unit 1: naming and constructing geometric figuresellis2020.org/itlg/itlg grade 4/u1.pdf · 4 unit 1...

Overview

2 Unit 1 Naming and Constructing Geometric Figures

OverviewThe principle focus of Unit 1 is geometry. Opening with geometryenables a relatively relaxed beginning of the school year and allowsteachers and students to get acquainted and establish yearlong routines.Starting the year with geometry also makes the point that mathematicsis more than numbers and is strongly linked to language and art. Unit 1 has five main areas of focus:

◆ To introduce students to the Student Reference Book,

◆ To practice using geometry tools,

◆ To classify quadrangles,

◆ To explore and identify polygons, and

◆ To review and practice addition and subtraction facts.


EM07TLG1_G4_U01_UO.qxd 2/16/06 4:06 PM Page 2

Unit Organizer 3

Lesson Objective Page

Contents

1◆1 Introduction to the Student Reference Book 18To acquaint students with the content and organization of the Student Reference Book.

1◆2 Points, Line Segments, Lines, and Rays 23To introduce tools for geometry; and to review points, line segments, lines, and rays.

1◆3 Angles, Triangles, and Quadrangles 29To guide students in the construction of angles, triangles, and quadrangles and in the classification of quadrangles.

1◆4 Parallelograms 35To model the classification of quadrangles based on their properties.

1◆5 Polygons 41To provide opportunities to identify properties of polygons and distinguish between convex and nonconvex (concave) polygons; and to explore geometric definitions and classification.

1◆6 Drawing Circles with a Compass 47To provide practice using a compass.

1◆7 Circle Constructions 52To guide students in defining a circle; and to provide opportunities to explore designs with circles.

1◆8 Hexagon and Triangle Constructions 57To guide students in the construction of figures with a compass and straightedge.

1◆9 Progress Check 1 62To assess students’ progress on mathematical content through the end of Unit 1.



Lesson Objectives Links to the Past Links to the Future

Learning In Perspective

1◆1

1◆2

1◆3

1◆4

1◆5

1◆6

1◆7

1◆8

To acquaint students with the contentand organization of the StudentReference Book.

To introduce tools for geometry; and toreview points, line segments, lines, andrays.

To guide students in the construction ofangles, triangles, and quadrangles andin the classification of quadrangles.

To model the classification ofquadrangles based on their properties.

To provide opportunities to identifyproperties of polygons and distinguishbetween convex and nonconvex(concave) polygons; and to exploregeometric definitions and classification.

To provide practice using a compass.

To guide students in defining a circle;and to provide opportunities to exploredesigns with circles.

To guide students in the construction of figures with a compass andstraightedge.

Grade 3: Use Student Reference Book. Grades 1and 2: Use My Reference Book.

Grade 3: Use straws and arrowheads to model lines,line segments, and rays; use notation to namepoints, line segments, lines, and rays. Grades 1 and 2: Name and draw points and line segments.

Grade 3: Use straws to model angles, triangles, andquadrangles. Grade 2: Trace pattern blocks, anduse geoboards to construct polygons.

Grade 3: Use straws to construct polygons withspecific characteristics. Grades 1 and 2: Exploresimilarities and differences among quadrangles.

Grades 2 and 3: Discuss common characteristics ofall polygons and of regular polygons; introduce theterm parallel. Grades 1–3: Explore polygons withstraws, geoboards, and dot paper. Name the partsof a polygon: side, vertex, and angle.

Grades 1 and 3: Use a ruler, Pattern-BlockTemplate, and dot paper to draw figures and createdesigns.

Grade 3: Explore relationship of diameter tocircumference.

Grades 1 and 3: Use a ruler, Pattern-BlockTemplate, and dot paper to draw figures and createdesigns.

Grades 5 and 6: Use Student Reference Book.

Grades 4–6: Applications and maintenance.

