tangrams across the curriculum by kim hanson

1

Tangrams Across the Curriculum

Kim Hanson

Dover Adult Learning Center

2012

2

Introduction .............................................................................................................................. 3

Directions .................................................................................................................................. 3

Attachment ............................................................................................................................... 3

History ...................................................................................................................................... 4

Background ........................................................................................................................... 4

Puzzle Set .............................................................................................................................. 4

Classic Rules ......................................................................................................................... 5

Interesting Facts ................................................................................................................... 5

History Activity ..................................................................................................................... 5

Puzzle Solutions .................................................................................................................... 8

Language Arts .......................................................................................................................... 9

Vocabulary Activity ............................................................................................................... 9

Parts of Speech Activity .......................................................................................................13

Puzzle Solutions ...................................................................................................................18

Writing .....................................................................................................................................19

Activity .................................................................................................................................19

Math .........................................................................................................................................19

Puzzle Solutions ...................................................................................................................26

Science .....................................................................................................................................27

Activity .................................................................................................................................27

Puzzle Solution.....................................................................................................................29

3

IntroductionIntroductionIntroductionIntroduction “Tangrams across the Curriculum” is a collection of tangram puzzle activities that provide

examples for teachers to use with students. The puzzles focus on practice for history,

language arts, writing, mathematics, and science skills which can be adapted to any lessons

in classes ranging from ESOL – Level 1 to Adult Diploma classes.

Each section is formatted in a similar manner: subject information, activity examples,

tangram puzzles, and tangram solutions.

DirectionsDirectionsDirectionsDirections Copy each Tangram onto cardstock and have students cut them out so that they have 7 puzzle pieces: 2 large right triangles, 1 medium right triangle, 2 small right triangles, 1 square, and 1 parallelogram. Once they are finished invite them to start matching vocabulary words with definitions, math problems with answers or questions with answers. As students continue matching a formation will appear. Allow students to switch and try different puzzles.

AttachmentAttachmentAttachmentAttachment Included at the end of this document are:

1. Blank Template of a Tangram Puzzle

2. Instructions on how to construct your own set of Tangrams by Tom Scavo

3. Examples of Tangram Puzzle Solutions.

4

HistoryHistoryHistoryHistory Tangrams are a dissection puzzle formed from 7 flat polygons called tans. The tans are

used to form specific shapes using all 7 pieces. Usually the player is only given an outline

or silhouette of the shape they are trying to make.

BackgroundBackgroundBackgroundBackground Known as “The Chinese Puzzle Game”, tangrams were invented in Imperial China long,

long ago. The earliest record of the puzzle is from a book dated 1813, but the puzzle was

very old by then and the publication date is unreliable. Due to the fact that it was a game

for women and children tangrams were not taken seriously and would not have been

written about early on. Captain M. Donnaldson was given Sang-hsia-ko’s two Tangram

books written in 1815 which he sailed to America on his ship “Trader.” The first book to

be written and published in America was based on these two books. In about 1891,

Freidrich Adolf Richter began making Tangram sets out of stone or fake earthenware which

were marketed under the name “The Anchor Puzzle” and became very popular in both

Germany and America.

Puzzle SetPuzzle SetPuzzle SetPuzzle Set The puzzle set includes 7 flat polygons: 5 isosceles triangles, 1 square and 1 parallelogram.

All the angles in the tans are either 45°, 90°, or 135°.

Triangles

The area of one of the large triangles is twice that of the medium triangle. The area of the medium triangle is twice that of the small triangles.

The 2 large right triangles have a hypotenuse of n and side lengths of �√�

�.

The medium right triangle has a hypotenuse of �√�

� and side lengths of

�

�.

The 2 small right triangles have a hypotenuse of �

� and side lengths of

�√�

�.

Squares

The area of the square is exactly twice that of one of the small triangles.

Each of side lengths of the square is �√�

�.

ParallelogramParallelogramParallelogramParallelogram

The area of the parallelogram is equal to the area of the square.

The side lengths of the parallelogram are �

� and

�√�

�.

5

Classic RulesClassic RulesClassic RulesClassic Rules 1. All 7 pieces must be used

2. All pieces must lie flat

3. All pieces must touch

4. No pieces may overlap

5. Pieces may be rotated and/or flipped to form desired shape

Interesting FactsInteresting FactsInteresting FactsInteresting Facts 1. There are over 6500 different tangram puzzles and still growing. The number of

puzzles is finite.

