(A) – Readiness

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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)

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8.3(C) Unit 7 Use Algebraic Representations to Explain the Eff ect of a Scale Factor

Prepare for the Unit Student Pages 55–62

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

Reporting Category 3 – Geometry and Measurement

The student will demonstrate an understanding of how to represent and apply geometry and measurement concepts.

Domain – Proportionality

TEKS 8.3 – The student applies mathematical process standards to use proportional relationships to describe dilations.

Readiness Standard – 8.3(C)Use an algebraic representation to explain the eff ect of a given positive rational scale factor applied to two-dimensional figures on a coordinate plane with the origin as the center of dilation.

Mathematical Process TEKS Addressed in This Unit8.1(A), 8.1(B), 8.1(D), 8.1(E), 8.1(F), 8.1(G)

Unpacking the TEKS

Grade 5 Students were introduced to the coordinate plane.

Grade 6Students graphed points in all four quadrants of the coordinate plane. Students also began representing problems involving ratios and rates in the sixth grade.

Grade 7Students extended their work to solving problems involving ratios and rates using proportions

Grade 8In grade 8, students compare and contrast attributes of shapes and their dilations graphed on the coordinate plane. Students are introduced to using an algebraic representation to show the eff ect a scale factor has when applied to two-dimensional figures. All dilations at this level are performed with the origin as the center of dilation. The use of coordinate planes will be utilized extensively in this unit and will be beneficial visual representations.

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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)

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Use Algebraic Representations to Explain the Eff ect of a Scale Factor Unit 7 8.3(C)Introduction

Activity: (10–15 minutes)

Students are placed in small groups, and each group is provided a graph of a diff erent figure and a dilation of the figure. Although the figures provided to each group are diff erent, the same scale factor is used for the dilations. Students record the coordinates of the vertices of the figures in tables. Group members discuss any patterns between the vertices of the original figure and the vertices of the dilation. Each group shares observations with the class. (DOK: 1, RBT: Analyze, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.C, (c)3.D, (c)3.E, (c)3.G)

y

x2 4 6 8 10 12 14 16 18 20

20

18

16

14

12

10

8

6

4

2

A’ B’

C’

B

C

A

Figure Dilation

x y x y

A A'

B B'

C C'

Formative Assessment (5–10 minutes) Each student is given a coordinate plane with a figure and its dilation graphed. Students record one complete sentence stating the pattern that exists between the coordinates of the vertices of the original figure and the coordinates of the vertices of the dilation. The teacher reviews responses to plan future instruction. (DOK: 1, RBT: Analyze, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)5.B, (c)5.G)

Connect to the Student Edition: Introduction, page 55

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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.

algebraic representation (transformation) dilation scale factoraxis/axes dimensions similar figurescenter of dilation ordered pair transformationcoordinate plane origin two-dimensional figurecoordinates prime notation (´) vertex/vertices

Vocabulary Activities

Activity: The Hot Seats (10–15 minutes) The teacher divides the class into two teams and randomly selects a student from each team to sit in one of two chairs facing the class. The teacher states a vocabulary term or reads the definition of a term. The first student in one of the hot seats to raise his/her hand and give a correct response receives a point for his/her team. Another team member takes the place of the student who responded correctly. If the first response is incorrect, the other student has the opportunity to respond and earn a point for his/her team. If neither student responds correctly, both students are replaced by team members. The teacher discusses the correct response with the class before continuing to a new term or definition. Play continues until all terms have been addressed. The team with more points wins. (DOK: 1, RBT: Understand, ELPS: (c)1.A, (c)1.C, (c)2.C, (c)2.D, (c)3.D)

Formative Assessment (5–10 minutes) The teacher distributes a response sheet printed with a figure and its dilation graphed on a coordinate plane to each student.

(x, y) (2x, 2y)

A(0, 3) A’(0, 6)B(3, 0) B’(6, 0)

C(0, -3) C’(0, -6)D(-3, 0) D’(-6, 0)

y

x-8 -6 -4 -2 2 4 6 8

8

6

4

2

-2

-4

-6

-8

A’

B’D’

C’

A

BD

C

8.4

8.4

4.2

4.2

Students locate and label an example of each unit vocabulary term on the response sheet. The teacher reviews student work to determine if additional instruction is needed. (DOK: 1, RBT: Remember, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.C, (c)2.I, (c)3.D, (c)3.E, (c)4.F, (c)4.G, (c)5.B)

Connect to the Student Edition: Vocabulary Activity, page 60

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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)


