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LEARNING GUIDEBASIC EDUCATION ASSISTANCE FOR MINDANAO

THIRD YEAR - MATHEMATICS III

GEOMETRY OF SHAPE AND SIZE

Module 2 - Types of Polygons

LEARNING GUIDE

COPYRIGHT NOTICE

Section 9 of the Presidential Decree No. 49 provides: “No copyright shall subsist in any work of the Government of the Philippines. However, prior approval of the government agency or office within the work is created shall be necessary for exploitation of such work for profit.” This material has been developed within the Basic Education Assistance for Mindanao (BEAM) project. Prior approval must be given by the author(s) or the BEAM Project Management Unit and the source must be clearly acknowledged.

Edited and produced by the Materials Development Center, July 2009

BASIC EDUCATION ASSISTANCE FOR MINDANAO

LEARNING GUIDE

THIRD YEAR – MATHEMATICS III

GEOMETRY OF SHAPE AND SIZE: TYPES OF POLYGONS

Mind MapThe Mind Map displays the organization and relationship between the concepts and activities in this Learning Guide in a visual form. It is included to provide visual clues on the structure of the guide and to provide an opportunity for you, the teacher, to reorganize the guide to suit your particular context.

Stages of LearningThe following stages have been identified as optimal in this unit. It should be noted that the stages do not represent individual lessons. Rather, they are a series of stages over one or more lessons and indicate the suggested steps in the development of the targeted competencies and in the achievement of the stated objectives.

1. Activating Prior LearningThis stage aims to engage or focus the learners by asking them to call to mind what they know about the topic and connect it with their past learning. Activities could involve making personal connections.

Background or purposeBefore performing the different tasks of this topic with the students, it is good to activate their understanding on the basic terms used in Geometry – points, lines, planes and angles in such a way that they can see the connections towards the study of polygons.

StrategyCOOPERATIVE LEARNING. A strategy incorporated by some structures used as a basic tool for group work skills. The activities prepared have definite aims and purpose and should not be seen in isolation but as an overall part of the learning environment. The activity that is considered in the strategy encourages the learners to enhance their mathematical intelligence and analytical thinking as well.

Basic Education Assistance for MindanaoLearning Guide, July 2009 3


LEARNING GUIDE



Activity 1: “Quilting Lines”Organize the students into six groups to perform the activity on quilting lines. To quilt means to fill, pad, stitch, sew or cover. Out of the figure, they will identify pairs of lines that are parallel (those that do not intersect) and perpendicular (those that form 90º angle). The more pairs they gather, the higher points they will get. Distribute to each group the activity sheets and the materials needed which includes manila paper, marking pen, and protractor. Allow them to complete the activity in eight minutes. Refer to Student Activity 1, Quilting Lines on page 17 of this learning guide for the students' task.

Formative AssessmentAsk the following questions to the students:

1. When can we say that two lines are parallel? perpendicular?

2. How many pairs of parallel lines your group had identified? How about perpendicular lines?

3. Look at the figure in your activity sheet. How many points lie therein? How many line segments? Can you name some plane figures illustrated in it? What kind of plane figures are they?

4. What figure is formed with plane ABCD? Can you name other planes in the figure similar to it?

RoundupStudents have fully grasped the concepts of points, lines, planes and angles and recognized the connections of these terms into the next level of study in Geometry specifically on polygons.

2. Setting the ContextThis stage introduces the students to what will happen in the lessons. The teacher sets the objectives/expectations for the learning experience and an overview how the learning experience will fit into the larger scheme.

Background or purposeIn presenting the context of this lesson, the students will be asked whether they agree or disagree in the BEFORE Column of the Agree and Disagree Chart containing statements on the basic concepts of polygons.

StrategyAGREE AND DISAGREE CHART. A strategy that elicits prior understanding of the students as to whether they agree or disagree certain issues/statements and later give reasons for the in depth understanding of the stipulated concept.

Activity 2: “Agree or Disagree?”Post the AGREE AND DISAGREE CHART on the board and ask students to raise their hands accordingly if they agree or disagree each statement. Tally their responses in the BEFORE Columns.