Grade 4: Introduce acute, obtuse, straight, and reflexangles; find the sum of measures of the angles of atriangle (Unit 6). Grade 5: Introduce vertical (opposite),adjacent, and supplementary angles; find the sum ofmeasures of the angles of any polygon; identifycorresponding sides of congruent and similar figures.

Grade 4: Measure, draw and classify types ofangles; review properties of parallelograms (Unit 6). Grade 5: Explore angle relationships inparallelograms; investigate whether all quadranglestessellate.

Grade 4: Construct polygons by folding paper and withcompass and straightedge; identify lines of symmetryfor polygons, and introduce congruent figures (Units 6,10, and 11). Grades 5 and 6: Explore transformations ofpolygons in a plane; investigate congruent and similarfigures; determine which regular pologons tessellate.

Grade 4: Construct equilateral triangles,parallelograms, and parallel lines. Grades 5 and 6: Review and extend compass andstraightedge constructions.

Grades 5 and 6: Use formulas to find circumference and area of a circle.

Grade 4: Construct equilateral triangles,parallelograms, and parallel lines. Grades 5 and 6: Review and extend compass andstraightedge constructions.


Use the symbols �, �, and � to compare numbers and numerical expressions. Number and Numeration Goal 6Solve simple �, �, �, and � problems. Operations and Computation Goals 1 and 3Describe relationships among U.S. customary units of length. Measurement and Reference Frames Goal 3

Identify and draw line segments, lines, and rays. Geometry Goal 1Describe characteristics of line segments, lines, and rays. Geometry Goal 1Use letter and symbol notation to name line segments, lines, and rays. Geometry Goal 1

Use letter notation to name angles. Geometry Goal 1Construct angles, triangles, and quadrangles. Geometry Goals 1 and 2Describe properties of and compare quadrangles. Geometry Goal 2Identify types of quadrangles. Geometry Goal 2

Develop a definition for parallel and intersecting line segments, lines, and rays. Geometry Goal 1Develop a definition for perpendicular line segments. Geometry Goal 1Describe characteristics of parallelograms. Geometry Goal 2Classify quadrangles based on side and angle properties. Geometry Goal 2

Construct convex and nonconvex (concave) polygons. Geometry Goal 2Develop definitions for convex and nonconvex (concave) polygons. Geometry Goal 2Describe properties of polygons and regular polygons. Geometry Goal 2Identify types of polygons according to the number of sides. Geometry Goal 2

Use a compass to measure distance. Measurement and Reference Frames Goal 1Use a compass to draw circles. Geometry Goal 2Construct an inscribed square. Geometry Goal 2Verify that the sides of a square are the same length. Geometry Goal 2

Measure line segments to the nearest centimeter. Measurement and Reference Frames Goal 1Demonstrate and explain the meaning of intersect. Geometry Goal 1Use a compass to draw circles. Geometry Goal 2Demonstrate and explain the meanings of concentric, radius, and congruent. Geometry Goal 2

Use a compass as a tool to measure distance. Measurement and Reference Frames Goal 1Copy a line segment with a compass and straightedge. Geometry Goal 1Use a compass to draw circles; construct a regular hexagon inscribed in a circle. Geometry Goal 2Verify that the sides of regular polygons are the same length. Geometry Goal 2

Key Concepts and Skills Grade 4 Goals*

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

Unit Organizer 5

1◆1

1◆2

1◆3

1◆4

1◆5

1◆6

1◆7

1◆8

Key Concepts and Skills


Ongoing Learning and Practice

▲Mixed practice [1◆ 1, 1◆3] , [1◆2, 1◆4] , [1◆5, 1◆7] , [1◆6, 1◆8]

Mixed practice with multiple choice 1◆1, 1◆ 4, 1◆5, 1◆ 8

Mixed practice with writing/reasoning opportunity 1◆3, 1◆4, 1◆6, 1◆ 7


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

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

132

4

Home Communication Study Links provide homework and home communication.

Home Connection Handbook provides more ideas to communicateeffectively with parents.