Use Algebraic Representations to Explain the Eff ect of a Scale Factor Unit 7 8.3(C)Instructional Activities

Activity 1: (20–30 minutes)

Student pairs receive a graph of a figure and its dilation on the coordinate plane. Students record a verbal description of the relationship between the coordinates of the original figure and the coordinates of the dilation. The class reviews how to translate from verbal representations to algebraic representations. The teacher introduces the technique for recording the scale factor applied to a figure using an algebraic representation: (x, y) → (ax, ay), where a is a positive rational scale factor. Each pair then records an algebraic representation for the relationship shown in their given graphs. The teacher selects several pairs of students to share their results for discussion. The teacher corrects any misunderstandings. (DOK: 2, RBT: Apply, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.C, (c)2.D, (c)3.D, (c)3.E, (c)5.B, (c)5.G)


Pairs of students are provided figures graphed on coordinate planes. One student receives a scale factor that is greater than one, and the other receives a scale factor between 0 and 1. Each student determines the coordinates of the dilation that results from his/her scale factor. Then each student graphs his/her dilation on the same coordinate plane as the original figure. Students determine the scale factor for the dilation graphed by their partners. Students record the algebraic representations of the scale factors beneath the graphed figures. (DOK: 2, RBT: Apply, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)1.C, (c)2.C, (c)3.D, (c)3.E)


Before class begins, the teacher posts signs around the classroom containing algebraic representations of various scale factors. Upon entering the classroom, each student receives an index card with the description of a figure and its dilation using only the coordinate points of the vertices. Each student determines the scale factor used to dilate the original figure on his/her card. When the teacher gives the signal, students move to the sign displaying the algebraic representation of the scale factor found. Student groups justify their choices, and students are given the opportunity to move to a diff erent group if they determine an error was made. The cards may be shuff led and the activity repeated as time allows. (DOK: 2, RBT: Apply, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.C, (c)2.D, (c)3.D, (c)3.E, (c)3.G)

Formative Assessment (5–10 minutes) Each student receives an index card with an algebraic representation of a dilation printed on one side. The teacher displays a graph of a figure on the coordinate plane. Students record the vertices of the displayed figure. Next, students use the given algebraic representation to dilate the given vertices and record the vertices of the dilation on the index cards. Students then write one sentence explaining how they know the vertices for the dilation are correct. The teacher collects the cards as students exit the classroom and uses the responses to plan further instruction or intervention. (DOK: 2, RBT: Apply, ELPS: (c)1.E, (c)5.B, (c)5.G)

Connect to the Student Edition: Guided Practice, page 56, Independent Practice, page 57

PartnersIndividual

Key for Recommended Groupings

Groups Whole Class

8


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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

Activity 1: (15–20 minutes) Students practice locating and naming points on the coordinate plane by playing a game of Sink the Ship. Each student is given a four-quadrant coordinate plane numbered from –6 to 6. Students draw four rectangular ships that cover 2, 3, 4, and 5 points on the coordinate plane, keeping their grids hidden from each other.

y

x -5 -4 -3 -2 -1 1 2 3 4 5

5

4

3

2

1

-1

-2

-3

-4

-5

Students take turns guessing coordinates to attempt to “hit” each other’s ships. When a student succeeds in guessing a correct coordinate pair, he/she places an X on the point. The student who has more hits when time is called wins. (DOK: 1, RBT: Understand, 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) To each student, the teacher provides an algebraic representation describing the eff ect of a scale factor applied to a figure. Students record everything they know about the figure and its dilation based on the algebraic representation. The teacher may ask probing questions as needed. The process may be repeated with a new algebraic representation.

(x, y) → (2.5x, 2.5y)

• What is the scale factor used to dilate the figure? (2.5) • Does the dilation show a reduction or an enlargement? How do you know? (Enlargement, because the scale factor is greater than 1) • How much larger or smaller are the dimensions of the dilation compared to the original figure? (The dimensions of the dilation are 2.5 times larger than the dimensions of the original figure.)

(DOK: 2, RBT: Understand, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.C, (c)2.D, (c)5.B, (c)5.G)

Formative Assessment (5–10 minutes) Students respond to the following prompt in math journals.

Triangle ABC is graphed on the coordinate plane. The triangle is dilated using a scale factor of 4 to form triangle A´B´C´. If point A is located at (2, 3), what would be the coordinates of point A´? How do you know?