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STATEMENT

BEFORE AFTER

Agree Disagree Agree Disagree

1. It is possible for a triangle to have two obtuse angles.

2. All angles of a scalene triangle are acute angles.

3. No right triangle is equiangular.

4. A heptagon is a seven-sided polygon which consists of seven triangles whose sum of the measures of angles is 1080º.

5. If the three angles of a triangle measure 60º each, the triangle is an acute triangle.

6. A square is a rectangle.

7. A polygon is convex if a segment joining any two points of the polygon does not lie inside the polygon.

8. A square is a rhombus.

9. If the length and the width of a rectangle and a parallelogram are equal, then their areas are also equal.

10. An equilateral triangle can be a right triangle.

RoundupStudents have gained understanding based on their analysis of the statements supported by their previous knowledge and experiences on the study of polygons.

3. Learning activity sequenceThis stage provides the information about the topic and the activities for the students. Students should be encouraged to discover their own information.

Background or purposeThe students will identify, illustrate and name different kinds of polygons, their basic and secondary parts and the facts as well beyond the context through certain properties.

Strategies(1) GROUP DISCUSSIONS. A consideration of a subject by a group through a formal

discourse on a topic.

(2) MIND MAP. A simple process for stimulating concepts through creative thinking, planning and summarizing. This encourages students' ideas stand out from the general view of a topic into specific.



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Activity 3: “No Matter What Shape, Your Fractions Are In”Start exposing your students to different figures/polygons through this activity. This aims to measure their prior knowledge on determining the relations of one object with another and to revisit their basic skills on fractions.

Organize the class into six groups to perform the Student Activity 3, “No Matter What Shape, Your Fractions Are In” on pages 18 to 20.

When all groups are finished, let them display their work for checking. Call a representative in each group to discuss their output. Process the activity they have just performed by asking the following questions:

1. What do you call those four geometric figures you cut and used in the activity?

2. Can you define what a polygon is?

3. What made one figure different from the others? What are the factors to consider in classifying these figures?

4. Can you cite other figures aside from those given in the activity?

Students may draw shapes/figures on the board or give the names of the polygons. Now, present to them these two sets of points,

Call students' attention with the two sets of points.

➢ Can you describe the first set of points? the second set?

➢ If you connect points from A to D in the first set and P to R in the second set, what figure is formed in each set? What do you call these figures?

Lead the students that the figures formed are polygons. These are closed figures made up of three or more line segments joined at their endpoints. The term polygon comes from the Greek words “poly” and “gonia” meaning many angles.

To help students understand deeply the polygons, present these two figures.

Circle TriangleLet them describe each figure. Make two columns. First column for circle and another for triangle. They may write as many descriptions as they can in each column. After which, check what they have enumerated.


Set 1 Set 2

A B

CD

P

Q

R


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This time, show to them this table. Call volunteers to tick (√ ) if each characteristic agrees with the circle or with the triangle. If it doesn't, mark (x).

CHARACTERISTICS CIRCLE TRIANGLE

1. Plane and flat figure

2. Closed figure (no open edges)

3. Sides are line segments

The descriptions in column 1 are the main characteristics of a polygon.Ask: From the two figures, which has all the properties of a polygon?A triangle is one of the several types of polygons.Have a look at the figures below. Are there similarities or differences between them? What are they?

Demonstrate to them using a ruler on how to measure the length of the sides.

Each side of triangle a measures 4 cm, while triangle b measures 4cm, 4cm and 3 cm. Use this time a protractor to measure the angles of each figure.


(a) (b)

(a) (b)

4 cm4 cm

4 cm

4 cm 4 cm

3 cm


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Compare now the two triangles.If all sides of a polygon have the same lengths and all angles are equal, it is a regular polygon. If any side or angle is different from another, the polygon is irregular.

● What is the sum of the measures of the angles in triangle a? In triangle b?

● What is a triangle?

A triangle is a three-sided polygon formed by three segments joining three noncollinear points. Each of the three points is the vertex of a triangle and the segments are the sides. The sum of the measures of angles is 180º.

Triangles can be classified according to SIDES and ANGLES. Sides can be congruent. Similar markings indicate congruent parts.

A. ACCORDING TO SIDES

B. ACCORDING TO ANGLES


60º

67º 67º

46º

SCALENE TRIANGLENo two sides are congruent.