Unit 1 Family Letter provides families with an overview, Do-AnytimeActivities, Building Skills Through Games, and a list of vocabulary.

▲

Lesson Game Skill Practiced

1◆ 1 Top-It Use symbols to compare numbers Number and Numeration Goal 6

1◆ 2 Addition Top-It Solve addition factsOperations and Computation Goal 1

1◆ 2 Sprouts Explore line segments and pointsGeometry Goal 1

1◆ 4 Subtraction Top-It Solve subtraction facts Operations and Computation Goal 1

1◆ 4 Sz’kwa Explore intersecting line segmentsGeometry Goal 1

1◆ 6, 1◆ 7 Polygon Pair-Up Describe properties of polygonsGeometry Goal 2

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


Problem SolvingProblem Solving

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

◆ Identifying patterns ◆ Using logical reasoning◆ Acting out a problem ◆ Drawing a picture◆ Listing all possibilitiess

Lesson Activity

1◆ 2 Look for geometric patterns in the classroom.

1◆ 3 Make triangles and different types of quadrangles with straws and twist-ties.

1◆ 4 Classify geometric shapes according to their properties.

1◆ 5 Explain what a polygon is.

1◆ 6 Discuss ways to draw a large circle on the playground.

1◆ 7 Use a compass to draw three designs that involve more than one circle.

1◆ 8 Construct a regular hexagon inscribed in a circle.

Lessons thatteach throughproblem solving,not just aboutproblem solving

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

Planning Tips

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 1, review your Content by Strand Poster to help you seta monthly pace.

NCTM StandardsUnit 1Lessons

NCTMStandards

1 ◆1 1 ◆ 2 1 ◆ 3 1 ◆ 4 1 ◆ 5 1 ◆ 6 1 ◆ 7 1 ◆ 8 1 ◆ 9

1–10 3, 8–10

3, 8–10

3, 8–10

1, 3, 8–10

3, 6–10

3, 6–10

3, 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

MOST CLASSROOMS

A U G U S T S E P T E M B E R O C T O B E R

Unit Organizer 7


http://standards.nctm.org


Balanced Assessment

1◆ 1 Demonstrate automaticity with addition facts.[Operations and Computation Goal 1]

1◆ 2 Describe a line segment and a line.[Geometry Goal 1]

1◆ 3 Compare and contrast plane figures.[Geometry Goal 2]

1◆ 4 Understand parallel line segments.[Geometry Goal 1]

1◆ 5 Explain the properties of polygons.[Geometry Goal 2]

1◆ 6 Understand right angles.[Geometry Goal 1]

1◆ 7 Construct circles with a compass.[Geometry Goal 2]

1◆ 8 Demonstrate automaticity with subtraction facts.[Operations and Computation Goal 1]

Lesson Content Assessed

Use the AssessmentManagement Systemto 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-solving strategies:

Lesson 1◆2 Connect points to other points

Lesson 1◆3 Consider the measures of angles rather than the lengths of rays

Lesson 1◆5 Distinguish regular polygons from other polygons

Lesson 1◆8 Connect consecutive marks to form a regular hexagon


Unit Organizer 9

Demonstrate automaticity with all addition and subtraction facts through 10 � 10.[Operations and Computation Goal 1]

Identify, draw, and describe points, intersecting and parallel line segments and lines, rays, and right angles.[Geometry Goal 1]

Describe and classify plane figures, including polygonsand circles using appropriate geometric terms, includingcongruent. [Geometry Goal 2]

CONTENT ASSESSED Self Oral/Slate Written Open Response

ASSESSMENT ITEMS

✔ ✔✔

✔ ✔✔

✔ ✔✔✔

Periodic Assessment1◆9 Progress Check 1

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

◆ Describing how to mentally solve an addition problem, Lesson 1◆3◆ Explaining a likely mistake in reading a graph, Lesson 1◆4◆ Describing properties of kites and rhombuses, Lesson 1◆5◆ Explaining why shapes are not polygons, Lesson 1◆6◆ Creating circle designs, Lesson 1◆6◆ Explaining how to solve extended subtraction facts, Lesson 1◆7◆ Drawing tangent circles, Lesson 1◆7◆ Sorting polygons, Lesson 1◆9