The teacher checks student responses for accuracy and understanding and plans further interventions as needed.(DOK: 2, RBT: Apply, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)5.B, (c)5.G)

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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


Use Algebraic Representations to Explain the Eff ect of a Scale Factor Unit 7 8.3(C)Extending Student Thinking Students select one of the following extension activities.

Activity 1: (complete outside of regular class time) Students use what they have learned about scale factors and dilations to create a scale model of a three-dimensional object. Students select the object they wish to recreate as a model and are assigned a scale factor. Students apply the scale factor to the dimensions of the object and create the model. Students share their models with the class and explain the process they used to create the model. (DOK: 3, RBT: Create, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)3.D, (c)3.G, (c)3.H, (c)4.G)

Activity 2: (complete outside of regular class time) Students research scale design used in movie-making in films, such as The Lord of the Rings, Star Trek, and Star Wars. Students design and create a scale model of a scene from a movie or a scene from a historical event, using realistic dimensions. Students give presentations to the class on their research and how they applied scale factor to create their scenes. (DOK: 3, RBT: Create, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)3.B, (c)3.C, (c)3.D, (c)3.H)

Connect to the Student Edition: Critical Thinking, page 59

Reflection/Closure Activity

Activity: (10–15 minutes) The teacher provides a graph of a figure on the coordinate plane, an algebraic representation of a dilation, and a set of coordinate points for the dilated figure to each student. One of the coordinate points should be incorrect. Students identify the incorrect point and explain why it is incorrect. Then students determine the correct point and graph the dilation on the coordinate plane with the original figure. The teacher reviews student work and plans further instruction or intervention as needed. (DOK: 1, RBT: Analyze, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)5.B, (c)5.G)

Connect to the Student Edition: Assessment, page 58, Journal, page 60, Motivation Station, page 61, Homework, page 62

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: Adapt, Examine, Link, Reflect, Strive.

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

8

MATH | LEVEL 6Student Edition Sample Page

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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 7 IntroductionStandard 8.3(C) – Readiness

1 Triangle DEF is dilated by a scale factor of 1 _ 3 to form triangle RST.

y

x2 4 6 8 10 12 14 16 18 20

20

18

16

14

12

10

8

6

4

2

F

E

D

S

R

T

Complete the table to show the relationship between the coordinates of the original figure and the coordinates of the dilated figure.

Vertices of Triangle

DEFRelationship

Corresponding Vertices of

Triangle RST

Write a general algebraic representation to describe the dilation of each x- and y-value of the vertices of triangle DEF to form triangle RST.

2 A construction company builds a rectangular parking lot.

y

x-8 -6 -4 -2 2 4 6 8

8

6

4

2

-2

-4

-6

-8

A B

DC

The company decides to enlarge the lot. If the new vertices can be represented by the algebraic representation (2.5x, 2.5y), what are the coordinates of point B’ ?

3 A dilation of a triangle can be represented by the coordinates (6x, 6y). How will this change the dimensions of the triangle?

What scale factor is used to dilate the triangle?

4 A rectangle is dilated by a scale factor of 2 _ 5 . Use an algebraic representation to describe the effect of the scale factor on the coordinates of the original rectangle.

8


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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 8.3(C) – ReadinessUnit 7 Guided Practice

1 Look at the dilation shown.

y

x-8 -6 -4 -2 2 4 6 8

8

6

4

2

-2

-4

-6

-8

A

B

D

C

A’

B’

D’

C’

Which best represents the change in the vertices of rectangle ABCD to form rectangle A’B’C’D’ ?

A (x, y) ( 1 _ 2 x, 1 _ 2 y)

B (x, y) (2x, 2y)

C (x, y) (4x, 4y)

D (x, y) (3x, 2y)

2 A triangle with a vertex at point Y (-3, 7) is dilated by a scale factor represented by the coordinate pair ( 2 _ 3 x, 2 _ 3 y) . What is the location of Y’ ?

F Y’ (-2, 4 2 _ 3 )

G Y’ (-6, 14)

H Y’ (-3 2 _ 3 , 7 2 _ 3 )

J Y’ (-2, 4)

3 Rectangle FGHJ has coordinates F (-8, 6), G (8, 6), H (8, -6), and J (-8, -6). The rectangle is dilated by a scale factor of 3. Which shows the effect of the scale factor on rectangle FGHJ to form rectangle F’G’H’J’ ?