AB ≠ BC ≠ CAA

B

C

EQUILATERAL TRIANGLEThree sides are congruent.

PQ ≅ QR ≅ RPP

Q

R

D

E

F

ISOSCELES TRIANGLEAt least two sides are congruent.

DE ≅ FEDE and FE are the legs of a triangle

and DF is the base. EG is the height/altitude of the triangle and determines

also its median.G


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What if a polygon has 4 or more sides? Can you name each polygon? What is the sum of the measures of their angles?

Now, look at the table below. Given the number of sides and the name of polygons, can you determine the sum of the measures of angles in each polygon?I want you to get a one-fourth sheet of paper. What figure is that? Now, fold and crease the paper diagonally. Make sure that the opposite endpoints are aligned. Unfold the paper.What happen to your one-fourth sheet of paper?Since angles of a triangle have a sum of 180º, what is the measure of the figure patterned in

a14

sheet of paper?

Now, complete the table below:

Number of Sides Name of Polygon Sum of Measures of Angles

Number of Triangles

3 Triangle 180º ?

4 Quadrilateral ? ?

5 Pentagon ? ?

6 Hexagon ? ?


B

C D

60°

60° 60°

EQUIANGULAR TRIANGLEAll angles are congruent.

∠B ≅ ∠C ≅ ∠ D

60°

72°

48°M

N

OACUTE TRIANGLE

All the angles are acute.∠ M, ∠N, and ∠O are all acute angles.

128° 30°

22°

J

K

L

OBTUSE TRIANGLEOne angle is obtuse.

∠ J is an obtuse angle.

RIGHT TRIANGLE One angle is a right angle.

∠ U is a right angle. 90° 40°

50° hypotenuse

leg

legU W

V


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Number of Sides Name of Polygon Sum of Measures of Angles

Number of Triangles

7 Heptagon ? ?

8 Octagon ? ?

9 Nonagon ? ?

10 Decagon ? ?

11 Undecagon ? ?

12 Dodecagon ? ?

n n-gon ? ?

➢ What if a polygon has 20 or 45 or 150 or n sides, (n is the number of sides), how will you obtain the sum of the measures of the angles ?

➢ How many triangles are there in each of the above polygons? In n-gon?

Show the following figures to the class and let them investigate whether each is a REGULAR or an IRREGULAR polygon. Ask them also to identify what type of polygon is the figure. You may enlarge the given figures to make them visible for your students.

Note: Show figures of hexagon, pentagon and quadrilateral with equal lengths and equal angles.



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Now, let the students observe and analyze the following figures.

Ask them: Which of the figures are polygons? Why?

Students may say that figures 2 and 3 are polygons for the following reasons:

✔ they are plane and flat figures

✔ both are closed (no open edges)

✔ figures are formed through line segments

Focus this time with figures 2 and 3. Draw segments from any side to its opposite side as illustrated below:

Ask students to compare the two figures when lines are drawn inside the polygon.

Finally, emphasize with them that polygons are also classified as convex and nonconvex. A polygon is convex only if a segment joining any two points of the polygon lies completely inside, otherwise the polygon is nonconvex.

Ask at least two volunteers to draw on the board one example of a convex and nonconvex quadrilaterals.

Another type of polygon is the quadrilateral. This is a polygon having four sides. Like any polygon, it has its main characteristics.

✔ A quadrilateral is named by its vertices. A vertex (singular for vertices) is the point of intersection of two sides of a quadrilateral.

✔ It consists of both consecutive and opposite sides and angles.

Ask students to look at the figure below wherein the main characteristics of a quadrilateral is illustrated.


(2)(1)

(3)

(2) (3)


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The figure is quadrilateral ABCD.

A, B, C, and D are its vertices.

Vertices A and C, B and D are opposite vertices.

Two sides with a common vertex like AB and BC , and AD and DC are consecutive sides.

AB and CD , BC and AD are opposite sides.

∠A and ∠B are consecutive angles.

∠A and ∠C, and ∠B and ∠D are the opposite angles.

Segments joining opposite vertices like AC and BD are the diagonals of quadrilateral ABCD.

