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Introduction
This collection of worksheets is meant to help English as second language (ESL) students to
learn how to present numerical/logical information in the form of graphics. The first part of
the lesson is meant to be presented b the teacher as a lecture. !fter the lecture" there are a
series of graphics and groups of students or indi#idual students can then present the
information to the other students. The graphics are online and the link to the lecture and
graphics is pro#ided with the lesson. There is an assumption that the teacher has access to a
computer connected to the internet and can pro$ect the graphic assigned to the students to a
screen. %sing this collection of worksheets" the student can get practice standing in front of
an audience and explaining the graphics pro#ided.
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Table of Contents
Topic Page
& &ntroduction '
' !pproximation
http://foxhugh.com/charts/approximation/
http://foxhugh.com/charts/approximationgraphics/
* +escribe a ,ar -hart
http://foxhugh.com/charts/approximationgraphics/
''
+escribe a +iagram
http://foxhugh.com/charts/approximationgraphics/
*
+escribe a lowchart
http://foxhugh.com/charts/describeaflowchart/
0 +escribe a Line 1raph
http://foxhugh.com/charts/describinggraphs/
2 +escribe a 3ie -hart
http://foxhugh.com/charts/describeapiechart/
4
5 +escribe a Scatter 3lot
http://foxhugh.com/charts/describeapiechart/
05
6 +escribe a Table of 3ercentages
http://foxhugh.com/charts/describeatable/
04
4 +escribe a Trend
http://foxhugh.com/charts/describetrends/
22
'7 +escribe a 8enn +iagram
http://foxhugh.com/charts/describea#enndiagram/
5'
'' +escribe an 9rganiational -hart
http://foxhugh.com/charts/describeorganiationalchart/
5
'* +onald in ;athmagic Land 9nline
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http://foxhugh.com/t#seriesesldiscussion=uestions/donaldin
mathemagicland/
' +escribe a Lo#e -hart
http://foxhugh.com/charts/describelo#echarts/
6'
' Lo#e -hart E#aluation orm 65
'0 >umerical 3refixes
http://foxhugh.com/#ocabulartables/numericalprefixestable/
66
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Approximation
http://foxhugh.com/charts/approximation/
Introduction
&n report writing it is good stle to use ?approximation? in the indings" -onclusions and@ecommendations. !pproximation means describing numbers or statistics b using a fraction
that is similar to the exact numberA e.g. using ?about onethird? instead of .52B" or an eas
toremember number such as ?$ust under one million? instead of ?445"20*?.
There are a number of reasons for doing this. irstl" it is easier for people to understand and
remember. Secondl" the numbers or statistics ma be more detailed than necessar.
') about" roughl" approximatel" around
*) under" less than" below" almost
) o#er" more than" abo#e
) nearl" close to" approaching
0) precisel" exactl
Cere are some examples:
a) 20B about twothirds of
b) *6B $ust o#er a =uarter of
c) *'B about a fifth
d) 4B $ust under a half of
e) 5B almost three=uarters of
f) .B a third of
g) 4*B most of
h) 46.0B almost all
i) '"7 o#er a thousand
$) ''0 o#er a hundred
k) 4 fewer than ten
l) * a small number
m) a few
n) 2 se#eral
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o) 54"46* about three=uarters of a million
=) '"*02"647"0 o#er '.* billion
r) '77"770 about one hundred thousand
s) 27.7B roughl sixt per cent
t) 7.0D- approximatel 7 degrees -elsius
u) 07*.7* around fi#e hundred pounds
Tips:
') +on?t use fractions where the denominator (the number under the line) is greater than 0
man people do not know that '/2F '2B or that 5/6F 65.0B .
*) +on?t forget the hphen in fractionsA e.g. ?onethird? (but not after ?a?A e.g. use ?a third?).
) +on?t forget to add an ?s? on the end of fractions starting with two or greaterA e.g. ?two
thirds?" ?three=uarters?.
) ;ost fractions can be followed b the preposition ?of ?A e.g. ?Three=uarters of the staff
were satisfied with working conditions.?
