Unit 10: Reflections and Symmetry - Ellis Familyellis2020.org/iTLG/iTLG Grade 4/U10.pdf · 782 Unit 10 Reflections and Symmetry ... Games are an essential component of practice in

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Overview

778 Unit 00 Unit Title

OverviewUnit 10 highlights a return to geometry from the point of view oftransformations or “motions” of geometric figures. It focuses primarilyon reflections and the related topic of symmetry. Unit 10 also introducesformal operations with positive and negative numbers. Unit 10 has threemain areas of focus:

◆ To guide the discovery of basic properties of reflections, involving 2-dimensional figures and the connection with line symmetry,

◆ To guide the application of reflections, rotations, and translations, and

◆ To introduce addition involving negative integers.

778 Unit 10 Reflections and Symmetry

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Lesson Objective Page

Contents

10◆1 Explorations with a Transparent Mirror 794To guide the exploration of reflections of 2-dimensional figures.

10◆2 Finding Lines of Reflection 799To guide the exploration of reflections; and to provide practice identifying lines of reflection.

10◆3 Properties of Reflections 805To guide the discovery of basic properties of reflections.

10◆4 Line Symmetry 810To guide exploration of the connection between reflections and line symmetry.

10◆5 Frieze Patterns 816To guide the application of reflections, rotations, and translations.

10◆6 Positive and Negative Numbers 822To introduce addition involving negative integers.

10◆7 Progress Check 10 828To assess students’ progress on mathematical content through the end of Unit 10.


To guide the exploration of reflections of2-dimensional figures.

To guide the exploration of reflections;and to provide practice identifying lines of reflection.

To guide the discovery of basicproperties of reflections.

To guide exploration of the connectionbetween reflections and line symmetry.

To guide the application of reflections,rotations, and translations.

To introduce addition involving negative integers.

Lesson Objectives Links to the Past Links to the Future

Learning In Perspective

Grade 3: Explore symmetry with geoboards andpattern blocks; complete symmetric figures; identifysymmetric shapes and draw lines of symmetry.




Grades 1–3: Use straws, geoboards, and bodyturns to demonstrate rotations. Grade 3: Modelpolygons; change the shapes of constructedpolygons; perform polygon calisthenics to form polygons and explore their properties.

Grade 3: Review uses of positive and negativenumbers to relate numbers to a zero point, as intemperatures and elevations, and to record change.Solve number stories about positive and negativenumbers.

Grade 5: Applications and maintenance.Grade 6: Study rotations, rotational symmetry, and point symmetry.




Grade 5: Transform ordered number pairs andexplore the resulting transformations of geometricfigures. Explore regular tessellations. Grade 6: Review regular tessellations; introducenotation for tessellations; find semiregulartessellations. Create translation tessellations.Explore topological transformations.

Grade 4: Play Credits/Debits Game (AdvancedVersion) to practice subtraction of positive andnegative integers. Grade 5: Solve addition/subtraction stories with positive and negativenumbers. Grade 6: Develop a rule for adding andsubtracting positive and negative numbers; practice adding and subtracting positive and negative numbers.

10◆1

10◆2

10◆3

10◆4

10◆5

10◆6

Key Concepts and Skills Grade 4 Goals*

* See the Appendix for a complete list of Grade 4 Goals.

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Key Concepts and Skills

10◆1

10◆2

10◆3

10◆4

10◆5

10◆6

Describe properties of congruent figures. Geometry Goal 2Identify, describe, and sketch reflections of two-dimensional figures. Geometry Goal 3Solve problems involving spatial visualization. Geometry Goal 3

Describe properties of congruent figures, right angles, and perpendicular lines. Geometry Goal 2Explore lines of reflection and reflected images. Geometry Goal 3Solve problems involving spatial visualization. Geometry Goal 3

Measure length. Measurement and Reference Frames Goal 1Draw and describe congruent figures. Geometry Goal 2Explore basic properties of reflections. Geometry Goal 3Solve problems involving spatial visualization. Geometry Goal 3

Identify polygons and describe properties of regular polygons. Geometry Goal 2Identify and draw lines of symmetry. Geometry Goal 3Explore the connection between reflections and line symmetry. Geometry Goal 3Solve problems involving spatial visualization. Geometry Goal 3Describe rules for patterns and use them to solve problems. Patterns, Functions, and Algebra Goal 1

Identify and draw congruent figures. Geometry Goal 2Identify, describe, and sketch reflections, rotations, and translations. Geometry Goal 3Extend, describe, and create geometric patterns. Patterns, Functions, and Algebra Goal 1

Compare and order integers. Number and Numeration Goal 6Add signed numbers. Operations and Computation Goal 2Identify a line of reflection. Geometry Goal 3

Ongoing Learning and Practice

Math BoxesMath Boxes are paired across lessons as shown in the brackets below.This makes them useful as assessment tools. Math Boxes also preview content of the next unit.