A (x + 3, y + 3)

B ( 1 _ 3 x, 1 _ 3 y)

C (x – 3, y – 3)

D (3x, 3y)

4 Pentagon QRSTU is dilated to form pentagon Q’R’S’T’U’.

y

x-8 -6 -4 -2 2 4 6 8

8

6

4

2

-2

-4

-6

-8

U’ T’

Q’ S’

R’

If Q is located at (-2, 1), which of the following can be used to determine the location of R?

F (0 · 4, 8 · 4)

G (0 · 1 _ 2 , 8 · 1 _ 2 )

H (0 · 1 _ 4 , 8 · 1 _ 4 )

J (0 · -2, 8 · -2)

8


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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 7 Independent PracticeStandard 8.3(C) – Readiness

1 A triangle with vertices T (0, 0), U (0, 3), and V (4, 0) is dilated, and the vertices of the new triangle are T’ (0, 0), U’ (0, 1.5), and V’ (2, 0). Which best represents the scale factor applied to the original triangle?

A (1x, 1y)

B (0x, 0y)

C (0x, -0.5y)

D (0.5x, 0.5y)

2 The city planning committee votes to change one of the baseball fields to be used as a softball field. The softball field is shown on the grid.

y

x-8 -6 -4 -2 2 4 6 8

8

6

4

2

-2

-4

-6

-8

N’

M’O’

L’

The algebraic expressions ( 2 _ 3 x, 2 _ 3 y) are used to describe the dilation of the baseball field. Which point does NOT correctly reflect the dilation?

F L(0, 7.5)

G M(6, 1.5)

H N(0, -3.5)

J O(-6, 1.5)

3 Parallelogram UVWX is dilated to form parallelogram U’V’W’X’.

y

x-8 -6 -4 -2 2 4 6 8

8

6

4

2

-2

-4

-6

-8

U’

X’ W’

V’

U

X W

V

Which best represents the dilation of parallelogram UVWX to parallelogram U’ V’W’X’ ?

A ( 1 _ 2 x, 1 _ 2 y)

B (2x, 2y)

C ( 2 _ 3 x, 2 _ 3 y)

D (3x, 3y)

4 A triangle with vertices E (-9, 6), F (-6, -5), and G (4, 0) is dilated to form a triangle with vertices E’ (-3, 2), F’ (-2, -1 2 _ 3 ) , and G’ (1 1 _ 3 , 0) . Which best explains the effect of the scale factor applied to triangle EFG to form triangle E’F’G’ ?

F (x, y) (-3x, -3y)

G (x, y) ( 2 _ 3 x, 2 _ 3 y)

H (x, y) (3x, 3y)

J (x, y) ( 1 _ 3 x, 1 _ 3 y)

8


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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 8.3(C) – ReadinessUnit 7 Assessment

1 Mr. Ramirez receives blueprints for his new house. The scale used to draw the blueprints is 1 _ 4 inch equals 1 foot. The blueprint is drawn on a coordinate plane. Which algebraic representation explains the dilation used to create the blueprint of Mr. Ramirez’s new house?

A (4x, 4y)

B (12x, 12y)

C ( 1 _ 4 x, 1 _ 4 y)

D ( 1 __ 12 x, 1 __ 12 y)

2 The figure shown is dilated using a scale factor of (0.75x, 0.75y).

y

x-8 -6 -4 -2 2 4 6 8

8

6

4

2

-2

-4

-6

-8

Which ordered pair will NOT be one of the new vertices?

F (-2.25, 2.25)

G (-1.5, -6)

H (3, 3.75)

J (4, -2.5)

3 A parallelogram with vertices H (-2, 2), J (5, 2), K (-3, 3), and L (-4, -3) is dilated to form a parallelogram with vertices H’ (-5, 5), J’ (12.5, 5), K’ (-7.5, 7.5), and L’ (-10, -7.5). Which representation best explains the effect of this dilation?

A (x, y) (3x, 3y)

B (x, y) (2.5x, 2.5y)

C (x, y) (2x, 2y)

D (x, y) (1.5x, 1.5y)

4 Triangle I is dilated to form Triangle II.

y

x-8 -6 -4 -2 2 4 6 8

8

6

4

2

-2

-4

-6

-8

Triangle I

Triangle II

Which shows the scale factor used to dilate Triangle I to form Triangle II ?

F (3x, 3y)

G ( 1 _ 2 x, 1 _ 2 y)

H (2x, 2y)

J ( 1 _ 3 x, 1 _ 3 y)

8


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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 8.3(C) – Readiness Unit 7 Critical Thinking

Triangle PQR is graphed on the coordinate plane as shown.

y

x -6 -4 -2 2 4 6

6

4

2

-2

-4

-6

P

Q

R

1 Dilate PQR using ( 1 _ 4 x, 1 _ 4 y) . Sketch and label triangle P’Q’R’ on the coordinate plane and list the new vertices.