Below is the diagram that gives the different transformations of a quadrilateral and how they relate to one another.

SCHEMATIC DIAGRAM OF QUADRILATERALS


A

B C

D

QUADRILATERAL

TRAPEZOID PARALLELOGRAM TRAPEZIUM

ISOSCELESTRAPEZOID RECTANGLE RHOMBUS

KITE

SQUARE


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Exercises: Refer to the diagram to answer the following questions.

1. A square is a rhombus. Yes or No?

2. Which parallelogram has four congruent sides and four congruent angles?

3. A quadrilateral with exactly one pair of parallel sides.

4. A parallelogram with four right angles where two opposite sides are of equal lengths.

5. A square is a rectangle. Yes or No?

6. Which figure in the diagram has no parallel sides?

In the diagram, a quadrilateral figure on top has no parallel sides. Parallel lines are lines that lie in the same plane but do not intersect. A quadrilateral with no parallel sides is called a trapezium.

Activity 4: “Polygon Map”This time, organize the class into six groups and test their visual and mathematical intelligences as they complete the mind map on polygons. Distribute to them the activity sheet, masking tape and marking pen. Let them finish the activity within 5 minutes. Refer to Student Activity 4, “Polygon Map” on page 21 for the task to complete.

Formative AssessmentLet the same groups of students complete the statements in Student Activity 5, “Always, Sometimes, Never” found on page 22.

RoundupStudents were able to comprehend the properties of the different polygons. They understood the basic and secondary parts of a triangle and a quadrilateral as well with its corresponding characteristics.

4. Check for Understanding of the topic or skillThis stage is for teachers to find out how much students have understood before they apply it to other learning experiences.

Background or purposeAt this stage, students will be assessed as to how much they have understood with the properties of polygons. To find out the relationship of one figure with the others, they will be performing tangrams and crossword puzzle.


B E

AM

Quadrilateral BEAM is atrapezium.


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Strategies(1) TWO-PIECE SQUARE TANGRAMS. These are puzzles made up of two or more

geometrical pieces which consist of a triangle, a parallelogram and a square. They are all cut from one large square. This aims to tap their spatial and logical intelligences.

(2) CROSSWORD PUZZLE. A strategy that enhances the logical thinking of the students and aims to tap their intrapersonal and mathematical intelligences.

Activity 6: “Two-piece Square Tangrams”Let the same groups of students perform the activity on two-piece square tangrams to assess their comprehension of the topic or skill in identifying, naming and determining polygons. Refer to Student Activity 6, “Two-Piece Square Tangrams” on page 23 for the tasks to do by the students.

Formative AssessmentLet the students complete the Crossword Puzzle on polygons by giving appropriate responses with what is required in each item. Distribute Student Activity 7, “Crossword Puzzle and Worksheet” for the activity proper. Sample puzzle is found on pages 24 to 25 of this module.

5. Practice and ApplicationIn this stage, students consolidate their learning through independent or guided practice and transfer their learning to new or different situations.

Background or purposeAt this stage, students are required to classify polygons according to more than one property at a time. Students will move from a simple description of shapes to an analysis of how properties are related, all in the context of an enjoyable game called Master Card Game.

StrategyMASTER CARD GAME. A teaching technique to motivate students to examine relationships among geometric properties. Through this, students will move from recognition or description to an analysis of the properties and they interrelate. This aims to tap their mathematical/logical intelligence and enhance as well their higher order thinking skills.

Activity 8: Polygon CaptureLet the students perform the MASTER CARD GAME. This activity requires the students to enhance their deeper understanding beyond the concepts on polygons. Refer to Teacher Resource Sheet 1, “Polygon Capture” for the background and the Basic Rules of the game. This is found on pages 26 to 30. A Learning Extensions for a Teacher is also provided which contains suggestions if necessary under Teacher Resource Sheet 2. Refer this to page 31 of this learning guide.

Formative AssessmentAsk the following questions to the students:

1. Did you enjoy playing the Master Card game? Share what have you gained from the activity.

2. What skills did you apply and were developed while performing the activity?

3. As you perform the Polygon Capture activity, what additional ideas about geometric shapes and their properties have you learned?