Ongoing Learning and Practice

10◆1 Over and Up Squares Locating and plotting points on a coordinate gridMeasurement and Reference Frames Goal 4

10◆2 Dart Game Experimenting with transparent mirrorsand reflectionsGeometry Goal 3

10◆2 Pocket-Billiards Game Experimenting with transparent mirrorsand reflectionsGeometry Goal 3

10◆2 Angle Tangle Estimating and measuring anglesMeasurement and Reference Frames Goal 1

10◆5 Polygon Pair-Up Identifying properties of polygonsGeometry Goal 2

10◆6 Credits/Debits Game Adding positive and negative numbersOperations and Computation Goal 2

Lesson Game Skill Practiced

See the Differentiation Handbook for ways to adapt games to meet students’ needs.


▲

Home Communication Study Links provide homework and home communication.

Home Connection Handbook provides more ideas to communicateeffectively with parents.

Unit 10 Family Letter provides families with an overview, Do-AnytimeActivities, Building Skills Through Games, and a list of vocabulary.

Practice through Games Games are an essential component of practice in the Everyday Mathematicsprogram. Games offer skills practice and promote strategic thinking.

132

4

Mixed practice [10◆1, 10◆4], [10◆2, 10◆5], [10◆3, 10◆6]

Mixed practice with multiple choice 10◆3, 10◆4, 10◆6

Mixed practice with writing/reasoning opportunity 10◆1, 10◆3, 10◆5

Encourage students to use a variety of strategies to solve problems and toexplain those strategies. Strategies that students might use in this unit:

◆ Drawing a picture ◆ Using a pattern◆ Acting out the problem ◆ Using computation◆ Using data in a table

Lesson Activity

See Chapter 18 in the Teacher’s Reference Manual for more information about problem solving.

10◆1 Use the transparent mirror to “move” and draw reflected images of shapes.

10◆2 Play games that involve reflections.

10◆3 Fold paper to observe reflected images.

10◆4 Find lines of symmetry of polygons.

10◆5 Create and continue frieze patterns.

10◆6 Use credits and debits to practice addition of positive and negative numbers.

MOST CLASSROOMS

M A R C H A P R I L M A Y

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Problem SolvingProblem Solving

Unit 10Lessons

NCTMStandards

10 ◆1 10 ◆2 10 ◆3 10 ◆4 10 ◆5 10 ◆6 10 ◆7

1, 3, 6–10 3, 5, 6–10 1, 3–5,6–10 3, 6–10 2, 3, 6–10 1, 2, 4,

6–10 6–10

Content Standards: 1 Number and Operations, 2 Algebra, 3 Geometry, 4 Measurement, 5 Data Analysis and ProbabilityProcess Standards: 6 Problem Solving, 7 Reasoning and Proof, 8 Communication, 9 Connections, 10 Representation

Planning Tips

Lessons thatteach throughproblem solving,not just aboutproblem solving

PacingPacing depends on a number of factors, such as students’ individual needsand how long your school has been using Everyday Mathematics. At thebeginning of Unit 10, review your Content by Strand Poster to help youset a monthly pace.

NCTM Standards

http://standards.nctm.org


Balanced Assessment

10◆1 Plot points in the first quadrant of a coordinate grid. [Measurement and Reference Frames Goal 4]

10◆2 Compare fractions with like numerators or like denominators; compare fractions to the benchmark �

12�. [Number and Numeration Goal 6]

10◆3 Use a transparent mirror to sketch and describe a reflection.[Geometry Goal 3]

10◆4 Describe a pattern and use it to solve problems.[Patterns, Functions, and Algebra Goal 1]

10◆5 Identify and sketch an example of a reflection and identify examples of translations and rotations.[Geometry Goal 3]

10◆6 Express the probability of an event as a fraction. [Data and Chance Goal 4]

Lesson Content Assessed

Use the Assessment

Management System

to collect and analyze dataabout students’ progressthroughout the year.