0) ;ost fractions are followed b a plural nounA e.g. ?half of the books?" except uncountable
nounsA e.g. ?Calf of the staff were satisfied with working conditions? (the #erb is ?were?" not
?was?" because ?staff ? is thought of as a plural after fractions).
2) &n strictl correct grammar use ?fewer than? for countable nouns and ?less than? for
uncountable nouns.
5) &t is more natural to use ?a? instead of ?one? in front of fractionsA e.g. ?a third of ...?
6) &n front of ?half ? ou do not need to use ?a? or ?one?A e.g. ?Calf of the staff were satisfied
with their working relationships.?
4) +o not use a number at the start of a sentence" because it?s bad stle. %se wordsA e.g. ?'77
9ne hundred of the staff were satisfied with working conditions.?
'7) ,e careful of the spelling of ?se#eral? it?s not ?se#eral?.
'') @emember that ?onl? and ?$ust? often ha#e a negati#e meanings" so use them onl if ou
want to show that something is badA e.g. ?9nl 'B of our staff were satisfied with working
conditions.?
Match the phrase to the correct number:
a) '4.46B ') $ust under a hundred
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b) '7'"445
c) *2B
d) .B
e) *6"''*
f) '"240"'4
g) 6.65B
h) 45
i) 5
$) 5.*0B
*) nearl three=uarters
) about '.5 million
) a =uarter of a million
0) about a fifth of
2) a third of
5) se#eral
6) almost a half of
4) $ust o#er a =uarter of
'7) about '77"777
Approximation Graphics
http://foxhugh.com/charts/approximationgraphics/
The following graphics are a#ailable online" at the abo#e address" and the students will
describe the graphic assigned to that student to the other students.
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Describe a Bar Chart
http://foxhugh.com/charts/describebarcharts/
Describing Bar Charts and Column Charts !"
,ar charts and column charts are similar: onl their orientations differ. ! bar chart is
orientated horiontall" whereas a column chart is arranged #erticall. Sometimes Gbar chartG
refers to both forms.
These tpes of charts are usuall used for comparison purposes (unlike line charts" which
describe change).
9bser#e the following chart:
&t shows the populations of #arious European countries in the ear *775. The populations are
onl for one ear" *775" and so we cannot make an comments about change in population:
we can onl compare one count with another.
&TS. 9n the Iaxis in this
chart the units are millions. The population of ,elgium in *775 was not '7" but '7 millionpeople.
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,ar and column charts show similarities and differences.
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long longer longest
low lower lowest
man more most
much more most
new newer newest
old older oldest
poor poorer poorest
rich richer richest
short shorter shortest
small small smallest
strong stronger strongest
weak weaker
To signal comparison and contrast within a sentence ou can use the following con$unctions:
as ....... as" not as ......... as" not so ........ as" whereas" but" while" although
To signal comparison and contrast between sentences ou can use the following words and
phrases:
Describing Bar Charts and Column Charts #"
,ar charts and column charts are often used to make multiple comparisons.
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&t shows the populations of ma$or European countries in the ears '442 and *775. &n this case
we can make two sets of comparisons. ow ou can compare indi#idual countries and ou can compare two things: Iou can
compare sies of populations and ou can compare the change in populations from '442 to
*775.
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&t is important to mention an exceptions to the changes ou describe. &n this case" the
exception is 3oland where the population fell #er slightl in the period described.
To write a short description of this graph ask yourself (and answer!) the following questions:
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These two charts show EH!-TLI the same information. Cowe#er" it is easier to see the
differences in the first chart because the I axis starts at 7" not ero. Sometimes charts are
formatted like this in order to make the differences more ob#ious.
Bar Chart Graphics
The following graphics are a#ailable online (http://foxhugh.com/charts/describebarcharts/ ).
The students will describe the graphic assigned to that student to the other students.
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Describe a Diagram
http://foxhugh.com/charts/describeadiagram/
Diagram Graphics
The following graphics are a#ailable online (http://foxhugh.com/charts/describeadiagram/).
