How To Set Up A Proportion Word Problem

Objective

The unit of measurement that I have written is based on developing and using word problems in the classroom to satisfy an important objective in the N Carolina curriculum. I teach 7th grade mathematics in an urban district, Charlotte Mecklenburg Schools. The commune itself is large and within the district in that location are 32 middle schools. The school where I teach, Carmel Heart School, has a culturally diverse population that is effectually sixty per centum white, twoscore percent minority: African-American, Asian, and Hispanic. In that location are a few obstacles that I would like to overcome with the students to make them successful.

There are three levels of math classes in my school district. Standard math is for students that are at or below grade level. Standard plus is for students that are on grade level. Honors is the 3rd level. Students in this grade are in a higher place grade level. Within the seventh grade, I teach a couple of different levels of students varying from ones that are below grade level to others that are well above form level. Likewise, within each form, there is an academically assorted grouping of students. This is the kickoff challenge or obstacle. The second challenge deals with reaching individuals in a culturally various grouping of students. Using several unlike types of give-and-take issues varying in difficulty and subject matter to successfully teach my students an important topic is my main goal for this unit of measurement.

In mathematics, it seems that the nearly difficult skill for students to grasp is solving word problems. This is noticeable in any age group. The students may exist able to perform basic math tasks such as multiplying or dividing, but if that same skill is surrounded by backlog words, it actually confuses most students. To solve my own math problem I will begin past introducing the students to word problems that are fairly simple to make the students feel successful and then they will be comfortable dealing with the more than difficult ones. In doing this, I hope it will build conviction in each of the students then they are not intimidated when looking at word problems. They will exist more confident when given the challenge of a difficult give-and-take problem.

One of the largest objectives in the 7th class math curriculum in the state of North Carolina is one that deals with ratios, rates and proportions. Within the state standards, at that place are several indicators that involve using proportions to solve a problem. Along with solving proportions, students also demand to be able to evaluate bug that bargain with scaling, similar figures, unit of measurement rates and percent proportions. Students tend to exist at ease solving a proportion that is already set up merely by using the method of cantankerous-multiplying. Information technology is more difficult to set it up on their own when reading a word trouble considering of the units. They tend to prepare them upwards incorrectly considering they choose the numbers in the order that they announced in the discussion problem and do not focus on the units that are attached to the numbers themselves. This occurs with the majority of the students that I teach, regardless of their bookish level. Setting upward proportions is a hard and sometimes confusing process that my unit volition exist able to address and help students to get more successful.

I have put together a large selection of problems based on the objective. I take taken the problems and split them into groups based on different topics inside the goal. From there, the problems are cleaved downwardly into different categories. The dissimilar groups or categories are word problems that include unit of measurement rates, like figures and scale drawings/models, along with percent proportions. All of the word problems that I have put together tin be solved by setting up proportions. Students demand an understanding of preparing a proportion because it is a skill that volition help them in school and throughout their lives. As adults, there are many dissimilar bug solved on a daily basis using proportions such equally reading maps, figuring out tips to leave at a restaurant and also determining a sale cost on an item. Students who are successful in setting upwardly proportions will be able to use that skill in many ways and situations.

I promise this unit will be beneficial to teachers at different levels. It is based on the standards for students in seventh form math, only information technology is not limited to only that form or subject. Proportions are used throughout middle school and high school. For example, in science, proportions are used in converting measurements, and in social studies, scales are used to read maps. The difficulty of the sample problems themselves, (run across Appendix A), can be modified to encounter the needs of other subject areas or grade levels.

Strategies

Inside the different groups of word problems based on using proportions to solve, there are several different types of situations or categories of bug. There are bug with unlike difficulty levels and varying subjects. Because the students that I teach have a wide diverseness of needs, information technology is important to focus on the main weakness that all of the students tend to have: difficulty setting upwards proportions to solve word problems. This unit focuses on helping the educatee to work through several types of problems and correctly put them into proportions. The problems will be used to help the students develop an agreement of the goal of setting upward proportions. The different subjects or situations in the discussion problems to make information technology possible to better relate to a diverse grouping of students. There are give-and-take problems that represent all different types of proportion issues.