Assessment HandbookUnit 1 Assessment Support

◆ Grade 4 Goals, pp. 37–50◆ Unit 1 Assessment Overview, pp. 52–59◆ Unit 1 Open Response

• Detailed rubric, p. 56• Sample student responses, pp. 57–59

Unit 1 Assessment Masters◆ Unit 1 Self Assessment, p. 154◆ Unit 1 Written Assessment, pp. 155–157◆ Unit 1 Open Response, p. 158◆ Unit 1 Class Checklist, pp. 248, 249 and 303◆ Unit 1 Individual Profile of Progress, pp. 246,

247, and 302

▲

◆ Exit Slip, p. 311◆ Math Logs, pp. 306–308◆ Other Student Assessment Forms, pp. 304, 305,

309, and 310



Differentiated Instruction

Language Arts LiteratureLesson 1◆ 1 Students discuss parts Lesson 1◆ 5 Students classify polygons

of reference book. after reading The Greedy Triangle.

Lessons 1◆ 5 and 1◆ 8 Students use ArtGreek and Latin roots to analyze words. Lesson 1◆ 6 Students create circle designs.

Lesson 1◆ 8 Students create 6-point designs.

Daily Lesson Support

ENGLISH LANGUAGE LEARNERS

READINESS ENRICHMENT

EXTRA PRACTICE1 ◆2 Building background for mathematics

words1 ◆3 Comparing and contrasting

quadrangles1 ◆7 Building a Math Word Bank

1 ◆1 Using relation symbols to comparenumbers

1 ◆2 Modeling line segments1 ◆3 Sorting pattern blocks1 ◆4 Exploring parallel line segments with

concrete models1 ◆5 Constructing polygons on a geoboard1 ◆5 Using straws to create polygons 1 ◆8 Identifying a regular hexagon

1 ◆1 Exploring mathematical symbols1 ◆2 Solving a collinear-points puzzle1 ◆2 Playing Sprouts1 ◆3 Solving an embedded-polygons puzzle1 ◆4 Solving a straw-squares puzzle1 ◆4 Playing Sz’kwa1 ◆5 Identifying properties of kites and

rhombuses1 ◆6 Solving an inscribed square puzzle1 ◆7 Drawing tangent circles1 ◆7 Using diameters, chords, and radii1 ◆8 Creating six-point designs

1 ◆6 Creating circle designs with a compass1 ◆8 Inscribing an equilateral triangle in a

circle

5-Minute Math 1 ◆3 Identifyingcharacteristics of two-dimensional shapes.

Adjusting the Activity1◆1 Labeling parts of a book ELL1◆1 Marking key terms ELL1◆2 Making visual references: line segment,

line, and ray ELL1◆2 Playing a variation of Addition Top-It1◆3 Labeling and displaying models of

triangles and quadrangles ELL1◆4 Using visualization to remember parallel;

using math symbols ELL1◆4 Examining quadrangle relationships with

visuals

1◆4 Playing a variation of Subtraction Top-It1◆5 Explaining the possibility of concave

triangles and quadrangles1◆5 Discussing meaning of regular ELL1◆6 Constructing an inscribed regular

octagon1◆6 Playing a variation of Polygon Pair-Up1◆7 Exploring concentric circles; measuring

radii1◆8 Constructing a parallelogram and a

perpendicular line segment

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

Cross-Curricular Links

Differentiation HandbookSee the Differentiation Handbook for materials on Unit 1.