2. The shapes of each of the 7 tans can be formed from the 7 tangram pieces, resulting

in a larger size version.

3. There are only 13 convex configurations: no indentation into the puzzle.

4. Tangrams were admired by many famous people such as Edgar Allen Poe, Lewis

Carroll, Thomas Edison, and Napoleon.

5. In 1908 Sam Loyd , a puzzle author and recreational mathematician, wrote a book

called “The Eighth Book of Tan”. The book was a fictitious history of tangrams.

6. Tangram paradoxes were discovered in 1958 by Henry E. Dudeney. A dissection

fallacy: when the same set of tangram pieces can apparently produce two different

figures. In fact this is not the case, the two puzzles have the same exact area and

the foot of the second monk is incorporated in the larger body of the first.

History History History History ActivityActivityActivityActivity History Puzzle #1 is based on the given Tangram facts above. History Puzzle #2 is based on facts about China. Invite students to look up facts about China on the internet or find some readings for them to participate in.

6

History #1History #1History #1History #1

Whe

re did

tang

rams

origi

nate

?

About

how m

any

numbe

rs of

know

n

puzz

les ar

e the

re?

Chi

na

6500 How

many tan

pieces are in thepuzzle?

7

What is the m

ostcom

mon tang

ram shape?

trian

gle

What subject is linkedto tangrams?

How m

anyrig

ht tr

iangl

es

are i

n the

puzz

le?

math

5

7

HHHHistoryistoryistoryistory #2#2#2#2

About

how m

any

peop

le are

inCh

ina?

Wha

t are

theco

lors

of th

e flag

?

China is located inwhat continent?

How

man

y l iv

ela

ngua

ges

are

t her

e?

How

man

ypr

ovin

ces

are

inCh

ina?

Wha

t is

the

capi

tal o

fChi

na?

1,350,000,000

22

Asia Beijin

g

Red &

Yello

w

292

8

Puzzle SolutionsPuzzle SolutionsPuzzle SolutionsPuzzle Solutions

HistoryHistoryHistoryHistory #1#1#1#1

History #2History #2History #2History #2

9

Language ArtsLanguage ArtsLanguage ArtsLanguage Arts Read the book “Grandfather Tang’s Story” by Ann Tompert.

Vocabulary ActivityVocabulary ActivityVocabulary ActivityVocabulary Activity

Share the meaning of the following words with students. Rivalry: competition for the same objective Tragic: suffering extreme distress or sorrow Boasted: talk with excessive pride and self-satisfaction Bared: uncover and expose it to view Lashed: beat forcefully Transformed: to change in form Sprang: a sudden dart or thrust Scrambled: to climb or crawl Swoop: to sweep through the air Peered: to look searchingly Tremble: to shake involuntarily with fear Fierce: violent in force Seize: to take possession of by force Plunge: to thrust suddenly into something Clamped: to impose controls on Flock: a large number of birds Discourage: to dissuade Forged: to move ahead slowly Flutter: to flap wings rapidly

10

VocabVocabVocabVocab #1#1#1#1

lashe

d

bared

rivalr

y

tragic

boast ed

transformed sp

rang

c om

pe t

iti o

nfo

rsa

me

obje

c tiv

es

suffe

ring ex

trem

e

distr

ess o

r sorro

w

talk with

excessive pride

or self-satisfaction

unco

ver &

expo

se

it to v

iew

beat

force

fully

to ch

ange

info

rm

a sudden dart or thrust

11


scra

mbl

edswoop

peered

tremble

fierce

seize

to climb or crawl

to sw

eep

thro

ugh t

he ai

r

to look searchinglyto

shak

e inv

olunt

arily

with

fear

violent inforce

to take possessionof by force

12


plun

ge

clamped

flock

dis c

o ura

ge

forged

flutter

to th

rust

sudde

nly

into s

omet

hing

to im

pose

cont

rols

on

a large numb

er of bird

s

to dissuade

to move ahead slowly

to flap wingsrapidly

13

Parts of Speech Parts of Speech Parts of Speech Parts of Speech ActivityActivityActivityActivity Share the 8 parts of speech chart with students.

Part of Speech

Function Example Words Example Sentence

Noun Person, place or thing

Teacher, student, park, school, cat, paper,

My catcatcatcat likes to sleep.

Verb Action Learn, sleep, run, sit, like

All of my students run run run run to school so they can learnlearnlearnlearn everything they can.