The students will be taught exactly how a proportion trouble is set by using the units in the problem. Earlier that tin be done, there volition be a word well-nigh what the trouble itself means. For example, allow'southward say Joey went out of town to visit his grandma, which was a 120-mile journey. He traveled at the same speed for the whole trip. If information technology took him 2 hours to get there, what was his speed in miles per hour? There would need to be a give-and-take with the class about the problem itself. I would discuss with them what it ways. If information technology took Joey two hours to get there, and he is traveling at the same charge per unit, what kind of conclusions can nosotros draw from that? Well, we could talk about if nosotros figure out how far he goes in one hour, and so all nosotros would take to practise is multiply it by two to get what it would exist for two hours.

After having the discussion about what the bodily problem is asking, I will then lead the students to write a proportion. Writing a proportion allows a person to correctly solve a problem. The students will need to understand that the problem itself is discussing two different units; hours and miles. I would write that equally a ratio, miles/hours. The ratio would be fix in forepart of the actual proportion then that the students could see where to identify the miles and where to place the hours. The post-obit proportion would demand to exist gear up along with the ratio of units in the front:

miles/hours —> 120 miles/ 2 hrs = ten miles/ 1 hour

There would then exist a discussion nigh why information technology should exist set in that fashion. It is like an analogy; 120 miles is to 2 hours in the same way that x miles is to ane hr. For the equation to make sense, both sides have to take the aforementioned units. The same units have to be on the top of the ratios, which is miles in this instance, and the same units need to be on the bottom of the ratios, which is hours in this instance. Having the students focus on where the units get is the principal key. They should always label the numbers that they place in a proportion form so that they can cheque the units to be sure it is set up correctly. In this case it is miles on elevation and hours on the lesser. Some students may want to know while miles are on the top and hours are on the bottom. It is crucial for them to understand that it does not matter as long as the units are the same in the numerator and the units are the same in the denominator. That is, for the equation to make sense, both sides have to take the same units. I would show students that the answer would turn out the same if the units in the proportion above were flipped from numerator to denominator. Equally a course, nosotros would discuss the similarities of the two proportions. The two ratios that make upward a proportion are essentially unit rates, which I will become into more than clearly below.

Unit rates

Unit rates are the basis of all proportion problems. Get-go with this topic allows the students to not merely become an understanding of ratios and proportions, only they begin to see the importance of both units and unit rates. Students must have an understanding of unit rates for several reasons. First, they need to sympathise what a unit rate actually is. Information technology is, for example how many miles a vehicle travels in one hour or how much it costs for ane ounce of cereal, etc. The following set of issues will be used to introduce this topic. The proportions below each of the bug are the correct way to set them upward.

A. Traveling cantankerous-country, the Beeper family rode 510 miles in 8.5 hours. At this rate, how many miles did the Beepers drive per hour?

        miles/hours —> 510 miles/ 8.5 hrs = 10 miles/ 1hr

B. Traveling cantankerous-country, the Beeper family went an average of 60 miles per hour. If they traveled for eight.5 hours, how many total miles did they travel?

miles/hours —> 10 miles/ 8.v hrs = 60 miles/1 hr

C. Traveling cross-state, the Beeper family unit went 510 miles at a speed of 60 miles per hr. How many hours did information technology take them?

