Tangrams Across the Curriculum - New Hampshire...
Transcript of Tangrams Across the Curriculum - New Hampshire...
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
VocabVocabVocabVocab #2#2#2#2
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
VocabVocabVocabVocab #3#3#3#3
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
Parts of Speech #2Parts of Speech #2Parts of Speech #2Parts of Speech #2
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
Puzzle SolutionsPuzzle SolutionsPuzzle SolutionsPuzzle Solutions
VocabVocabVocabVocab #1#1#1#1
VocabVocabVocabVocab #2#2#2#2
VocabVocabVocabVocab #3#3#3#3
Parts of SpeechParts of SpeechParts of SpeechParts of Speech #1#1#1#1
Parts of Speech #2Parts of Speech #2Parts of Speech #2Parts of Speech #2
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
Fractions #2Fractions #2Fractions #2Fractions #2
13
23
165
6
15
25
515
1421
636
1845
4048
1050
45
2025
24
Fractions #3Fractions #3Fractions #3Fractions #3
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
Puzzle SolutionsPuzzle SolutionsPuzzle SolutionsPuzzle Solutions
Geometric ShapesGeometric ShapesGeometric ShapesGeometric Shapes
QuadrilateralsQuadrilateralsQuadrilateralsQuadrilaterals
Fractions #1Fractions #1Fractions #1Fractions #1
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
30
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
33
34
35
36
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/>.