Ongoing Assessment

Recognizing Student AchievementOpportunities to assess students’ progress toward Grade 4 Goals:

Informing InstructionTo anticipate common student errors and to highlight problem-solvingstrategies:

Lesson 10◆2 Find a common factor to use as intervals when labeling an axis

Lesson 10◆4 Understand the difference between line symmetry androtation symmetry

Lesson 10◆6 Encourage strategies for adding positive and negativenumbers to evolve over time

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Name equivalent fractions, decimals, and percents.[Number and Numeration Goal 5]

Add signed numbers.[Operations and Computation Goal 2]

Add and subtract fractions.[Operations and Computation Goal 5]

Make reasonable estimates for multiplication anddivision problems. [Operations and Computation Goal 6]

Measure an angle.[Measurement and Reference Frames Goal 1]

Locate multiple lines of symmetry in a two-dimensionalshape. [Geometry Goal 3]

Identify and sketch examples of reflections; identify examples of translations and rotations.[Geometry Goal 3]

CONTENT ASSESSED Self Oral/Slate Written Open Response

ASSESSMENT ITEMS

✔ ✔✔

✔✔✔

✔✔

✔ ✔

✔

✔ ✔

✔ ✔✔

Periodic Assessment10◆7 Progress Check 10

Portfolio OpportunitiesOpportunities to gather samples of students’ mathematical writings, drawings, and creations to add balance to the assessment process:

◆ Inserting decimal points, Lesson 10◆1◆ Creating a paint reflection, Lesson 10◆2◆ Interpreting a cartoon, Lesson 10◆4◆ Calculating the mean, Lesson 10◆5◆ Creating frieze patterns to practice reflections, rotations, and translations, Lesson 10◆5◆ Solving problems involving pentominoes, Lesson 10◆7

Assessment HandbookUnit 10 Assessment Support

◆ Grade 4 Goals, pp. 37–50 ◆ Unit 10 Open Response◆ Unit 10 Assessment Overview, pp. 126–133 • Detailed rubric, p. 130

• Sample student responses, pp. 131–133

Unit 10 Assessment Masters◆ Unit 10 Self Assessment, p. 200◆ Unit 10 Written Assessment, pp. 201–203◆ Unit 10 Open Response, pp. 204 and 205◆ Unit 10 Class Checklist, pp. 284, 285, and 303◆ Unit 10 Individual Profile of Progress, pp. 282, 283, and 302◆ Exit Slip, p. 311◆ Math Logs, pp. 306–308◆ Other Student Assessment Forms, pp. 304, 305, 309, and 310

Daily Lesson Support

Differentiated Instruction

ENGLISH LANGUAGE LEARNERS

READINESS ENRICHMENT

EXTRA PRACTICE10◆2 Building a Math Word Bank10◆4 Creating a Line Symmetry Museum

10◆1 Exploring reflections with paperfolding

10◆2 Creating a paint reflection 10◆3 Creating reflections10◆5 Exploring geometric patterns10◆6 Using a calculator to skip count10◆6 Using a number line to add positive

and negative integers

10◆4 Creating shapes with line symmetry10◆5 Creating frieze patterns

5-Minute Math 10◆3 Solving problemsinvolving reflections

Cross-Curricular Links

Adjusting the Activity10◆2 Devising a scoring system for

Pocket-Billiards Game10◆3 Determining the latitude and longitude

of a capital city10◆4 Summarizing the discussion of line

symmetry ELL

10◆4 Having a volunteer cut out shapesahead of time

10◆5 Sketching frieze patterns on centimeter grid paper ELL

10◆6 Experimenting with a calculator

A U D I T O R Y � K I N E S T H E T I C � T A C T I L E � V I S U A L


Using the ProjectsUse Project 4, Making a Quilt, after Unit 10 to explore and apply ideas of pattern, symmetry,rotation, and reflection in the context of quilts. See the Differentiation Handbook formodifications to Project 4.

Differentiation HandbookSee the Differentiation Handbook for materials on Unit 10.

Language Arts Lesson 10◆1 Students discuss the use of the prefix pre-.

ArtLesson 10◆2 Students create a paint reflection to explore the concept of reflection.Lesson 10◆5 Students complete three frieze patterns and design one oftheir own.Lesson 10◆5 Students create and continue patterns using pattern blocks.Lesson 10◆5 Students make frieze patterns by following directions.