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RoundupStudents recognized some interesting mathematical ideas related to polygons which helped them understand not just the simple definition and description of objects/shapes, but also the relevance of understanding the properties of shapes and their properties.

6. ClosureThis stage brings the series of lessons to a formal conclusion. Teachers may refocus the objectives and summarize the learning gained. Teachers can also foreshadow the next set of learning experiences and make the relevant links.

Background or purposeStudents will revisit the Agree and Disagree Chart and check appropriately as to whether they agree or disagree the statements after they understood the notions of polygons.

StrategyAGREE AND DISAGREE CHART REVISIT. A strategy that elicits actual understanding of the students from the topic discussed as to whether they agree or disagree with certain issues/statements. Later, they will prove their reasons in a convincing manner based from the stipulated concept.

Activity 9: “Agree or Disagree? Let's Revisit”Post the Agree and Disagree Chart again and let the students answer each statement in the table. Ask them to raise their hands whether they agree or disagree each statement. Tally this time the results under AFTER Column and later, let them compare their answers in the BEFORE Column. You may ask volunteers to explain and give proofs in the following statements.

STATEMENT

BEFORE AFTER


1. It is possible for a triangle to have two obtuse angles.

2. All angles of a scalene triangle are acute angles.

3. No right triangle is equiangular.

4. A heptagon is a seven-sided polygon which consists of seven triangles whose sum of the measures of angles is 1080º.

5. If the three angles of a triangle measure 60º each, the triangle is an acute triangle.

6. A square is a rectangle.

7. A polygon is convex if a segment joining any two points of the polygon does not lie inside the polygon.



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STATEMENT

BEFORE AFTER


8. A square is a rhombus.

9. If the length and the width of a rectangle and a parallelogram are equal, then their areas are also equal.

10. An equilateral triangle can be a right triangle.

Formative AssessmentLet the students perform this Brain Twister using the four puzzle pieces of polygons to form different challenging designs. Refer to Teacher Resource Sheet 3 found on page 32 on how to make the four puzzle pieces and the designs for the students to form on page 33.

Adapted: Eureka Toys and Games

RoundupStudents were able to define, identify and illustrate different kinds of polygons according to the number of sides and the basic properties applied in a certain polygon that entails the relationships of sides and angles.

Teacher Evaluation(To be completed by the teacher using this Teacher’s Guide)

The ways I will evaluate the success of my teaching this unit are:

1.

2.

3.



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STUDENT ACTIVITY 1

“Quilting Lines”

Objective: To identify parallel and perpendicular line segments from the given figure.

Directions: The quilts of Colonial Americans had a precise pattern based on Mathematics. Find all of the parallel (those that do not intersect) and perpendicular (those that formed 90º angle) line segments in this original quilt. Write your answers in a manila paper.


A F B

E

IN

J

M O

PL K

D H C

G

Source: Math Games – Judith A. Muschla and Garry Robert Muschla


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STUDENT ACTIVITY 3“No Matter What Shape, Your Fractions Are In”

Objective: To determine the relation of one geometric figure/shape with another supported by their comprehension on fractions.

Directions: (1) Name each shape below and give at least one description.

(2) In the grid that follows, cut each darkened figure. Use these cut-outs to answer the questions given. You may fold or trace these figures to find the answers.

Materials: scissors, masking tape, manila paper, grid

SHAPES NAME DESCRIPTION



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SAMPLE GRID

Directions:

Cut carefully the darkened figures in the grid.



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QUESTIONS:

ANSWERS:1. How many are there in ?

2. How many are there in ?







LESSON PLANNER FOR THIRD YEAR – MATHEMATICS

GEOMETRY OF SHAPE AND SIZE – TYPES OF POLYGONS

STUDENT ACTIVITY 4

“Polygon Map”Objective: To identify the types of polygons based on their classifications, main characteristics and properties.

Directions: Complete the mind map below by naming the different types of polygons. Consider the classifications, characteristics and properties in naming each polygon. Write each name inside the figure.


POLYGONS


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STUDENT ACTIVITY 5

“Always, Sometimes, Never”

Objective:To complete each sentence with the appropriate word to make it correct.

Directions:

Complete each statement by writing the word ALWAYS if the statement is always true, SOMETIMES if the statement may be true, or NEVER if the statement is never true.

