EnglishbytheNumbers.doc

English by the Numbers Unit 11. Numbers, Decimals and FractionsHundredsThousandsFractions & DecimalsQuizThis Unit prepares students to understand andclearly express small and large numbers, as wellas fractions, decimals and percents.Sample Languagenumbersfive hundred and eighteen (518), sixty-three thousandfour hundred and twelve (63,412), seven hundred andseventy thousand (770,000)decimalsfive one-thousandths (.005), one point zero five(1.05), point eight five percent (.85%)fractionsone-fifth (1/5), twelve and an eighth (12 1/8), three-fiftieths (3/50)Key Sentences & ExamplesThese numbers are all greater than one hundred and lessthan one thousand.Be careful not to confuse teen numbers such as thirteenwith ty numbers such as thirty.Five hundred eighteen. Three hundred eighty.These numbers are all greater than one thousand and lessthan one million.Nine thousand seven hundred forty-three. Ninety-seventhousand four hundred thirty-six. Nine hundred seventy-four thousand, three hundred and sixty-one.Sometimes the number nine thousand seven hundredforty-three is read as ninety-seven hundred and forty-three.Here are some fractions. One-half, one-third, one-fourth.One-fiftieth, one-hundredth, one-thousandth.Here are some decimal fractions and percents. Pointfive. One point zero five. Zero point one percent.For very small numbers, such as 0.00001, you can read itas one point zero times ten to the minus fifth.English by the Numbers Unit 22. Numerical Operations and RelationsNumerical OperationsNumerical RelationsQuizThis Unit prepares students to understand andclearly express small and large numbers, as wellas fractions, decimals and percents.Sample Languagenumerical operationsa plus b equals c, a divided by b, the nth root of x, xsquared, twice the sum of a and b, fifty percent morethan fournumerical relationsthe second largest number, the third smallest number, thedifference between the two largest numbers, half the sumof the smallest and largest numbersKey Sentences & ExamplesThe sum of a and b is c; or a plus b equals c. Thedifference of c and b is a; or c minus b is equal to a.Here we have a times b equals x; or a multiplied by b isx. In this example, we have the sum of a and bmultiplied by c. In this example, a is divided by b; or aover b. This is the nth root of x. For example, the squareroot of four is the second root of four, which is two.Here we have the cube root of eight, or the third root ofeight, which is two. This is x to the nth. For n equal totwo, we say x squared. For n equal to three, we say xcubed, or x to the third.Take the sum of two plus six and divide it by two.Multiply the sum of a plus b by fifteen and divide theresult by a times b. What number is the sum of eighty-five and five? What is two to the fourth? What is twentypercent more than ten? If x is fifty percent more thanfour, what is x? Which of these five numbers is thesmallest? Which numbers are the two largest numbers?Which number is ten percent of the largest number?Which number is equal to the difference between thelargest and smallest numbers?English by the Numbers Unit 33. Related ChangesPart 1Home BuyersSample GraphsSample LanguageGraphsremained fairly constant, didnt change, rise, increased,went up, made steady gains, gets weaker, decreases,went down, declined, droppedrelated changesX remained fairly constant, but y increased significantly.As the price of an average house increased, thepercentage of U.S. families able to buy a new housedecreased.Part 2Speed & DistanceLanguage LearningBlood PressureQuizThis Unit prepares students to describe how onequantity correlates to another. Sometimes thereis no relationship. Sometimes a change in onequantity causes a change or in another.Key Sentences and ExamplesThis graph shows the percentage of US families able tobuy an average-priced new home. As the price of anaverage house increased, the percentage of U.S. familiesable to buy a new house decreased. Between 1970 and1976, the average price of a new house rose from$23,400 to $44,200. As a result, fewer U.S. familieswere able to buy new houses. In this graph, both X andY are increasing. In this graph, X is increasing while Yis decreasing. Here we are looking at changes in X andY during the ten-year period from 1978 to 1988. Duringthat period, whenever Y increased, X decreased, andwhenever Y went down, X went up. In this case, asexports, X, went up, unemployment, Y, declined. WhileX stayed about the same, Y increased. X remained fairlyconstant, but Y increased significantly. X increasedrapidly at first, but then it fell even though Y continuedto climb. As the dollar gets weaker, the number ofAmerican workers employed by Japanese firmscontinues to climb. An increase in