Adjective Describes a noun Purple, little, good, some

The purplepurplepurplepurple hat was a fantastic addition to her costume.

Adverb Describes a verb, adjective or adverb

Well, very, really, quickly

My sister quicklyquicklyquicklyquickly ran next door to borrow some sugar.

Pronoun Replaces a noun I, he, she, they, you SheSheSheShe quickly ran next door to borrow some sugar.

Preposition Links a noun to another word

To, at, after, on, but OnOnOnOn Sunday we went totototo the apple orchard.

Conjunction Joins clauses or sentences or words

And, but, when Kelly andandandand Misty like to play. The girls like to play butbutbutbut they do not like to work.

Interjection Short exclamation Oh!, Ouch!, Hi! Hi!Hi!Hi!Hi! How are you today? Have the students use the two sentences below to practice identifying the parts of speech. These sentences were taken from the story “Grandfather Tang’s Story” by Ann Trompert. #1 “They were sitting under their favorite willow tree beside a river talking about their magic powers.” #2 “Wu Ling climbed up on a mossy rock in the middle of the river.” Reinforce these skills by using the tangram puzzles below.

14

Parts of Speech #1Parts of Speech #1Parts of Speech #1Parts of Speech #1

noun

besid

e

river

verb

verb

they

sitting

tree

talking

mag

ic

pro

noun

prep

ositi

on

adject

ive

noun

15


Wu Ling

clim

bed

mossy

rock

river

middle

up

prop

er nou

n

verb

adje

ctive

noun

noun

adje

ctiv

ead

verb

16

SynonymsSynonymsSynonymsSynonyms

cry

fly

sink

flap

watch

catch

honk

wee

p

mov

edrop

beat

obse

rve

seize

beep

17

AntonymsAntonymsAntonymsAntonyms

close

dow

nra

n

goodin

under

above

far

up

idle

bad

out

ove

r

below

loud

soft

18





Parts of SpeechParts of SpeechParts of SpeechParts of Speech #1#1#1#1


SynonymsSynonymsSynonymsSynonyms

AntonymsAntonymsAntonymsAntonyms

19

WritingWritingWritingWriting Sparking the imagination before having students sit down with a blank piece of lined paper

and a prompt may make the process of writing a little bit easier. It will create a visual story

with a theme, setting, and characters.

ActivityActivityActivityActivity Writing Sentences:

1. Ask students to think about their favorite animal and why it’s their favorite. 2. Have students create an ATC “Artist Trading Card” of their favorite animal using

all of the tans from a tangram set and art supplies, such as construction paper, card stock, scrapbook paper, crayons, markers, paint, glitter glue, yarn, fabric, etc. Get creative here! An ATC is a piece of art usually about the size of a baseball card (2.5” X 3.5”), but it can be any size you see fit.

3. On lined paper invite students to write a sentence or two about their ATC animal and why they like it.

4. Display students ATC and sentence in or around the classroom. Writing Paragraphs: Using the same idea as above invite students to create a series of ATCs and have students write a paragraph or two about the cards. The illustrations can be limited or not. Prompts:

• Write about the most memorable day of your life. • Write about the time when you went out of your way to help someone in need. • Do you think families are important? Explain using reasons and examples. • What are the good things and bad things about living in your town? • What would you do if you could fly? • How do you like to spend your free time?

MathMathMathMath There are six Math puzzles: geometric shapes, quadrilateral definitions, Fractions #1:

converting fractions from improper to mixed numbers, Fractions #2: reducing fractions,

Fractions #3: perform the indicated operation with fractions, and solve algebraic equations.

Use these puzzles after a lesson on the skill or as a warm-up.