1. A right angle ______________ has a measure of 90°.

2. Three angles of a triangle are __________________ congruent.

3. An obtuse triangle _______________ has an acute angle.

4. A square ____________________ has four right angle.

5. A rhombus ____________________ has four right angles.

6. Two squares are ___________________ congruent.

7. A rectangle is _______________ a square.

8. Opposite sides of a quadrilateral _________________ are congruent.

9. Opposite angles of a rhombus are ______________ congruent.

10. An obtuse triangle __________________ has a right angle.



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STUDENT ACTIVITY 6

“Two-Piece Square Tangrams”

Objectives:

To create two-piece square tangrams and discover the relationships of one geometrical figure with the other.

Materials:

colored papers, scissor, paste/glue, manila paper, marking pen and masking tape

Instructions:

1. Cut three squares, each having a side of 10 cm. Draw a line from the midpoint of one side of a square to an opposite vertex. Cut along this line, thus cutting the square into two pieces. Do the same with the other two squares.

Each square becomes a two-piece figure this time. Using these two “cut pieces”, make a:

(a) square

(b) triangle

(c) parallelogram

2. Questions:

➔ How many right angles are there in each piece?

➔ What fraction of the original square is the triangle?

➔ What fraction of the larger piece is the triangle?

➔ Is it possible to make an irregular quadrilateral (one that has no equal sides) out of these pieces? Show it.

➔ Is it also possible to make a quadrilateral that has only one pair of parallel opposite sides? Show this and name the figure.

Adapted: Mathematical Adventures for Teachers and Students by Wally “Wallypop” Green





STUDENT ACTIVITY 7

CROSSWORD PUZZLE – Worksheet 1Objective: To determine the word described in each item across and down.

Directions: Complete the Crossword Puzzle below by writing the empty boxes with a correct word.


4

8

16

15

19

9

6

5

2

10

18

13 12

3

1

17

14

7

11


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STUDENT ACTIVITY 7

CROSSWORD PUZZLE – Worksheet 2

DOWN

1. a Greek word for angles

2. six-sided polygon

4. a closed figure made up of two or more line segments joined at their endpoints

6. a polygon with four congruent sides and four congruent angles

7. a triangle with no two congruent sides

10. a polygon having ten sides

13. triangles are classified according to ______ and angles

14. a triangle that has a 90º angle

15. the point of intersection of two sides of a polygon

ACROSS

3. a triangle with one angle measure more than 90º

5. lines that lie in the same plane but do not intersect

8. a figure formed by two noncollinear rays have a common endpoint

9. a four-sided polygon

11. a triangle having three acute angles

12. a quadrilateral with four congruent sides

16. a quadrilateral with four right angles

17. a twelve-sided polygon

18. a polygon having nine sides

19. isosceles, scalene and equilateral are three of its several classifications



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TEACHER RESOURCE SHEET 1

“Polygon Capture”

OBJECTIVES: (1) To precisely describe, classify and understand the relationships among types of two- and three-dimensional objects using their properties.

(2) To create and critique inductive arguments concerning geometric ideas and relationships.

(3) To generate analysis, aside from descriptions on geometric shapes and their properties.

MATERIALS:

Master A – Rules of the Game

Master B – Angle and Side Cards

Master C – The Polygons

A heavier-than-normal paper such as cartolina, or carton of cigarette pack

MASTER A: RULES OF THE GAMEPreparation

Before the game, cut the cards on Master B. Mark the back of the first eight cards with “A” for angle. Mark also the back of the remaining eight cards with “S” for side. Cut the polygons on Master C. Place the 20 polygons in the center of the playing area. Put the cards in two decks: ANGLE and SIDE cards.

Basic Play

1. Player 1 picks and turns over one card from the angle deck and then one card from the side deck. All polygons that match both these properties may be captured. Captured polygons are removed from play and will be kept by Player 1.

2. If player 1 has missed any figures, player 2 may now capture them.

3. Player 2 chooses a card from each deck and tries to capture polygons.

If no polygons can be captured with the cards chosen, that turn is over. If the piece was incorrectly chosen, it will be placed or returned back in play at the center. Play until two or fewer polygons remain. If you run out of cards, reshuffle the deck. The player with the most polygons wins.