the value of theJapanese yen is generally followed by an increase inJapanese productivity.Goals:To be able to ask and answer questions abouthow one factor relates to another.To be able to express an opinion about onequantity is related to another.English by the Numbers Unit 44. Line GraphsPart 1Auto salesForeign Share of Steel MarketUnemployment RateHome BuyersAverage Family SizeSample Language & Learning Pointsline graphssales declined to a low of around 300,000, salesincreased steadily, sales were around 900,000 units, salesat Union Motors surpassed sales at Federal Motors, thenumber of potential first-time home buyers peaked, thelargest share of the market, changes in theunemployment ratepresent perfect (have + V(n)sales have stopped their decline, have remained fairlysteady, the number of potential first time buyers haschanged, the number has been droppingPart 2City Government ApprovalPopulation GrowthWorld Energy ConsumptionPassenger Car ExportsTraffic FatalitiesKey Sentences and Examples:This first example shows how auto sales at Union Motorshave changed since 1960. In 1960, sales were about500,000 units. From 1960, sales declined to a low ofaround 300,000 in 1965. From 1965, sales increasedsteadily until they reached a high of around 900,000 in1974. Then, because of increasing imports, sales began along decline, to a low of around 500,000 units. Since1980, sales have stopped their decline and have remainedfairly steady.This graph shows how the foreign share of total US steelsales changed during the period from 1965 through 1985.Between 1970 and 1980, the lowest foreign share of themarket was about 12%. The largest share of the marketbefore 1970 was about 17%, in 68.This graph shows how the number of potential first timehome buyers has changed. The number of potential first-time home buyers peaked at around 45 million at the endof the 80s. Since the beginning of 1990, the number hasbeen dropping.This graph shows the decrease in average family size inthe US. US families in 1989 averaged only 3.16 people,the smallest size since 1940. This drop is primarily theresult of lower birthrates and continued increases in thenumber of single-parent families. This graph indicatesthat the average family has been getting smaller.Part 2This line graph shows how the voter approval rating for acity government has changed during the past 12 months.Note that the approval rating was at its highest during thefirst 3 months and at its lowest in month 8. It reached itslowest point in month 8. During month 8, 60% of thevoters disapproved of the governments performance.This graphs shows the rate of population growth inseveral countries. It also shows the literacy rate in eachof the countries. The adult literacy rate is the percentageof adults who can read and write. The axis on the leftgives the percentage growth rate, and the axis on theQuizThis Unit prepares students to present data froma line graph, especially changes over time.Goals:To be able to use the present perfect (have+V(n) to express change.right gives the literacy rate. For example, thepercentage annual growth rate of Brazil is about1.4%. Its literacy rate is 0.83 or 83%. For thesecountries, the graph suggests that countries with ahigher literacy rate have a lower rate of populationgrowth.This graph shows how the worlds consumption ofenergy is increasing. The scale on the left is in unitsof quadrillion BTUs or British Thermal Units. In1983, the worlds energy consumption was 283quadrillion BTUs. The worlds energy consumptionin 1990 was 347 quadrillion BTUs.This graph shows how passenger car exports changedin the 5 year period ending in 2003 It shows the valueof exports in billions of dollars for seven exportingcountries.This graph gives the causes of traffic fatalities basedon 4000 separate accidents. Each bar shows thenumber of fatalities for each cause. The axis on theright gives the percentage. For example, about 1200deaths were due to speed. The line graph above thebar graph shows the cumulative percentage offatalities due to each cause. It shows that 72.3 percentof the traffic fatalities were due to two causes, lanechanges and unsafe speed.Sample Questions:When did the approval rating reach 50%?When did the approval rating reach its lowest point?What has happened to the approval rating during thepast 4 months?