20

Geometric ShapesGeometric ShapesGeometric ShapesGeometric Shapes

square

triangle

rectangle

circle

pent

agon

octagon

hexa

gon

parallelogram

21

QuadrilateralsQuadrilateralsQuadrilateralsQuadrilaterals

square

rect

angle

parallelogram

trape

zoid

kite

rhombus

four

right

ang

les

all s

ides

equ

al

fourright anglesopposite sides equal

oppo

site sid

es

para

llel &

equ

al

at le

ast 1

pair o

f

para

llel s

ides

2 pair of equal

adjacent sides

all 4

side

s equ

al

oppo

site sid

es

para

llel

22

Fractions #1Fractions #1Fractions #1Fractions #1

173

132

344

235

1 48

194

345

485

73

165

334

359

153

456

23


13

23

165

6

15

25

515

1421

636

1845

4048

1050

45

2025

24


14

12+

76

2312

+

121

2X

512

133

4-

14

34

12

23 X

14927

X

35

12X

310

4 91

3

25

Algebra EquationsAlgebra EquationsAlgebra EquationsAlgebra Equations

2+4x=1

0x=2

3x-1=20

x=7

10-6x=-8

x=3

7x-3=-24

x=-3

x=-5

x=0

3+x

-1

=2

5x-10 2

=-5

26


Geometric ShapesGeometric ShapesGeometric ShapesGeometric Shapes

QuadrilateralsQuadrilateralsQuadrilateralsQuadrilaterals


FractionsFractionsFractionsFractions #2#2#2#2

FractionsFractionsFractionsFractions #3#3#3#3

Algebra Algebra Algebra Algebra EquationsEquationsEquationsEquations

27

ScienceScienceScienceScience

ActivityActivityActivityActivity Listening and recalling facts.

Read the Red Fox Fact to the students. Make sure they understand that this is a listening

exercise. Encourage them to take notes or jot down important facts. Reread the paragraph

again. Then have them try the tangram puzzle.

Red Fox Facts

These very adaptable mammals which belong to the animal kingdom live around the world

in many different habitats: grasslands, forests, mountains, and deserts. The red fox makes

its home in a small cave like hole called a den. They are intelligent and sly with an

excellent sense of hearing. With all these skills combined the red fox hunts extremely well.

They eat almost any small animal some examples include rodents, birds, and rabbits. The

animals they need to watch out for include bears, wolves, coyotes, eagles, and humans. The

fox’s bushy tail has many uses. It helps the fox keep its balance, communicate with other

foxes, and as a blanket to keep the animal warm. Foxes mate in the winter giving birth in

the spring. They usually have 2-12 pups.

28

Red Fox PuzzleRed Fox PuzzleRed Fox PuzzleRed Fox Puzzle

tail use

best

sens

e

foodsource

kingdom

pred

ator

mate

hom

eforest

blanket

hearing

rabbitanimal

bear

winter

den

habit

at

29

PuzzPuzzPuzzPuzzle Solutionle Solutionle Solutionle Solution

Red Fox PuzzleRed Fox PuzzleRed Fox PuzzleRed Fox Puzzle

31

Constructing Your Own Set of Tangrams by Tom Scavo

1. Fold a rectangular piece of paper so that a square is formed. Cut off the extra flap.

2. Cut the square into two triangles.

3. Take one triangle and fold it in half. Cut the triangle along the fold into two

smaller triangles.

32

4. Take the other triangle and crease it in the middle. Fold the corner of the triangle opposite the crease and cut.

5. Fold the trapezoid in half and fold again. Cut along both folds.

6. Fold the remaining small trapezoid and cut it in two.

http://mathforum.org

37

Works Cited

"ATC TANGRAMS." ATC. N.p., n.d. Web. 25 Sept. 2012. <http://tangrams.ca/atc>.

Baxamusa, Batul Nafisa. Buzzle.com. Buzzle.com, 29 Dec. 2011. Web. 25 Sept. 2012.

<http://www.buzzle.com/articles/writing-prompts-for-kids-in-elementary-and-

middle-school.html>.

"Parts of Speech Table." Parts of Speech. N.p., n.d. Web. 25 Sept. 2012.

<http://www.englishclub.com/grammar/parts-of-speech_1.htm>.

Scavo, Tom. "The Math Forum @ Drexel University." The Math Forum @ Drexel

University. N.p., n.d. Web. 25 Sept. 2012. <http://mathforum.org/>.

"Tangram Cards." Educational Technology Clearinghouse. N.p., n.d. Web. 25 Sept. 2012.

<http://etc.usf.edu/clipart/galleries/681-tangram-cards>.

"Tangram, the Incredible Timeless 'Chinese' Puzzle." Tangram the Incredible Timeless

'Chinese' Puzzle 2. N.p., n.d. Web. 25 Sept. 2012. <http://www.archimedes-

lab.org/tangramagicus/pagetang1.html>.

Wikipedia. Wikimedia Foundation, n.d. Web. 25 Sept. 2012. <http://www.wikipedia.org/>.

tangrams across the curriculum by kim hanson

Documents