TechnologyLesson 10◆2 Students investigate theuse of a mirror as a virtual manipulative.Lesson 10◆5 Students use technologyto explore tessellations.

Social StudiesLesson 10◆3 Students visit a secondcountry in Region 4.

10◆1 Exploring shadows and reflections10◆2 Solving paper-folding puzzles10◆2 Using technology to investigate the

mirror as a virtual manipulative10◆3 Constructing 3-dimensional buildings

and their reflections 10◆4 Interpreting a cartoon involving

line symmetry10◆4 Exploring turn or rotation symmetry10◆5 Exploring arrangements of four straws10◆5 Exploring tessellations

Language SupportEveryday Mathematics provides lesson-specific suggestions to help allstudents, including non-native English speakers, to acquire, process, andexpress mathematical ideas.

Connecting Math and LiteracyLesson 10◆1 Shadows and Reflections, by Tana Hoban, Greenwillow, 1990 Lesson 10◆3 Count Your Way through Japan, by Jim Haskins, Carolrhoda

Books, 1988Lesson 10◆3 Count Your Way through Russia, by Jim Haskins, Carolrhoda

Books, 1987Lesson 10◆3 Count Your Way through India, by Jim Haskins, Carolrhoda

Books, 1992Lesson 10◆3 Count Your Way through Israel, by Jim Haskins, Carolrhoda

Books, 1992How the Second Grade Got $8,205.50 to Visit the Statue of Liberty,

by Nathan Zimelman, Albert Whitman & Company, 1992 Reflections, by Ann Jonas, Greenwillow, 1987

Student Reference Bookpp. 60, 108, 109, 230, 238, 257, and 258

Multiage Classroom ◆ Companion LessonsCompanion Lessons from Grades 3 and 5 can help you meet instructionalneeds of a multiage classroom. The full Scope and Sequence can be foundin the Appendix.

Unit 10 Vocabularycongruentcreditdebitfrieze patternimageline of reflectionline of symmetryopposite (of a number)preimagerecessed reflectionreflection (flip)rotation (turn)rotation (turn) symmetrysymmetrictranslation (slide)transparent mirror

Grade 3

Grade 4

Grade 5

6◆3,6◆9

6◆9 6◆3,6◆9

6◆3,6◆9

1◆12,6◆3

10◆1 10◆2 10◆3 10◆4 10◆5 10◆6

3◆8 3◆8 7◆7–7◆9,7◆11

Professional Development

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Teacher’s Reference Manual LinksSection

3.2.4

13.13.5

13.7.1

13.6.2

Topic

Geometry Tools

Transparent Mirrors

Reflections, Rotations, andTranslations

Congruence and Similarity

See 10◆2.

Lesson

10◆1

10◆2

10◆3

13.8.1

13.4.2

9.4

10.2.2

Section

Line Symmetry

Polygons

See 10◆2.

Positive and Negative Numbers

Operations with Positive andNegative Numbers

Topic

10◆4

10◆5

10◆6

Lesson


Materials

Lesson Masters Manipulative Kit Items Other Items

* Denotes optional materials

Technology Assessment Management System, Unit 10iTLG, Unit 10

Teaching Masters, pp. 304 and slate sheets of paper; colored pencils; 305 2 six-sided dice crayons*; scissors; Shadows and Reflections

Study Link Master, p. 306 transparent mirrorGame Master, p. 494Teaching Aid Master, p. 389

Study Link 10◆1 slate ruler; large sheets of paper; paints,Study Link Master, p. 307 Geometry Template brushes, and dark marker; computer with Game Master, p. 457 transparent mirror Internet access (if available); scissors;Teaching Master, p. 308 protractorTeaching Aid Master, p. 389

Study Link 10◆2 slate ruler; blank paperTeaching Master, p. 309 centimeter cubesStudy Link Master, p. 310 pattern blocksTeaching Aid Masters, pp. 389, transparent mirror

403, 419–421*, and 447

Study Link 10◆3 slate scissors; magazines and newspapers; tapeTeaching Masters, pp. 311–314, pattern blocks

316, and 317 Geometry TemplateTeaching Aid Master, p. 389 transparent mirrorStudy Link Master, p. 315

