Chapter 3. Mathematics

Academic Vocabulary: Academic Words - Olsen Amy E. 2012

Chapter 3. Mathematics

Work It Out

Complete the questions on this introductory worksheet by the next class meeting. These topics will be the focus of the class for the first half of the semester. Bring any concerns you have about these exercises to the next class meeting, or stop by during my office hours.

1. The company's monthly quota is 800 units. Use the following graph to answer the questions about the company.

A. How many months has the company met its allowance?

B. Use statistics to show how far the company was below its quota for March.

C. Which month was the company 50% below its quota?

2. Use the following prices to figure out the mean, median, and mode for a pair of pants at a local department store.

A. Mean, or average (add up all the numbers and divide by the number of items)

B. Median (or middle number)

C. Mode (the number that appears the most often)

3. Calculate what the variable x and the variable y stand for in the following equations.

A. 3 + x + 6 = 14 x = ...

B. 4y + 11 = 27 У= ...

C. 2x-6 = 60 x = ...

4. Use the lines to the right to answer the following questions.

A. Next to each line, indicate whether the line is horizontal, vertical, or diagonal.

B. Use the variable A to indicate where two lines intersect and the variable B to show where three lines cross.

C. Label the parallel lines C.

5. Which of the following shapes is symmetrical?

Does the balanced shape cause a different reaction in you than the other shape? If it does, why do you think that might be so?

Predicting

For each set, write the definition on the line next to the word to which it belongs. If you are unsure, return to the reading on page 20, and underline any context clues you find. After you've made your predictions, check your answers against the Word List on page 25. Place a checkmark in the box next to each word whose definition you missed. These are the words you'll want to study closely.

Set One

numerical facts

the middle number in a specified sequence of numbers

the average

to figure

a part of a total amount or an allowance

□ 1. quota (line 4)

□ 2. statistics (line 7)

□ 3. mean (line 10)

□ 4. median (line 10)

□ 5. calculate (line 16)

Set Two

balanced

lines that go in the same direction and never meet

to cross

parallel to level ground

a symbol that represents a changeable amount

□ 6. variable (line 16)

□ 7. horizontal (line 21)

□ 8. intersect (line 23)

□ 9. parallel (line 25)

□ 10. symmetrical (line 26)

Self-Tests

1 Put a T for true or F for false next to each sentence.

1. If a person decides to take a statistics class, it would help to be good at math.

2. It is a good idea to calculate how much your purchases will be before you check out to make sure you have enough money.

3. The mean for the three ages 11, 19, and 33 is 21.

4. Having a small triangle on one side of a picture and five large circles on the other side would be a symmetrical arrangement.

5. The weather in the United States is rarely variable.

6. Elevators usually travel horizontally.

7. The parallels between pyramid designs in Egypt and Central America have caused some people to speculate that the pyramids were built by aliens.

8. When a vertical and a horizontal line cross, they intersect.

9. It could be difficult to fill one's quota of strawberries to be picked if the person stops to eat several every five minutes.

10. The median number in the following series is 9: 2, 4, 9, 12, 15, 23, 35.

2 Complete each sentence using the vocabulary words. Use each word once.

Vocabulary list

calculate

horizontal

intersect

quota

symmetrical

mean

median

parallel

statistics

variable

1. The most recent ... show that enrollment is up 20% in all math classes this semester compared with the last two semesters.

2. Our study showed that people were more attracted to the display with the ... design than to the one with the irregular pattern.

3. From my past experiences of driving north, I ... that it will take us nine hours to reach Grandma's house.

4. When I worked in retail, my hours were ... . I started anywhere between 7 a.m. and 6 p.m., and I worked from four to eight hours a day.

5. The new road has been designed to ... the town, so tourists have to come right through downtown, and we hope that will cause them to stop and do some shopping or spend the night.

6. As soon as I got my ... of dona­tions for the auction, I quit asking. Even though it is for a worthy cause, I am not really comfortable ask­ing businesses to contribute items.

7. The ... house price in our city has dropped 30% in the last year.

8. I was offered a(n) ... transfer at work. I would have stayed at the same level but would have been in a different department. Because I like the people I work with now, I turned it down.

