Teaching the Lesson materials

Key ActivitiesStudents review the meanings of parallel lines, line segments, and rays. They comparevarious parallelograms and quadrangles.

Key Concepts and Skills• Develop a definition for parallel and intersecting line segments, lines, and rays.

[Geometry Goal 1]• Develop a definition for perpendicular line segments. [Geometry Goal 1]• Describe characteristics of parallelograms. [Geometry Goal 2]• Classify quadrangles based on side and angle properties. [Geometry Goal 2]

Key Vocabulary parallel lines • intersect • parallel line segments • parallel rays • perpendicular line segments

Ongoing Assessment: Recognizing Student Achievement Use journal page 10.[Geometry Goal 1]

Ongoing Learning & Practice materials

Students play Subtraction Top-It to practice subtraction facts.

Students practice and maintain skills through Math Boxes and Study Link activities.

Differentiation Options materials

Students explore parallelline segments with rubberbands and geoboards.

Students solve a puzzleinvolving properties ofparallelograms.

Students play Sz’kwa.

� Student Reference Book, p. 310� Teaching Masters (Math Masters, pp. 16

and 17)� Game Master (Math Masters, p. 505)� geoboards; rubber bands; straws;

straightedge; 40 counters (20 each of 2 different colors)

ENRICHMENTENRICHMENTREADINESS

3

� Math Journal 1, p. 9� Student Reference Book, pp. 263 and 264� Study Link (Math Masters, p. 15)� Game Master (Math Masters, p. 506)� number cards 1–10 (4 of each); six-sided

or polyhedral dice (optional)

2

� Math Journal 1, pp. 10 and 11� Student Reference Book, p. 100 (optional)� Study Link 1�3� Teaching Master (Math Masters, p. 14)� +, – Fact Triangles� Geometry Template or straightedge

See Advance Preparation

1

Lesson 1�4 35

Objective To model the classification of quadrangles based ontheir properties.

Technology Assessment Management SystemJournal page 10, Problems 2 and 3See the iTLG.

Additional InformationAdvance Preparation For Part 1, place copies of Math Masters, page 14 near the Math Message.

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36 Unit 1 Naming and Constructing Geometric Figures

LESSON

1� 4 Math Message: Properties of Polygons

Name Date Time

All of these have something in common.

None of these has it.

1. Which of these has it? Circle them.

2. What property do the circled polygons have in common?

3. Use your straightedge to draw a polygon that has this property.

sides. All of the polygons are quadrangles.Sample answer: All of the polygons have 4

Sample answer:

Math Masters, p. 14

Teaching Master

� Math Message Follow-Up(Math Masters, p. 14)

Invite volunteers to identify what the shapes have in common and indicate which shapes have that property. Students indicatethumbs-up if they agree. Have partners share the polygons theydrew for Problem 3.

Explain that geometric shapes can be classified by their properties. For example, any polygon with four sides is a quadrangle. As illustrated on Math Masters, page 14, some quadrangles are squares, some are trapezoids, and so on.

WHOLE-CLASS ACTIVITY

1 Teaching the Lesson

Getting Started

Study Link 1�3 Follow-Up Have students compareanswers with a partner. Askvolunteers to share how the rectanglesand trapezoids they drew in Problems 1and 2 are similar and different.

Math Message Take a Properties ofPolygons sheet (Math Masters, page 14) and follow the directions.

Mental Math andReflexes In Lesson 1-1, students were asked tosort their �, � Fact Triangles into twopiles: OK and Try Again. Have studentspractice the facts in the Try Again pile andtransfer appropriate facts to the OK pile.When they are finished, have studentsfasten the piles with paper clips and storethem until the next practice session.

NOTE Some students may benefit fromdoing the Readiness activity before youbegin Part 1 of the lesson. See theReadiness activity in Part 3 for details.

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Adjusting the Activity

� Developing Definitions of Parallel Lines, Line Segments,and RaysTell students that the number of sides is an obvious property of ashape, but there are many other properties that are less obvious.This lesson involves one of those properties.

1. Draw two parallel lines on the board, and ask students what these lines are called. Remind them that a line goes on without end in both directions.

Parallel lines

● When you look at a long stretch of straight railroad tracks,the tracks appear to meet far in the distance. Do they actually meet? no Do two parallel lines ever meet or cross? no

Parallel lines are lines on a flat surface that never meet orcross; they do not intersect.

● What would happen if railroad tracks were not parallel?Sample answer: The train’s wheels could not stay on thetracks.

2. Draw two parallel line segments on the board. Two line segments in the same plane are parallel if they do not intersect and they will never intersect no matter how far theyare extended. Parallel line segments are parts of lines that areparallel. Have students demonstrate parallel line segmentswith their arms—either by holding them straight up or by lining up their forearms, elbow to finger, with a small distancebetween them.

Parallel line segments

3. Draw two parallel rays on the board. Two rays in the sameplane are parallel if they do not intersect, and they will neverintersect no matter how far they are extended. Parallel raysare parts of parallel lines.