Unit 1 Vocabularyangle parallel line segmentscenter (of a circle) parallel linescircle parallel rayscompass parallelogramconcentric circles pentagoncongruent perpendicular line convex segmentsendpoint pointequilateral triangle polygonheptagon quadranglehexagon quadrilateralinscribed square radius interior rayintersect rectanglekite regular polygonline rhombusline segment right anglen-gon sidenonagon squarenonconvex or trapezoid

concave triangleoctagon vertex (vertices)

Grade 3

Grade 4

Grade 5

1◆3 6◆1,6◆2

3◆4, 3◆5,6◆3–6◆8

3◆4,6◆5

1◆4, 5◆6,6◆5, 6◆6

3◆9 1◆4,3◆9

1◆4, 3◆4,3◆6

1◆1 1◆ 2 1◆ 3 1◆ 4 1◆ 5 1◆ 6 1◆ 7 1◆ 8

1 ◆1 3 ◆4,3 ◆5

3 ◆3–3 ◆5,3 ◆7

3 ◆4–3 ◆5,3 ◆7

3 ◆7 3 ◆5 5 ◆10,5 ◆11

9 ◆5,9 ◆6

Professional Development

Teacher’s Reference Manual LinksLesson Topic Section

Unit Organizer 11

Lesson

1◆1

1◆2

1◆3

Topic

Math Boxes

Math Message

Mental Math and Reflexes

Student Reference Book

Study Links and Family Letters

Points

Lines, Segments, and Rays

Slates

Games

Study Links

Angles and Rotations

Section

1.2.2

1.2.3

1.2.4

1.2.9

8.1

13.2

13.3

1.2.8

1.2.1

1.2.10

13.4.1

1◆4

1◆5

1◆6

1◆7

1◆8

Polygons (n-gons)

Straws and Twist-ties

Parallel and Perpendicular

Polygons (n-gons)

Geometry Tools

Compass-and StraightedgeConstructions

Circles and Pi (π)

Compass-and-StraightedgeConstructions

Compass-and-StraightedgeConstructions

13.4.2

13.13.4

13.6.1

13.4.2

3.2.4

13.13.1

13.4.3

13.13.1

13.13.1

Language SupportEveryday Mathematics provides lesson-specificsuggestions to help all students, including non-nativeEnglish speakers, to acquire, process, and expressmathematical ideas.

Connecting Math and LiteracyMath Curse, by Jon Scieszka, Puffin, 2004 Lesson 1◆5 The Greedy Triangle, by Marilyn Burns, Scholastic Inc., 1994Ed Emberley’s Picture Pie: A Circle Drawing Book, by Ed Emberley, Little Brown, 1984Shape Up!, by David A. Adler, Holiday House, 2000Gregory and the Magic Line, by Dawn Piggot, Orion, 2004

Student Reference Bookpages 88–91, 97, 100, 114, 117, 118, 258, 263,

264, 310, and 313

Multiage Classroom ◆ Companion LessonsCompanion Lessons from Grades 3 and 5 can help youmeet instructional needs of a multiage classroom. Thefull Scope and Sequence can be found in the Appendix.



Materials

1◆ 2

1◆ 4

1◆ 6

1◆ 8

1◆ 1

1◆ 3

1◆ 5

1◆ 7

Lesson Masters Manipulative Kit Items Other Items

* Denotes optional materials

Technology Assessment Management System, Unit 1iTLG, Unit 1

Study Link Masters, pp. 2–5Teaching Aid Masters,

pp. 384–387Teaching Masters, pp. 6 and 7

Teaching Aid Masters, pp. 388 or 389*

Study Link Master, p. 8Game Master, p. 506Teaching Masters, pp. 9 and 10

Study Link 1◆ 2Teaching Aid Masters, pp. 388 or

389* and 390Study Link Master, p. 11Teaching Masters, pp. 12 and 13

Study Link 1◆ 3Teaching Masters, pp. 14, 16,

and 17Study Link, p. 15Game Masters, pp. 505

and 506

Study Link 1◆ 4Study Link Master, p. 18Teaching Masters, pp. 19–22

Study Link 1◆ 5Study Link Master, p. 23Game Masters, pp. 496

and 497Teaching Master, p. 24

Study Link 1◆ 6Teaching Masters, pp. 25

and 27–29Study Link Master, p. 26Polygon Pair-Up Property Cards

and Polygon Cards, pp. 496 and 497

Study Link 1◆ 7Study Link Master, p. 30Teaching Masters, pp. 31–33

Study Link 1◆ 8Assessment Masters,

pp. 154–158Study Link Masters, pp. 34–37

per group: number cards 0–9 (4 of each)