P’ __________ Q’ __________ R’ __________

2 Dilate P’Q’R’ using (2x, 2y). Sketch and label triangle P”Q”R” on the coordinate plane and list the new vertices.

P” __________ Q” __________ R” __________

3 Determine a single scale factor that can be used to dilate PQR to create P”Q”R”. _______

Record the algebraic representation that explains the effect of the dilation on PQR.

________________________________________________________________________

4 Is it possible to still get P”Q”R” if the order of the dilations is reversed, i.e. perform the dilation (2x, 2y) on PQR first, followed by ( 1 _ 4 x, 1 _ 4 y) ? Explain your answer.

________________________________________________________________________

________________________________________________________________________

Analysis

Analyze

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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 8.3(C) – ReadinessUnit 7 Journal/Vocabulary Activity

Anissa dilates a triangle drawn on a coordinate plane using the following: (3x, 5y). Are the triangles Anissa creates similar? Explain your answer.

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

Complete the activity with a partner. Player 1 rolls a die and uses the three terms in the row or column associated with the number rolled to create a true statement, make connections, or discuss similarities or differences between the terms. Player 1 records his/her information, briefly, in the table. The process is repeated by player 2. If a number is rolled a second time, the information given must be different than what has already been written. Players continue taking turns until time is called.

Information

two-dimensional figure

4

1

3

Info

rmat

ion

2

5 6

coordinates

axis/axes

coordinate plane

scale factor

ordered pair

dilation

origin

algebraic representation

(transformation)

Vocabulary Activity

Analysis

Analyze

Journal

8


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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 7 Motivation StationStandard 8.3(C) – Readiness

What Number Did You Dilate?

Play What Number Did You Dilate? with a partner. Each pair of players needs a game board and a paper clip to use with the spinner. Each player needs a pencil. Player 1 begins by spinning the spinner and using the number spun as a scale factor, using an algebraic representation to explain the effect of the scale factor on the triangle shown. Then player 1 determines the coordinate points of the dilated figure. If the points are correct, player 1 graphs the figure on the coordinate plane and initials the section of the spinner used. If the points are incorrect, play passes to player 2. If a player spins a scale factor that has already been initialed, he/she loses a turn. The game ends when all sections of the spinner have been initialed. The player with more initials on the spinner wins.

1.25

0.75

0.25

1_2

3_2

3_8

y

x-5 -4 -3 -2 -1 1 2 3 4 5

5

4

3

2

1

-1

-2

-3

-4

-5

Player 1Algebraic

Representation Coordinates

(_____, _____)

(_____, _____)

(_____, _____)

(_____, _____)

(_____, _____)

(_____, _____)

(_____, _____)

(_____, _____)

(_____, _____)

Player 2Algebraic

Representation Coordinates

(_____, _____)

(_____, _____)

(_____, _____)

(_____, _____)

(_____, _____)

(_____, _____)

(_____, _____)

(_____, _____)

(_____, _____)

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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 8.3(C) – ReadinessUnit 7 Homework

Measure the dimensions of a room in your house. On a sheet of graph paper, use one unit to equal one

foot, and sketch the room. Dilate the room using a scale factor of ( 1 _ 2 x, 1 _ 2 y) . What are the coordinates of the

dilated room? Dilate the room by a scale factor of (3x, 3y). What are the coordinates of the dilated room?

1 The neighborhood park planning committee has decided to enlarge the rose garden by a scale factor of 2.25. The original garden is shown on the graph.

y

x-8 -6 -4 -2 2 4 6 8

8

6

4

2

-2

-4

-6

-8

A

C

B

Write an algebraic representation to describe the effect of the scale factor on the original garden.

What are the coordinates of the enlarged garden?

Sketch the enlarged garden on the coordinate plane.

2 Rectangle EFGH with vertices E (-3, 5), F (6, 5), G (6, -4), and H (-3, -4) is dilated by a scale factor of 1.75. Use an algebraic representation to explain how the scale factor is used to find the coordinates for F’.

3 A dilation of quadrilateral QRST is shown.

y

x -2 -1 1 2

2

1

-1

-2

R’

S’

T’

Q’

If the dilation can be represented by the ordered pair ( 1 _ 4 x, 1 _ 4 y) , what are the coordinates for the vertices of QRST ?

Connections

8

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