The students will describe the graphic assigned to that student to the other students.
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Describing a %lo&chart
http://foxhugh.com/charts/describeaflowchart/
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Describing a 'ine Graph
http://foxhugh.com/charts/describinggraphs/
Look at the following simple line graph:
&t shows the population of +enmark from '442 to *775. Iou can see that in '442 the
population was 0.*0 million and that b the ear *775 it had grown to 0.0 million.
&TS. 9n the Iaxis in this
graph the units are millions. The population of +enmark in '442 was not 0.*0" but 0.*0
million people.
Line graphs describe change.
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Pie Chart
http://foxhugh.com/charts/describeapiechart/
3ie -harts normall show proportion" which can be measured in percentages or fractions.
This chart shows the relati#e sie of populations of countries of the European %nion in *775.
So we can onl make comparisonsA we cannot sa anthing about change.
>9T sa that 3oland has the smallest population: *' other countries ha#e
populations smaller than 3oland?s.
The twentone smallest countries of the European %nion make up nearl 7B of the
population.
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This chart shows the relati#e sie of populations of countries of the European %nion in both
'446 and *775. &n this case we can make two sets of comparisons:
') ote that ou -!>>9T sa that 1erman?s population fell or that rance?s population grew.
These charts onl show population share" not population numbers.
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Pie Chart Graphics
The following graphics are a#ailable online (http://foxhugh.com/charts/describeapiechart/).
The students will describe the graphic assigned to that student to the other students.
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http://foxhugh.com/charts/45
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Describe a *catter Plot
http://foxhugh.com/charts/describeascatterplot/
Scatter plots are used to displa the relationship between two =uantitati#e #ariables.
9ne #ariable on horiontal axis" one on #ertical. ;easure both #ariables on each indi#idual.
Each indi#idual appears as one point in the plot. -an use different smbols (tags) to show the
effect of a categorical #ariable. &f there is an explanator #ariable" always put the explanatory
ariable on the hori"ontal axis#
Example ;anatees are a large" gentle sea creature li#ing along the lorida coast. ;an
manatees are killed or in$ured b powerboats.
Explanator 8ariable F
@esponse 8ariable F
Scatter plot: Cow describe the relationshipJ
&nterpreting Scatter plots:
') Look for o#erall pattern
direction form strength
*) Look for de#iations from o#erall pattern
9utliers an indi#idual obser#ation that falls outside the o#erall pattern of the graph.
+irection:
3ositi#e !ssociation: Two #ariables are positi#el associated when high #alues on first
#ariable occur with high #alues on second #ariable" and low #alues occur with low #alues.
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e.g. Students with higher S!T scores tend to ha#e higher frosh 13!s
>egati#e !ssociation: Two #ariables are negati#el associated when high #alues of one
#ariable occur with low #alues of the other" and #ice #ersa.
e.g. 3eople who smoke tend to ha#e shorter life spans.
9#erall 3attern: To describe a scatterplot" state the direction (positi#e or negati#e)" form (is it
linearJ)" how strong the relationship appears (how large is the scatter)" and identif an
outliers.
3roblems with Scatter plots
-hanges in scale can drasticall effect the picture presented.
+escribe the following Scatter plot:
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Describe a Table of Percentages
http://foxhugh.com/charts/describeatable/
This table shows the percentage of women in tertiar education in selected countries from
'446 to *770 :
9bser#ing trends in a table is not as eas as it is when ou examine a graph" so ou need to
look carefull. The most striking thing to notice is that in all countries except Mapan women
made up significantl more than half of the student population in tertiar education.
&n general" the trend was for an increasing percentage of women in tertiar education. The
onl exception to this was ,ulgaria where the trend is in re#erse: in '446" 27.4B of the
tertiar student population was made up of women" whereas b *770 this figure had fallen to
0*.'B.
The countr with the highest percentage of women in tertiar education was &celand and thiswas also the countr with the largest increase" rising from from 27B to 2.4B.