(a) It has stayed flat. (b) It has improved. (c) It hasgotten worse.What percent of voters disapproved of thegovernments performance during month 8?What conclusion can be drawn from this graph?Which country has a negative growth rate?Which country has the highest growth rate?Of these countries, which country has the lowest rateof literacy?About what is Vietnams literacy rate?What was the worlds energy consumption in 1990?What was the increase in energy consumption from2000 to 2005?In which 5-year period did energy consumptionincrease the most?Which country was the leading exporter of passengercars for the entire 5-year period?Which country saw a decline in its exports ofpassenger cars from 1999 to 2003?Which country made the largest gain?What was the value of Frances passenger car exports in2003?Which country made the largest percentage gain in sales?During which year did Germany make its largest gain?About what percentage of traffic fatalities were causedby people who were distracted in some way?Which two causes are responsible for 72.3 percent oftraffic fatalities?What caused a little more than 500 of the fatalities?What was the 2nd most common cause of the trafficfatalities?What was the leading cause of traffic fatalities?Lane changes caused what percentage of the fatalities?English by the Numbers Unit 55. Bar GraphsPart 1Math Scores & SpendingBirth RatesIncome DistributionTax RatesDefense SpendingSample Language & Learning Pointsbar graphsThis graph compares the tax rates at various incomelevels. Students from Japan scored 65%. West Germanyspent almost 3% of its GNP for defense in 1979.ComparisonsIn the US, there is a higher ratio of spending for highereducation than for basic education. Britains tax rate forthe working poor is the highest, at more than 20%.Key Sentences and Examples:This first example compares math scores for fivecountries: Japan, France, the UK, the US, and Sweden.Each bar indicates the mean percent of items answeredcorrectly on a mathematics test of 8th grade students.Students from Japan scored 65%, which is the highest.French students didnt do as well as the Japanese, butthey scored over 50%, which was second best.Now lets compare the amount of money which is spenton education in each of these countries.In the US, for example, there is a higher ratio ofspending for higher education than for basic education.Even though Sweden and the U.S. spend the most oneducation, their test scores are the lowest.This graph compares how income is distributed amongthe richest and poorest segments of each country. Theincome ratio here means the top 20% of householdsdivided by the bottom 20%. In Brazil, for example, thetop 20% of households receive 66.6% of the nationsincome, compared to the bottom 20%, which receive just2.0%. This works out to an income ratio of 33. Thisgraph suggests that one factor in economic growth mightbe how income is distributed throughout a country.This graph compares the tax rates at various incomelevels in Japan, the U.S., and the U.K. for the year 1987.Britains tax rate for the working poor is the highest, atmore than 20%. The U.S. has the lowest tax rate for therich.This graph compares the defense spending of sixcountries. Japan spent about 1% of its GNP for defensein both 1979 and 1984. The U.S. spent just over 5% ofits GNP for defense in 1979. By 1984 it had increasedits defense spending to 6.4%.Part2This graph gives life expectancy information. Withoutexception, it shows that women live longer than men. Onthe far left, we see that the life expectancy throughout theworld is about 64 years. Men live about 62 years andwomen live about 66 years. In France and Brazil,women live considerably longer than men. In bothPart 2Life ExpectancyMedian AgesCigarette SmokingBlood Pressure & ObesityCO2 EmissionsSources of EnergyElectricity ProductionQuizThis Unit prepares students to participate in adecision-making situation where they have toexpress alternatives or give reasons for decidingon one course of action over another.In the Unit, the Sales Manager at FederalMotors, Sonia Scott, needs to decide whether tosend Bob or Ed to Australia to open a newbranch office.Goals:To be able to understand and express differentdegrees of certainty in linking ideas and events.To develop oral fluency and confidence toexpress more complex ideas.countries, the difference is more than 5 years. Theoverall life expectancy in Australia is the highest, at80 years.This graph gives the median age in several countries.The left bar shows that the median world age is 27.6years. France has the highest median age of thesecountries. That means you would expect to see feweryoung people in France. Their population is aging. Incontrast, Egypt and Malaysia have a median age ofless than 24. In these two countries, you wouldexpect to see many young people.This graph shows how cigarette smoking hasdeclined in a region of England. The bars on the leftgive the smoking data from 1978 and the bars on theright give the data in 1998. It shows that smoking hasdeclined rather dramatically. The percentage of ex-smokers increased from 35% to 55%, and thepercentage of heavy smokers dropp