Parallel rays

ELL

To help students remember the definition of parallel, point out that thethree l’s in the word parallel are, in fact, parallel.Some students may be interested in the mathematical symbols used to indicateparallel lines or line segments. For example, instead of writing “Line segment ABis parallel to line segment CD,” students can write AB� �� C�D�.

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

WHOLE-CLASS ACTIVITY

Lesson 1�4 37

NOTE To be parallel, lines must be in thesame plane. Two lines that do not meet andare not in the same plane are called skewlines. Lay a pencil on a table and stand another pencil upright a few inches away. The two pencils suggest skew lines.

Links to the Future

In Unit 11 of Fourth Grade EverydayMathematics, students apply their understanding of the term parallel as theydescribe the relationships between the facesand edges of geometric solids.

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38 Unit 1 Naming and Constructing Geometric Figures

NOTE The term rhombus comes fromGreek by way of Latin. The plural is eitherrhombuses or rhombi.

� Exploring Parallelograms(Math Journal 1, pp. 10 and 11)

Have students identify the parallel line segments in Problem 1 onjournal page 10. Ask why the other pairs of line segments are notparallel. If the line segments in Problems 1e and 1f are extended,they will meet or cross. The line segments in Problem 1b intersect.Line segments (or lines) that intersect and form right angles, likethose in Problem 1b, are called perpendicular line segments(or lines).

Have students do Problems 2 and 3 on their own before completingjournal page 11 with a partner.

Ongoing Assessment:Recognizing Student Achievement

Use journal page 10, Problems 2 and 3 to assess students’ understanding ofparallel line segments. Students are making adequate progress if they are ableto draw appropriate quadrangles. Some students may be able to draw more thanone example.

[Geometry Goal 1]

Ask students to help you list relationships, similarities, and differences among various quadrangles. For example:

� Parallelograms are quadrangles with two pairs of parallel sides.

� Squares, rectangles, and rhombuses are parallelograms, buttrapezoids and kites are not.

� All squares are rectangles, but not all rectangles are squares.

� All four sides of a square or rhombus are the same length.Squares have right angles; rhombuses can have right anglesbut usually do not.

� All squares are rhombuses, but not all rhombuses are squares.(Rhombuses are usually thought of as “slanted” or diamondshaped.) A rhombus that is not a square is also not a rectangle.

Rhombuses

� The key difference between a kite and a rhombus is that all thesides of a rhombus are equal, but a kite has two adjacent sidesof one length and two adjacent sides of another length.

Kite

Journal page 10Problems 2 and 3 �

PARTNER ACTIVITY

10

ParallelogramsLESSON

1� 4

Date Time

1. Circle the pairs of line segments below that are parallel. Check some of your answers by extending each pair of segments to see if the two segments in the pair meet or cross.a. b.

c. d.

e. f.

Use your Geometry Template or straightedge to draw the following quadrangles:

2. Draw a quadrangle that has 2 pairs of parallel sides.

This is called a .

3. Draw a quadrangle that has only 1 pair of parallel sides.

This is called a .trapezoid

parallelogram

94–100

Sample answers:�

�

Math Journal 1, p. 10

Student Page

11

Date Time

For Problems 4 and 5, circle the best answer(s). Some items have more than 1 correct answer, so you may need to circle more than 1 answer.

4. A parallelogram is a quadrangle that 5. A rhombus is a parallelogram in whichhas 2 pairs of parallel sides. all sides are the same length.Which are parallelograms? Which are always rhombuses?

A. squares A. squares

B. rectangles B. rectangles

C. rhombuses C. trapezoids

D. trapezoids D. kites

A rectangle is a parallelogram that has all right angles. Which of the followingare rectangles? Write always, sometimes, or never to complete each sentence.Explain your answers.

6. Squares are rectangles. Explain.

7. Rhombuses are rectangles. Explain.

8. Trapezoids are rectangles. Explain.

9. A kite is a parallelogram. Explain.

have 2 pairs of parallel sides.A kite does notnever

only 1 pair of parallel sides.A trapezoid hasnever

a rectangle (square) if it has all right angles.A rhombus issometimes

rectangle with all sides the same length.A square is aalways

Parallelograms continuedLESSON

1� 4

Try This

Math Journal 1, p. 11

Student Page

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Adjusting the Activity

9

Math Boxes LESSON

1�4

Date Time

5. Subtract mentally or with apaper-and-pencil algorithm.

a. 76 � 41 �

b. 52 � 38 � 1435

1. Subtract mentally.

a. 10 � 4 �

b. � 8 � 5

c. 7 � 4 �

d. 15 � 7 �

e. 13 � 8 �

f. � 17 � 89583

36

3. Complete.

Luz sold boxes.

Ana sold boxes.

Mya sold boxes.

Pei sold boxes.

7

9

10

84. Which of these can go in a name-collection

box for the number 50? Circle the bestanswer.

A. 10 � 35

B. 136 � 51

C. 200 � 4

D. 4 � 15

76

2. Draw and label line AB.Draw point C on it.

What are two other names for line AB?