miles/hours —> 510 miles/ 10 hrs = 60 miles/1 hr

The previous issues are all discussing the same state of affairs. The just difference is in each problem a different variable needs to be solved for. Each of the problems are asking the students to await at the amount of miles driven, the corporeality of hours driven and the speed in miles per 60 minutes. Using these three different bug allows students to run into the same type of problem could be ready up several ways depending on the missing variable. The students will be able to run into that in each of the proportions miles are on the top of the two ratios and hours are on the bottom of the ratios. The right side of the proportion represents the unit rate because the Beeper family collection 60 miles in one hr. I specifically chose a word problem that deals with miles per 60 minutes for a reason. My students never seem to understand that finding out how many miles per hour a car travels is a unit rate. Unit rates are individual rates of items. For instance, if a problem states that a person is driving a sure altitude and it takes them a given corporeality of time to go to a destination, finding the miles per hr would be the unit of measurement charge per unit. I e'er need to stress with them that it is so many miles per 1 hour. The problems above are ones that I would exercise with my students. I would and so give them issues to work on either individually or in pairs to ensure they can practise information technology on their own. I would take these bug from the appendix. (See Appendix A, numbers i-xiii for boosted sample problems based on unit rates.)

The first category that I dealt with was separating proportion bug into 3 different groups: unit rates, similar figures/scale drawings, and percents. Above I described how I would innovate unit rates to my students. Within unit rates, I determined some other group. I constructed issues pertaining to the aforementioned topic, but with a different variable left out each time. This will requite the students a variety of different ways to see the problems and likewise ways to set them up given dissimilar information. Over again, ane of the more difficult topics for students is to set up proportions correctly from word problems. This gives them practice in doing it several different ways.

Percents

Some other category that I will innovate focuses on percents. Proportions that are set with percents slightly differ from unit rates. Percents are used in students' lives every day. They come across percents on their tests or study cards in the form of a grade. They go shopping and see discounts in stores that are a certain percentage off of the original toll. The students volition work with word problems that involve percents to fix proportions. Percent proportions are ever ready the same way; with one of the ratios being a percent over 100. This is something that I stress to my students. The other ratio in the proportion needs to exist fix in a sure way. The students need to await at it two different ways, depending on the type of problem they are working on as either is/of or office/whole. For example: At that place were eight equal pieces of pizza and Bobby ate two. What per centum of the pizza did Bobby consume? Equally a class we would discuss the contents of the trouble and figure out its pregnant. If he ate ii pieces out of the total eight pieces, that would be ane-fourth of the pizza. If we idea of ane-fourth as a pct the reply would then be 25%. Subsequently understanding the problem, we would every bit a class come upwards with a way to fix upwards a proportion. Kickoff, we need to identify what information technology is that is known in the problem. I run into that Bobby ate 2 pieces out of the total 8 pieces of pizza. In this example information technology needs to exist set up as a ratio in the form, role/whole. Focusing on the pizza every bit a whole broken into parts, I would set upwardly the following proportion:

3 pieces (function) / 8 pieces (whole) = x % / 100

The proportion in a higher place is set upwards in then that the pct is the unknown. In the problem itself, it specifically asks what percent of pizza Bobby ate. Using the previous problem as a standard for solving other percent bug, the following examples would exist given to the class.

D. At that place are 206 bones in the human body. There are 33 basic in the spinal column. To the nearest whole percent, what percent of your bones are in your spine?

33 bones (part) / 206 bones (whole) = x % / 100

Due east. In that location are 206 bones in the human torso. About 16% of them are in the spinal column. Virtually how many bones are in the spinal column?

x bones (part) / 206 bones (whole) = 16% / 100

F. Near sixteen% of the full number of bones in your body are in you spinal column. If in that location are about 33 bones in the spinal cavalcade, nearly how many total basic are in the human body?