Wild Card

If the Wild Card is picked up, you may choose any “side property”. For example, if you have chosen “All angles are right angles” and the Wild Card, you may change it to, “All pairs of opposite sides have equal length” and capture all rectangles.

Steal Card

If you select the Steal Card, do not turn over a second card. This card allows you to steal polygons from your opponent. Without selecting another card, pick two properties, one for sides and one for angles, that will allow you to steal as many polygons from your opponent as possible. Keep these properties on your own. If your opponent has no card to be stolen, put the Steal Card back in the angle deck and choose two new cards.



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Example

Player 1 turns over the cards “All angles have the same measure” and “It is a quadrilateral”.

Player 1 captures shapes D, E, and G.

Player 2 may now capture shape T, since it was missed by player 1.

Player 2 now turns over two cards.

MASTER B – ANGLE AND SIDE CARDS

At the back of each top eight or first eight cards, write an “A” for angle. At the back also of each of the bottom eight cards (the remaining cards), write “S” for side. Then cut the cards.


All angles are right angles.

At least one angleis obtuse.

No angle is aright angle.

At least one angleis less than 90º.

At least one angleis a right angle.

At least two anglesare acute.

All angles have thesame measure.

STEAL CARDSelect a pair of properties. Steal all those polygons from your opponent.

No pairs of sidesare parallel.

All sides are ofequal length.

Only one pair ofsides is parallel.

At least one pair of sides is perpendicular.

All pairs of sidesare parallel.

It is a quadrilateral.

All pairs of opposite sideshave equallength.

WILD CARDPick your ownside property.


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MASTER C – THE POLYGONS

Carefully cut the polygons below.



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SAMPLE STEPS IN PLAYING A GAMEInstruct the students to read the rules on Master A. Teachers may find it helpful to play the first game with or against the class. This may be done also in the first 2 or 3 games to familiarize students on the game rules. For the first game, remove the Steal Card to simplify the game.

To introduce the game as a whole-class activity, lay all twenty (20) polygons in the center of the overhead projector or display them all in the manila paper. Students may lay out their shapes and follow along.

Here is an introductory game observed in one of the classrooms (Figure 1) proceeded as follows.

1. The teacher picks the cards “All angles have the same measure” and “All sides are of equal length”. He/she takes figures D, G, Q, and S, placing them in his/her pile to be out of the play.

2. Students then pick the cards “At least two angles are acute” and “It is a quadrilateral”. They choose figures I, J, K, M, N, O, and R.

Figure 1

3. On his/her second turn, the teacher picks the cards “At least one angle is a right angle” and “No pairs of sides are parallel”. He/she chooses figures A and C and then asks students to find a figure that she could have taken but forgot or missed it. One student points out that figure H has a right angle and no parallel sides. Other students are not sure that this polygon has a right angle, which leads to a discussion of how they might check.

4. The students then proceed to take two new cards.


G S

D Q

M

N

J

I

K

D

R

M

N

J

I

K

O

R

(a) Teacher selects cards.Angle card: All angles have the same measure.Side Card: All sides are of equal length.

(b) Students select cards.Angle card: At least two anglesare acute.Side Card: It is a quadrilateral.


LEARNING GUIDE



When no polygons remain in play that match the two cards chosen, the player may turn over additional card – either an angle or a side card. This move calls for some planning and analysis to determine whether an angle card or a side card is most likely to be useful in capturing the most polygon. If the player still cannot capture any polygons, “play” moves to the opponent. When all cards in a deck are used up before the end of the game, they are reshuffled. Play continues until two or fewer polygons remain. The player with the most polygons is the winner.

When the “Wild Card” is selected, the player may pick one side property from the deck.

Steal CardWhen the “Steal Card” comes up, a card from the deck will not be drawn. Instead, the player has the opportunity to capture some of the opponent's polygons. The person who has chosen the Steal Card picks two properties (one side and one angle) and “steals” the polygons with those properties from the opponent. If the opponent has no polygons yet, the Steal Card is put back in the deck and a new card will be chosen.