slate or marker board; calculator;Geometry Template; per group: numbercards 1–10 (4 of each); per group: 3six-sided or 2 polyhedral dice*;geoboard; rubber bands

slatestraws and twist-tiespattern blocksGeometry Template

Geometry Template*number cards 1–10 (4 of each)six-sided or polyhedral dice*geoboard; rubber bands; straws

straws; twist-ties; geoboard; rubber bands

slatecompass

slateGeometry Templatecompass

compassGeometry Template

Geometry Template; compass

sticky notes*; paper clips; small resealable plastic bags or regularenvelopes; scissors

chalk or dry-erase marker; socks broughtby students; yardstick or ruler; compass;index cards

straightedge; chart paper; tape*

�, � Fact Triangles; straightedge; 40 counters (20 each of 2 different colors)

�, � Fact Triangles; straightedge; The Greedy Triangle

paper (colored*); straightedge; cardboard; scissors; glue; Ed Emberley’sPicture Pie: A Circle Drawing Book

tape; scissors; board compass; straightedge; red pencil

�, � Fact Triangles; straightedge; tape;scissors; board compass; crayons ormarkers; paper

1◆ 9


Unit Organizer 13

The discussion below highlights the major content ideas presented in Unit 1 and helps establish instructional priorities.

Why Geometry?The title of this series is Everyday Mathematics, not Everyday Arithmetic.This title reflects the authors’ belief that arithmetic, though important, is only a fraction of what most people should know about mathematics to cope intelligently with today’s world.

High school students often have a great deal of trouble in geometrycourses because they have had little prior experience that builds spatialreasoning. Everyday Mathematics provides a remedy to that situation with geometry-oriented action and experience in elementary school. Theactivities, written so that they are interesting and fun for elementarystudents, build a foundation for geometry—an intuition about geometry.In Everyday Mathematics, informal geometry is featured throughoutGrades K–3, along with other mathematical ideas beyond arithmetic.

The Student Reference Book(Lesson 1◆1)

The Student Reference Book is a resource bookcontaining summaries of the principal conceptsand skills that students encounter in theirstudy of mathematics. It provides review andreinforcement of critical mathematics topicsand calculator usage, as well as rules formathematical games, a reference table, aglossary of mathematical terms, and otherhelpful information. These materials, presentedin a concise, reference-oriented format, invitestudents to look up information on their own,thereby encouraging them to take responsibilityfor their own learning. The book also serves as

a resource for students who must make up work and for parents, orothers, who help students at home.

From time to time, an icon appears in the journal to indicateStudent Reference Book pages on which there is information on the topic at hand.

See Section 1.2.9 of the Teacher’s Reference Manual for additionalinformation about using the Student Reference Book.

Mathematical Background

NoteResearch on childdevelopment supportsthe belief that waitingtoo long to provideexperience with suchthings as geometricfigures and relationshipsmay be harmful. Manypathways to thinkingthat are easy to buildwith young children maybe lost permanently ifappropriate and timelyexperiences are not provided.

NoteThe EverydayMathematics authorsbelieve that studentsshould learn andpractice the special skillsinvolved in obtaininginformation frommathematics books,almanacs, encyclopedias,and other resources.Regular use of theStudent Reference Bookcan be an importantasset for your language arts program.


Beyond Informal Geometry (Lessons 1◆2–1◆5)Geometric figures are all well-defined sets of points. Geometry deals withthe properties of those sets of points and the relationships between andamong them. As Everyday Mathematics begins a more systematic study offigures in fourth grade, the lessons will emphasize more rigorous geometry:

◆ clear notations (naming),◆ clear definitions, and◆ clear statements of properties and relationships.