Study Link 10◆4 Geometry Template straightedge; computer with Internet access;Teaching Aid Master, p. 389, 403*, straws index cards; scissors; overhead or regular

and 437 pattern blocks pattern blocks*; Polygon Pair-Up PolygonStudy Link Master, p. 318 slate Cards and Property CardsTeaching Master, p. 319 transparent mirror

Study Link 10◆5 deck of number cards masking tapeTeaching Master, p. 320 calculatorGame Master, p. 468 number linetransparencies of Math Masters, transparent mirror

pp. 318* and 321*Study Link Master, p. 322

Study Link 10◆7 slate scissorsAssessment Masters, pp. 200–205 transparent mirrorStudy Link Masters, pp. 323–326 Geometry

Template

10◆1

10◆2

10◆3

10◆5

10◆6

10◆7

10◆4

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The discussion below highlights the major content ideas presented in Unit 10 and helps establish instructional priorities.

Types of Geometry (Lessons 10◆1 and following)You may remember your high school geometry course as dealing withdefinitions, axioms, theorems (“Given ..., To Prove ...”), and perhapsstraightedge-and-compass constructions. This form of synthetic geometrywas first developed by Euclid about 300 B.C. and has been the model forteaching geometry ever since.

However, there are two modern geometries that cover the same topics:

Analytic geometry The study of figures in a coordinate plane.

Transformation geometry The study of certain operations on figures.These operations, or “transformations,” produce figures that are the sameshape as (similar to) the original figures, or the same size and shape as(congruent to) the original figures.

These two geometries are probably more useful than synthetic geometry.Both are featured in Grades 4–6 of Everyday Mathematics, with Unit 10introducing the transformation approach.

Learn more about types of geometry in Chapter 13 of the Teacher’sReference Manual.

“Isometric” or “Congruence”Transformations (Lessons 10◆1 and following)You may remember from your high school geometry course theemphasis on congruent figures, especially on proving trianglescongruent by theorems called “side-angle-side” or “SAS,” and so on.

This topic is handled in transformation geometry by rigidmotions or isometric transformations, which do notchange the size or shape of figures. These transformations—translations (slides), reflections (flips), and rotations(turns)—can duplicate any figure. (SAS and similartheorems of synthetic geometry apply only to triangles.)

See the Teacher’s Reference Manual, Section 13.7,for more information about isometric transformations.

Mathematical Background

Figure in a coordinate plane

(1,1)

(3,9)

(8,5)

12

43

56789

10

1 2 3 4 5 6 7 80

9 100

Reflections (Flips) and Symmetry with TransparentMirrors (Lessons 10◆1–10◆4)Everyone is familiar with mirrors and the exact—but reversed—imagesone sees in them. The device used in this unit, the transparent mirror,has an advantage over a regular mirror: It allows students to look througha mirror and reach behind it to touch or trace the mirror image (almostlike Alice going “through the looking glass”).

As with any new tool, developing the skills for its use takes time, practice,and patience. For accurate placement of images, have students practicethese skills:

◆ Lean down and look directly through the transparent mirror.◆ Use the ends of the transparent mirror to keep it perpendicular

to the paper.◆ Use the inner part of the recessed edge to place the transparent

mirror on points or lines or to draw mirror lines.◆ Hold the transparent mirror firmly in position with one hand while

drawing behind it or along its recessed edge. (This is one of the mainskills to be learned.)

It is probably a good idea to acquire or practice these skills yourself before teaching the lessons. Do the mirror exercises on journal pages andmasters until you feel comfortable using the transparent mirror.

To learn more about reflections and symmetry with a transparent mirror,refer to Section 13.8 in the Teacher’s Reference Manual.


Transparent mirror

Transformations as Design Tools(Lesson 10◆5)Geometric patterns are part of many designs—in arts and crafts fromaround the world, in architecture and engineering, and in paintings andother works of art (sometimes in disguised forms). Lesson 10-5, on friezepatterns, encourages students to explore reflections, symmetry, rotations,and translations in order to analyze and create designs. The authorsbelieve that fourth graders will find these design tasks enjoyable. Some oftheir creations may be quite elegant.

An interesting property of transformations is that two successivereflections across parallel mirror lines are equivalent to one translation.(The original image is reversed in the first reflection, but the mirror imageof the first reflection can be a translated image.) Hence one can makefriezes either by translating and tracing or by using transparent mirrorstwice for each frieze copy.

The authors hope that the principles learned here can be linked toteaching visual arts in your school. Geometry that is useful in both artand practical matters will be applied many times throughout EverydayMathematics.