Sample answers:

C AB

AC, BC, BA,CA, CB 91

149

0

2

4

6

8

10

Luz Ana Mya Pei

Cookie Sale

Num

ber o

f Box

es

Students

12–15

Math Journal 1, p. 9

Student Page

STUDY LINK

1� 4 Classifying Quadrangles

Name Date Time

99 100

1. A parallelogram is a quadrangle(quadrilateral) that has 2 pairsof parallel sides.

Draw a parallelogram.

2. Answer yes or no. Explain your answer.

a. Is a rectangle a parallelogram?

b. Is a square a parallelogram?

c. Is a square a rhombus?

d. Is a trapezoid a parallelogram?

3. Draw a quadrangle that has at least1 right angle.

no

yes

yes

yes

4. Draw a quadrangle that has 2 pairsof equal sides but is NOT a parallelogram.

This is called a . kite

Practice

5. 12 � 6 � 6. 16 � 7 � 7. 210 � 150 �

8. � 140 � 80 9. � 93 � 58 10. 123 � 76 � 4735606096

Sample answer:

Sample answer:

Sample answer:

It has 2 pairs of parallel sides.

It has 2 pairs of parallel sides.

It has just 1 pair of parallel sides.

It is a parallelogram with equal sides.

Math Masters, p. 15

Study Link Master

Lesson 1�4 39

Adjusting the ActivityHave students open their Student Reference Book to page 100 to see

a visual organizer displaying relationships among quadrangles.

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

� Playing Subtraction Top-It(Student Reference Book, pp. 263 and 264; Math Masters, p. 506)

Students play Subtraction Top-It to develop automaticity withsubtraction facts. Consider having students record several roundsof play on Math Masters, page 506.

Use these game variations as appropriate:� Use a regular six-sided die and a polyhedral die with numbers 1–20. Roll both

dice, and subtract the smaller number from the larger one.� Use two polyhedral dice with numbers 1–20. Roll both dice, and subtract the

smaller number from the larger one.� Use only the number cards 1–9. Turn over four cards, form two 2-digit

numbers, and find the difference.

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

� Math Boxes 1�4(Math Journal 1, p. 9)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 1-2. The skill in Problem 5 previews Unit 2 content.

Writing/Reasoning Have students write a response to thefollowing: For Problem 3, some students wrote that Mya sold 4�

12� boxes of cookies. Explain the mistake they

might have made when reading the graph. Sample answer: They counted the number of squares. They did not look at the scale tosee that one square represents two boxes of cookies.

� Study Link 1�4(Math Masters, p. 15)

Home Connection Students answer questions and draw figures to demonstrate their understanding of the classifications of different quadrangles.

INDEPENDENTACTIVITY

INDEPENDENTACTIVITY

PARTNER ACTIVITY

2 Ongoing Learning & Practice

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40 Unit 1 Naming and Constructing Geometric Figures

� Exploring Parallel Line Segments with Geoboards(Math Masters, p. 16)

To explore the concept of parallel line segments using a concretemodel, have students make line segments on a geoboard. Askthem to share their answers to Problem 4. Some students mightuse gestures to support their words.

� Solving a Straw-Squares Puzzle(Math Masters, p. 17)

To apply students’ understanding of the properties of parallelograms, have them solve a puzzle that requires altering a rectangular arrangement of straws to create two squares.

� Playing Sz’kwa(Student Reference Book, p. 310; Math Masters, p. 505)

To apply students’ understanding of intersecting line segments,have them play Sz’kwa. Students take turns placing markers onthe Sz’kwa game mat (Math Masters, page 505) at any intersection that is not already covered by a marker. The goal is tocapture the most markers.

Sz’kwa Game Mat from Math Masters, page 505

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Wrig

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raw

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15–30 Min

PARTNER ACTIVITYENRICHMENT

15–30 Min

PARTNER ACTIVITYENRICHMENT

5–15 Min

PARTNER ACTIVITY

READINESS

3 Differentiation OptionsLESSON

1� 4

Name Date Time

Parallel Line Segments

1. All of these are parallel line segments. Make each pair on your geoboard.

2. None of these are parallel line segments. Make each pair on your geoboard.

3. Some of these are parallel line segments. Make each pair on your geoboard.Circle the parallel line segments.

4. How would you describe parallel line segments to a friend?

5. Practice making other parallel line segments on your geoboard.

they would never meet or cross.in the same plane were to go on forever,Sample answer: If 2 parallel line segments

94

Math Masters, p. 16

Teaching Master

LESSON

1� 4

Name Date Time

Straw-Squares Puzzle

1. Gather 17 straws of the same length. Arrange them as shown to the right.

The arrangement of straws forms a rectangle. The object of this puzzleis to remove straws from the arrangement so that only 2 squares remain.

� You must remove exactly 6 straws from the arrangement.

� You may not move any of the other straws.

2. Record your work on the picture above by marking an X on the strawsyou removed. Trace over the remaining straws that form the 2 squares.

Math Masters, page 17

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