numerical communication workbook

7/29/2019 Numerical Communication Workbook

1/77

Numerical Communication

http://foxhugh.com/charts/1

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.


2/77



Table of Contents

Topic Page

& &ntroduction '

' !pproximation

http://foxhugh.com/charts/approximation/

http://foxhugh.com/charts/approximationgraphics/

* +escribe a ,ar -hart


''

+escribe a +iagram


*

+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


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


3/77



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


4/77



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


5/77



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


6/77



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


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.
http://foxhugh.wordpress.com/charts/approximation-graphics/http://foxhugh.wordpress.com/charts/approximation-graphics/


7/77


8/77


9/77



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.
http://foxhugh.wordpress.com/charts/describe-bar-charts/http://foxhugh.wordpress.com/charts/describe-bar-charts/


10/77



,ar and column charts show similarities and differences.


11/77



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.


12/77



&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.


13/77



&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:


14/77


15/77



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.
http://foxhugh.wordpress.com/charts/describe-bar-charts/http://foxhugh.wordpress.com/charts/describe-bar-charts/


16/77




17/77




18/77




19/77




20/77



Describe a Diagram

http://foxhugh.com/charts/describeadiagram/

Diagram Graphics

The following graphics are a#ailable online (http://foxhugh.com/charts/describeadiagram/).



21/77




22/77




23/77




24/77




25/77




26/77




27/77




28/77



Describing a %lo&chart

http://foxhugh.com/charts/describeaflowchart/


29/77




30/77




31/77




32/77




33/77




34/77




35/77




36/77



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.


37/77




38/77




39/77




40/77




41/77




42/77



Pie Chart


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.


43/77



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.


44/77



Pie Chart Graphics

The following graphics are a#ailable online (http://foxhugh.com/charts/describeapiechart/).



45/77




46/77




47/77




48/77



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.


49/77



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:


50/77



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.
http://foxhugh.wordpress.com/charts/describe-a-table/http://foxhugh.wordpress.com/charts/describe-a-table/


51/77



Table of Percentages Graphics

The following graphics are a#ailable online (http://foxhugh.com/charts/describinggraphs/).



52/77




53/77




54/77




55/77




56/77



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


57/77



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/).



58/77




59/77




60/77



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


61/77



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


62/77



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_organization


63/77




64/77




65/77




66/77




67/77




68/77



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


69/77



5

6

4

'7

''

'*

'

222

666


70/77



Describe a 'o9e Chart


%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


71/77



-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


72/77



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


73/77


74/77



@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


75/77




76/77



>ame Student &+

>ickname -lass

'o9e Chart ,9aluation %orm


%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
http://foxhugh.wordpress.com/charts/describe-love-charts/http://foxhugh.wordpress.com/charts/describe-love-charts/


77/77



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

numerical communication workbook

Documents