The largest percentage change was that of ,ulgaria" from 27.4B to 0*.'B" a '.B drop.
The lowest rise was in inland" where" although the percentage fluctuated o#er the period in
=uestion" the percentage rose from 0.0 to 0.2.
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Table of Percentages Graphics
The following graphics are a#ailable online (http://foxhugh.com/charts/describinggraphs/).
The students will describe the graphic assigned to that student to the other students.
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Describe a Trend
(ocabular) for Describing Trends
+ord Part of *peech ,xample *entences
increase
erb: to increase" is increasing"
has increased" increased
noun: an increase ofN0"00m
an increaseinspending of
N0"00m
Total expenditure increasedfrom
N"2''m to N4"'20m from '440 to
'442.
rom '440 to '442 there was an increase
inexpenditure of N0"00m.
decrease
erb: to decrease" is decreasing"
has decreased" decreased
noun: a decrease of7.5Ba decrease inspending of 7.5B
Expenditure on primar education
decreasedfrom **.*B to *'.0B from
'440 to '442.rom '440 to '442 there was a decrease
inexpenditure of 7.5B.
rise
erb: to rise" is rising" has risen"
rose
noun: a rise of N0"00m
a rise in spending of N0"00m
Total expenditure rosefrom N"2''m to
N4"'20m from '440 to '442.
rom '440 to '442 there was a rise in
expenditure of N0"00m.
fallerb: to fall" is falling" has fallen"fell
noun: a fall of7.5B
a fall inspending of 7.5B
Expenditure on primar education fellfrom **.*B to *'.0B from '440 to '442.
rom '440 to '442 there was a fall in
expenditure of 7.5B.
drop
erb: to drop" is dropping" has
dropped" dropped
noun: a drop of7.5B
a drop inspending of 7.5B
Expenditure on primar education
droppedfrom **.*B to *'.0B from '440
to '442.
rom '440 to '442 there was a drop in
expenditure of 7.5B.
to be
financed b)
erb: to be financed b" is
financed b" has been financed
b" was financed b
meaning: to be paid for (e.g.
mone is transferred from one
budget to another)
The increase in spending in this sector
was financed b decreases in other
sectors.
-ing forms !fter an introductor clause that
includes some analsisA e.g.?Spending rose in all three ears?"
Spending rose in all three ears"
increasingfrom '5.2B to '6B from '440to '442" and then risingagain to '6.*B in
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an ?Oing? form can be used to
describe numbers and dates.
'4456.
,xpenditure on ,ducation in .ong /ong !001 to !002
Brea3do&n of spending !00145 !00546 !00642
Total expenditure 7 million" "2'' 4"'20 0"'0
As 8 of go9ernment budget '5.2B '6B '6.*B
8 spent on
primar) education
secondar) education
tertiar) education
**.*B
.5B
0.4B
.
*'.0B
.*B
2.5B
.
*'.2B
.0B
0.4B
.
Source:Hong $ong %&&'#Cong Kong: 1o#ernment 3rinter
Trend Graphics
The following graphics are a#ailable online (http://foxhugh.com/charts/describetrends/).
The students will describe the graphic assigned to that student to the other students.
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Describe a (enn Diagram
http://foxhugh.com/charts/describea#enndiagram/
! 8enn diagram" sometimes referred to as a set diagram" is a diagram that graphicall
displas all the possible relationships between a finite number of sets. !t their simplest" 8enndiagrams are made up of o#erlapping circles. The interior of each circle represents a set of
ob$ects" or ob$ects that ha#e something in common. The exterior of the circle represents all
that each set excludes. The areas where circles o#erlap show the relationship between sets.
or instance" if one circle represents the set PwomenQ and another circle represents the set
PpoliticiansQ the area of o#erlap would represent women who are politicians.
Ke
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1roup ' R The group will make a 8enn diagram comparing ;icke ;ouse and +onald +uck.