The standard notations used in secondary school geometry are introducedin Lessons 1-2 and 1-3. The symbols that distinguish lines, line segments,rays, and angles are used. Basic geometric figures are named with letters.All of these naming conventions have proven to be quite accessible tofourth graders.

Students quickly realize that the same figure can have many names.Triangle ABC, for example, may also be named ACB, BAC, BCA, CAB, orCBA. The idea that many equivalent names can be used for the samething appears throughout Everyday Mathematics. The equivalent namesare like synonyms, or multiple names, in language arts.


Line AB, or AB, or BA

BA DC

Ray CD or CD

A

B

C

Triangle ABC, ACB, BAC, BCA, CAB or CBA


Lessons 1-4 and 1-5 help students develop more precise definitions offigures and their properties than was possible in earlier grades. The mainemphasis in these lessons is on developing a grasp of how geometricfigures are classified and of the relationships among figures. In Lesson 1-4,for example, students explore the properties of parallelograms. They applytheir understanding of these properties by listing the similarities anddifferences between and among various quadrangles. In Lesson 1-5,students examine the properties that characterize polygons and regular polygons.

Feel free to use the vocabulary of geometry. Although students may not befamiliar with all of the terms, consistent and frequent use of these termsenables students to develop the working vocabulary that is essential fordiscussing the characteristics of figures, as well as the similarities anddifferences among them.

Whenever you have the opportunity, take time to discuss the meanings ofroots, prefixes, and suffixes of geometric terms (see Lesson 1-5 and 1-8).

For additional information about standard notation and definitions offigures and their properties, see Section 13.4 of the Teacher’sReference Manual.

Unit Organizer 15


Using a Compass and Straightedge(Lessons 1◆6–1◆8)Using a compass skillfully requiresquite a bit of practice, and doing so iseasier for some students than forothers. Since “practice makesperfect,” there is no substitute for it.Good tools help a lot, too. A compassshould have a sharp anchor point toprevent slipping; it should hold thepencil securely. Use a sharp, soft leadpencil that is short enough so that itdoes not interfere with the rotation ofthe compass.

Make certain that when students usea compass, they draw on a piece ofcardboard, pad of paper, or the like sothat the compass anchor does not slipand damage the desk or tabletop. Twomethods for drawing circles with a compass are described in Lesson 1-6.Practice both methods yourself before teaching them.

Section 13.13.1 of the Teacher’s Reference Manual contains additionalinformation about using a compass and a straightedge to construct figures on paper.


NoteThe main difficulty inusing a straightedge orruler to draw segmentsand rays is allowing forthe width of the pencillead. The straightedgeshould be placed slightlyoff the points. Again,there is no substitute fortrial and error and then practice.

Rotating the paper is oneway to use a compass.

On journal page 19, students use compasses to create circle designs.


Unit Organizer 17

Addition and Subtraction FactsUnit 1 includes reminders about addition facts and the links betweenaddition and subtraction facts. While most of your students will have achieved mastery of these facts, those who have not need to practice regularly.

For additional information about addition and subtraction facts refer to Section 16.3.3 of the Teacher’s Reference Manual.

CalculatorsCalculators are useful teaching tools. Encourage students to use theircalculators whenever they encounter interesting numbers or problems thatmay be easier to handle with a calculator.

However, some journal pages, Study Links, and masters havebeen marked with a no-calculator icon. When students see thisicon, they should employ a problem-solving strategy that doesnot involve a calculator. When this icon is not shown, permit,

even encourage, students to use calculators as appropriate. Since theprincipal focus of this unit is geometry, there are few opportunities forstudents to reach for a calculator as a problem-solving tool.

Section 3.1.1 of the Teacher’s Reference Manual contains additionalinformation about using calculators.

Unit Organizer 17


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