9. The ... structures, so perfectly spaced in the park, make for an ideal passageway.

10. I calculated the ... for my math test scores by dividing the sum of my scores by the number four (that is how many tests we have had), and I am averaging 87%.

3 Complete the following analogies. See Completing Analogies on page 4 for instructions and practice.

Vocabulary list

parallel

horizontal

intersect

median

symmetrical

mean

quota

calculate

statistics

variable

1. long : short:: vertical: ...

2. skyscrapers : tall :: interest rates : ...

3. old: elderly :: compute : ...

4. boring : exciting :: unbalanced : ...

5. 10, 15, 20, 24, 43, 56 = 22 : ... :: poodle : dog

6. portion : ... :: silence : hush

7. hem : a skirt:: ... : a circle

8. railroad tracks : ... :: fog : weather

9. house : home :: average : ...

10. government: ... :: cook : stove

Collocations

The pilot took a calculated risk and landed the plane in an onion field minutes before running out of fuel. (Chapter 3)

The median income for a job as a teacher in my state is $35,000 a year. (Chapter 3)

I am enjoying the story line about the parallel universe more than the one about life on Earth in the recent Tremendous Team comic book series. (Chapter 3)

Word Pairs

Symmetrical/Asymmetrical: Symmetrical (Chapter 3) means "balanced." Asymmetrical means "unbalanced; irregular." The symmetrical building attracted people to its graceful design. The asymmetrical building shocked people and displeased several of them.

Connotations and Denotations

Quota (Chapter 3): denotation—"the number or percentage of people of a specified type allowed into a group." In recent years, quota systems have upset people, and quota has taken on a negative connotation for many people. How do you feel when you hear that a college or other organization must fulfill a quota for admitting people?

Interactive Exercise

Answer the following questions to practice using the vocabulary words.

Imagine you eat lunch out Monday through Friday for a week. On Monday, you have a tuna sandwich that costs $6.60; on Tuesday, teriyaki chicken for $6.00; on Wednesday, curry for $5.20; on Thursday, a burrito for $4.80; and on Friday, a slice of pizza for $2.40. Use this information to answer the following questions.

1. Calculate the median price of your five meals.

2. Calculate the mean price of your five meals.

3. Supply the answers for these statistics:

A. One day you spend 50% less than on the previous day. Which day was that? ...

B. One day you spent 10% more than on the following day. ^thich day was that? ...

4. If your quota for meals out a month is 18, and, so far this month, you have eaten out four other times besides the five times this week, what percentage of your quota have you used up? ...

5. Calculate what the variable x stands for in these equations:

A. Monday's meal + Friday's meal + x = $15.00

x = ... (which day's meal)

B. A burrito + curry — x = $ 7.60

x = ... (which food item)

Answer the following questions about the sketch of the house.

6. How many horizontal lines are in the frame of the house? ...

7. How many sets of parallel lines are in the frame of the house? ...

8. What are two symmetrical elements of the house? ...

9. What area of the front yard does the entrance pathway intersect? ...

Multiple Meanings

Most words have more than one meaning. For some words, one meaning is used more often than the others. but for other words, two or three of their meanings are equally used. For example, a bat is "a wooden club used to hit a ball" or "a mammal that flies. usually at night." Both mean­ings for bat are frequently used. However. among the meanings for cure as a noun, most people would know "a means of healing" and possibly "a process of preserving meat, fish, etc. by smok­ing, salting, or the like," but the meaning of "the office or district of a curate or parish priest" is not seen as often. This book usually gives alternate meanings as long as they are fairly common. One meaning will be used in the reading for the chapter, but the Self-Tests that follow the reading may use the additional meanings, so carefully look over the Word List before you start the Self-Tests. If you ever see a word used in a way you are not familiar with, check a dictionary to see if it has an­other meaning you do not know. You may be surprised at how many meanings even a short and seemingly simple word may have. Webster's Collegiate Dictionary lists twenty-four meanings for the word so. Be prepared for the fun and challenges that multiple meanings provide.

Words to Watch

Which words would you like to practice with a bit more? Pick 3-5 words to study, and list them below. Write the word and its definition, and compose your own sentence using the word correctly. This extra practice could be the final touch to learning a word.

Word

Definition

Your Sentence

1.



2.



3.



4.



5.