One interesting aspect of the game is the various strategies that students use. Some students go through the figures one at a time, using a trial-and-error method to match them to properties on the cards. Some students perform two sorts; they find the polygons that match the first card and, of this group, those that also match the second card. Others seem to analyze the properties and mentally visualize the polygons that are possible.

In analyzing properties (“Is this angle acute?”), students quickly learn to use angles and sides in other figures as benchmarks, for example, using the right angle in a rectangle to check whether a triangle has a right angle. Generally, this game may be played with no time limits, but students could choose a limit as an option.


(c) Teacher selects cards.Angle card: At least one angle is aright angle.Side Card: No pairs of sides areparallel.

(d) Students capture the piece that the teacher missed.

AA

C

H


LEARNING GUIDE



TEACHER RESOURCE SHEET 2LEARNING EXTENSIONS FOR A TEACHER

Some teachers have found that coordinating two points is initially too difficult for their students and have simplified the game by placing all cards into a single pile. For this simpler version, only one card is turned over, and students choose all polygons with that property. In this adaptation, it is probably best to remove the Wild Card and the Steal Card. The other rules are the same as described previously. Because only one property is being analyzed at a time, this game will go more rapidly.

The polygons on the Master C can also be used for various sorting games and activities. For example, students may work in pairs, with one student separating the shapes into groups based on some rule or set of rules, and the other students may begin with simple classifications (rectangles and non-rectangles), other may use more complex relationships (regular polygons, polygons with equal sides but not equal angles, and other figures). With a little experience, many students will find interesting ways to sort the polygons. You may also use the figures to review geometry vocabulary before the game: “Find all of the figures that have a pair of perpendicular sides”. “Pick all regular polygons”. These activities provide a nice warm-up to the game and other Geometry activities.

Several extensions of the game are possible. More polygons can be added, either by yourself or by the students, including some that are more difficult to capture, such as a kite or a nonconvex hexagon. Nonpolygons, such as figures with curves, can be added for sorting activities. Additional property cards can also be added to the basic deck. For example, as students learn more about polygons, you may wish to add angle cards, such as “Opposite angles have equal measure” or “The number of vertices is a prime number”. Similarly, questions about diagonals can be added to the side cards, such as “All diagonals have the same length”. If you have a set of geometric solids available, you can adapt this game to the three-dimensional Geometry. Instead of side and angle cards, make one set of surface and face cards (“I have one curved surface”) and edge and vertex cards (“I have an even number of vertices”). If three-dimensional solids are not available, make a third set of picture cards. Instead of polygon cards, students choose the geometric solids.

The Polygon Capture game cards can also be used to generate figures. As in the game, students turn over two cards. Instead of capturing polygons, they use a geoboard or dot paper to make a figure that has the two properties. Rather than a game, this is simply an activity to help students learn to coordinate the features of a polygon.

Adapted: http://illuminations.nctm.org/


http://illuminations.nctm.org/


LEARNING GUIDE



TEACHER RESOURCE SHEET 3

BRAIN TWISTER - 1

Objectives:

To make challenging designs out of the four pieces of polygons and to see the connections among these figures.

Material:

a harder-than-normal paper such as thick cartolina/carton of cigarette formed into polygons as shown below

Directions:

1) Trace the following figures below using the indicated dimensions in a thick cartolina/carton.

2) Cut them.


3.5 cm

2.5 cm 2.5 cm

2.5 cm3.5 cm

3.5 cm

1 cm

2.5 cm

3.5 cm

4 cm

7.8 cm

1 cm

3.5 cm

5.2 cm

7.8 cm

2.5 cm


LEARNING GUIDE



BRAIN TWISTER – 2

CHALLENGING DESIGNS


1 2 4

6 7 8

10 11 12

13 14 15

18 19 20

3

9

5

17

16




For the Teacher: Translate the information in this Learning Guide into the following matrix to help you prepare your lesson plans.

Stage 1. Activating Prior Learning

2. Setting the Context

3. Learning Activity Sequence

4. Check for Understanding

5. Practice and Application

6. Closure

Strategies

Activities from the Learning Guide

Extra activities you may wish to include

Materials and planning needed

Estimated time for this Stage

Total time for the Learning Guide Total number of lessons needed for this Learning Guide


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