1roup * R The group will make a 8enn diagram comparing an two +isne 3rincesses the
group chooses: Snow
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Describe an rgani;ational Chart
!" Describe the t)pe of organi;ation the chart is dealing &ith< +hat t)pe of organi;ation
are )ou describing=
1o#ernmentJ
,usinessJ
9therJ
#" Describe the t)pe of organi;ation chart )ou are dealing &ith< +hat sort of
organi;ational chart are )ou describing=
Cierarchical
;atrix
lat(also known as Coriontal)
$" *tart from the top and &or3 )our &a) do&n le9el b) le9el
!" Describe the t)pe of organi;ation the chart is dealing &ith< +hat t)pe of organi;ation
are )ou describing=
1o#ernmentJ
,usinessJ
9therJ
#" Describe the t)pe of organi;ation chart )ou are dealing &ith< +hat sort of
organi;ational chart are )ou describing=
Cierarchical
;atrix
lat(also known as Coriontal)
$" *tart from the top and &or3 )our &a) do&n le9el b) le9el
The following graphics are a#ailable online (http://foxhugh.com/charts/describe
organiationalchart/). The students will describe the graphic assigned to that student to the
other students.
http://en.wikipedia.org/wiki/Hierarchical_organizationhttp://en.wikipedia.org/wiki/Matrix_managementhttp://en.wikipedia.org/wiki/Flat_organizationhttp://en.wikipedia.org/wiki/Horizontal_organizationhttp://en.wikipedia.org/wiki/Hierarchical_organizationhttp://en.wikipedia.org/wiki/Matrix_managementhttp://en.wikipedia.org/wiki/Flat_organizationhttp://en.wikipedia.org/wiki/Horizontal_organizationhttp://en.wikipedia.org/wiki/Hierarchical_organizationhttp://en.wikipedia.org/wiki/Matrix_managementhttp://en.wikipedia.org/wiki/Flat_organizationhttp://en.wikipedia.org/wiki/Horizontal_organizationhttp://en.wikipedia.org/wiki/Hierarchical_organizationhttp://en.wikipedia.org/wiki/Matrix_managementhttp://en.wikipedia.org/wiki/Flat_organizationhttp://en.wikipedia.org/wiki/Horizontal_organization7/29/2019 Numerical Communication Workbook
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Donald in Mathmagic 'and nline +or3sheet
http://foxhugh.com/communication/donaldinmathemagicland/
,xamples of Mathmagic>
3thagoras and music
The pentagram" the golden section" and the golden rectangle
!rchitecture and art
The human bod and nature
1ames
;ental exercises
&nfinit and the future
The 'ife of P)thagoras
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5
6
4
'7
''
'*
'
222
666
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Describe a 'o9e Chart
http://foxhugh.com/charts/describelo#echarts/
%se the Lo#eo1raphsite to create lo#e charts of one famous couples on the list below.
3resent our results to the class. Iou can post the links to our results on our acebook walland share the results with the class from there. Iou can also email the link to ourself and
share the results from our email account. Tell us a little about the couple ou picked and
wh ou picked the couple. !lso" do ou think the charts is an accurate reflection of the
couples real life relationshipJ The Lo#eo1raph site generates ascatter plot"pie chartand
8enn +iagram.