For more about transformations as design tools, see Section 13.8 in the Teacher’s Reference Manual.

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�

�

Operations with Positiveand Negative Numbers(Lesson 10◆6)Since Kindergarten, Everyday Mathematicsstudents have been using positive and negativenumbers to identify locations on timelines, numberlines, number grids, and thermometers. Since firstgrade, students have informally used addition andsubtraction in going from one place to another andin finding distances. But Lesson 10-6 may bestudents’ first exposure to operations with positiveand negative numbers. In this lesson, the numbersare limited to integers—whole numbers and their(negative) opposites.

“Credits and debits” number stories are used tohelp make addition concrete. Single-digit numbersensure that most problems can be done mentally.It is important in these “accounting” situations toname both the operation and the number.

◆ “Add +$3” is read “Add positive 3 dollars” (a credit transaction).

◆ “Add –$5” is read “Add negative 5 dollars” (a debit transaction).

This distinguishes the addition operation from thenumbers involved.

Later lessons in Grade 4 introduce subtraction ofpositive and negative numbers and teach the use of the “change sign” key, which enables calculatorsto work with negative as well as positive numbers.Many practice and review exercises are included.Other operations with positive and negativenumbers, as well as applications using them, arefeatured in Grades 5 and 6.

See Section 10.2.2 of the Teacher’sReference Manual for more informationabout operations with positive and negativenumbers.


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Note

Public or privatespeech is very helpfulin dealing withcomplexities ofmeanings. It is verifiableand observablecommon sense forstudents to use speech,as well as sight, to sortout complicatedsymbolic expressions.(This is a key tenet ofthe learning theory ofLev S. Vygotsky. Anexcellent article onVygotskian learningtheory is “WhyChildren Talk toThemselves,” by Laura E. Berk, in theNovember 1994 issueof ScientificAmerican.)

Confusing Notation for Positive andNegative Numbers (Lesson 10◆6)The use of the same notation with several meanings can be confusing.This is true of the symbol “�”:

◆ The symbol “�” attached to a numeral, as in �3, �0.5, or�37, is read “negative” and is used in naming numbers onthe number line (“negative three,” “negative five-tenths,”“negative thirty-seven”).

◆ The symbol “�” in a number model, preceding a positiveor negative number, as in �(�3) or �(�17), is read“opposite of.” The opposite of a positive number is anegative number; the opposite of a negative number is a positive number. For example, the “opposite of positive 3” is negative 3, and the “opposite of negative 17”is positive 17.

◆ The symbol “�” in a number model, as in 17 � 3 � 14, isread “minus,” “subtract,” or “take away” and indicatesthe familiar subtraction operation.

Example 17 � 3 � 14 is read “17 minus 3 equals 14.”

17 � (�3) � 14 is read “17 minus 3 equals 14.”

�(�17) � 3 � 14 is read “the opposite of negative 17 minus 3 equals 14.”

17 � (�3) � 14 is read “17 plus negative 3 equals 14.”

17 � (�3) � 20 is read “17 minus negative 3 equals 20.”

The meanings of the symbol “�” can get quite tangled in number modelslike �17 � 3 = �20 (“Negative 17 minus 3 equals negative 20”) or 12 � �(�4) = 8 (“12 take away the opposite of negative 4 equals 8”).

Some mathematics programs of the past tried to reduce confusion by using“�” only for subtraction. Positive and negative numbers were designatedwith small raised symbols (for example, �3, �7, �17), and opposites wereindicated by “opp.” But everyday usage and nearly all algebra bookscontinued to use the traditional notation, so students eventually had toreconcile the two notations.

Given the problems associated with both notations, the authors havedecided to use the traditional system. Help students sort it out when youread expressions by consistently saying “plus” or “minus” for addition or subtraction, and “positive,” “negative,” or “opposite” for numbers, asindicated by the context. Encourage students to do likewise when theyeventually read expressions to each other and to themselves.

To further explore confusing notation for positive and negative numbers,refer to Section 9.4.1 in the Teacher’s Reference Manual.

�9 �8 �7 �6 �5 �4 �3 �2 �1 9876543210

Opposites

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Unit 10: Reflections and Symmetry - Ellis Familyellis2020.org/iTLG/iTLG Grade 4/U10.pdf · 782 Unit 10 Reflections and Symmetry ... Games are an essential component of practice in