!dam U E#e
!l 1ore and Tipper 1ore
!l 3acino U ,e#erl +?!ngelo
!lec ,aldwin U Kim ,asinger
!ndre !gassi U ,rooke Shields
!ngelina Molie U ,ill ,ob Thornton
!nnie 9akle U rank ,utler
!nthon U -leopatra
!ntoine La#oisier U ;arie!nne 3ierrette 3aule
!ntonio ,anderas U ;elanie 1riffith
,arbie U Ken
,ert U Ernie
,ill -linton U Cillar @odham
,ob ;arle U @ita ;arle
,onnie 3arker and -lde ,arrow
,rian +e 3alma U >anc !llen
,ruce ,oxleitner U ;elissa 1ilbert
,ruce
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-hristie ,rinkle U ,ill Moel
-ind -rawford U @ichard 1ere
-liff U -laire Cuckstable
-lint ,lack U Lisa Cartman
-onnie -hung U ;aur 3o#ich
+agwood ,umstead U ,londie ,oopadoop
+an !krod U +onna +ixon
+a#id !r=uette U -ourtene -ox
+a#id ,owie U &man
+a#id -opperfield U -laudia Schiffer
+a#id Lnch U &sabella @ossellini
+onald and +ais +uck
+onald Trump U ana Trump / ;arla ;aples
+ouglas airbanks U ;ar 3ickford
+ouglas airbanks Mr. U Moan -rawford
+rew ,arrmore U Tom 1reen
Eddie 8an Calen U 8alerie ,ertinelli
Eliabeth Talor U @ichard ,urton
Ellen ,arkin U 1abriel ,rne
El#is 3resle U 3riscilla 3resle
Ernest ,orgnine U Ethel ;erman
Ethan Cawke U %ma Thurman
ranWois Truffaut U ann !rdant
rank Sinatra U !#a 1ardner
ranklin +. @oose#elt U Eleanor @oose#elt
red lintstone U
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1arr Trudeau U Mane 3aule
1ene @oddenberr U ;a$el ,arrett
1eorge ,urns U 1racie !llen
1eorge ,ush U ,arbara ,ush
1erald ord U ,ett ord
1ome U ;orticia !ddams
1race Stafford U
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@obert -rumb U !line Kominsk
@obert atalie anc +a#is
@o @ogers U +ale E#ans
@uss ;eer U E#e ;eer
Samson U +elilah
Sarah Messica 3arker U ;atthew ,roderick
Serge 1ainsbourg U Mane ,irkin
Sharon !rden U 9 9sbourne
Shelle abares U Lou !dler
Shirle Temple U Mohn !gar
Siegfried U @o
Sofia -oppola U Spike Mone
Sonn ,ono U -her
Ste#en Spielberg U !m &r#ing
Superman U Lois Lane
Susan Sarandon U Tim @obbins
Ted Turner U Mane onda
Tina Turner U &ke Turner
Tom -ruise U >icole Kidman
8i#ienne Leigh U Ton -urtis
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>ame Student &+
>ickname -lass
'o9e Chart ,9aluation %orm
http://foxhugh.com/charts/describelo#echarts/
%se the Lo#eo1raph site to create lo#e charts of one famous couples on the list online.
3resent our results to the class. The Lo#eo1raph site generates a scatter plot" pie chart and
8enn +iagram. &n addition" create a @elationship Timeline" using M1raph" of the couples
histor. 3ro#ide an o#erall assessment of the couples relationship. Each of the fi#e sections
of the assignment listed below will be worth fi#e points for a total of *0 points.
Sections 3ts.
') Scatter plot
*) 3ie chart
) 8enn +iagram
) @elationship Timeline
0) 9#erall !ssessment
Total 3oints
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Numerical Prefixes
http://foxhugh.com/#ocabulartables/numericalprefixestable/
Prefix Prefix meaning *ample &ords
') uni ' unicorn: mthical creature with one horn
*) mono ' monorail: train that runs on one track
) bi * biccle: twowheeled #ehicle
) tri triceratops: threehorned dinosaur
0) =uadr =uadruped: fourfooted animal
2) =uint 0 =uintuplets: fi#e babies born at a single birth
5) penta 0 pentagon: figure with fi#e sides
6) hex 2 hexapod: ha#ing six legs" an insect" for example
4) sex 2 sextet: group of six musicians
'7) hept 5 heptathlon: athletic contest with se#en e#ents
'') sept 5 septuplets: se#en babies at asinglebirth
'*) octo 6 octopus: sea creature with eight arms
') no#em 4 no#ena: praers said o#er nine das
') deka or
deca
'7 decade: a period of '7 ears
'0) cent hundred centur: a period of '77 ears
'2) hecto hundred hectogram: '77 grams
'5) milli thousand millennium: a period of '"777 ears
'6) kilo thousand kilogram: '"777 grams
'4) mega million megaton: one million tons
*7) giga billion gigawatt: one billion watts
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