33 bones (role) / ten bones (whole) = sixteen% / 100

The problems above are proportions that are fix up with percents. All of the problems are similar in bailiwick matter; they simply differ with the variable that is missing. (To see more examples, encounter Appendix A, numbers 14 - 18.) Within this dimension of pct proportions, I accept further cleaved the bug downward. Above, I began by working with ones that were fairly simple, ane-step problems that just had a different variable that was missing in each one. I will also vary the bug by making the bug a little more difficult by using gratuitous percents and multi-stride problems. Complimentary percents are a different blazon of pct problem. The question in the discussion problem is formed in such a style that it takes more than solving the proportion to complete the problem. There may be more steps included. For example, Amy went shopping and institute a shirt that was on sale for 50% off. How much would the shirt exist after the discount if the original cost was $26? In this problem, the pupil is not just looking for the answer to the proportion; they need to accept information technology to a higher level. If the students have the respond to the proportion, that would only tell me what the discount would be. In order to get the correct answer, the educatee would have to accept the answer from solving the percentage and subtract it from the original cost. That would and so give the discounted price of the shirt. The following are examples of complimentary percents and/or multi-footstep percent problems.

G. Bob has a coupon for 15% off the price of any particular in a sporting goods store. He wants to buy a pair of sneakers that are priced at $36.99. About how much will the sneakers cost after the discount?

ten / $ 36.99 = 15% / 100 —> x = $5.55 —> $36.99 - $five.55 = $31.44

H. Lisa went to an electronics store that was going out of business. The sign on the door read "All items on sale for sixty% off of the ticketed cost." A figurer has a toll of $649, and a printer has a price of $199 and she needed both items. What was the total cost of the items after the disbelieve?

$199 + $649 = $848 —> x / $ 848 = 60% / 100 —> $848 - $508.fourscore = $339.20

I. Betwixt 1924 and 1998, the United States won a total of 161 medals in the Winter Olympic Games. If the Usa won 59 silver and 42 bronze medals, about what percent of its medals were golden medals?

59 + 42 = 101 —> 161 - 101 = lx —> 60 aureate / 161 full = x% / 100 —> x ≈ 37%

Similar Figures and Scale Models/Drawings

The tertiary chief category that my problems are cleaved into is based around similar figures and scale drawings/models. This group works with setting upwardly proportions in the style that the students learned with unit rates. It is important for students to understand the reasoning for keeping the same variables in the numerators, for example miles, besides as the same variables in the denominators, for instance hours. The students will need to be certain to set a ratio in the start labeling what goes on top and what goes on the lesser. They will also need to label all units on every number that they write into the proportions.

Similar figures and calibration drawings/models are used in math and other subjects very regularly. In social studies, for example, students are given maps of different countries and cities around the earth. The students demand to exist able to read the maps in lodge to sympathize them. Proportions give students an agreement of what a calibration actually is. Scales are based on a calibration factor. A shape may be stretched in every direction by a certain number or calibration factor, which then makes the shape similar to the original. If I am trying to figure out how long information technology will take me to become somewhere, I use the scale to estimate the amount of time.

Similar figures are used regularly also. Whether it is enlarging or shrinking a picture or drawing bluish prints for a new house, proportions are essential to figuring out the ratios. Like figures are related by a scale change. If you know a length in one figure and the corresponding length in the other, their ratio is the scale figure. This cistron and so tells y'all the ratio of any pair of respective lengths in the two figures. The equality of the ratios of pairs of corresponding lengths gives a proportion.

The commencement step in solving the problems is to first depict a sketch. When dealing with similar figures or scale drawings/models, the problem for students is usually introducing two different figures. In order for students to see the correct mode to ready a proportion, they need to exist able to identify the corresponding sides. Corresponding sides of ii shapes are ones that directly relate to each other. For example, if there are two similar triangles given, such equally the ones below, identifying the sides that correspond to each other is key. The students would take to identify that the side that is marked 4cm on the first triangle corresponds to the side that is marked 6cm on the larger triangle.

Looking at the 2 similar triangles there are a few observations that the students need to make and sympathise. First of all, the two triangles are the same shape but different sizes. That is what actually defines like figures. Secondly, each side in the pocket-sized triangle has a corresponding side in the larger triangle. With that information, a proportion can be fix up. The ratio of whatever corresponding sides gives the scale factor. Therefore, the ratios between two pairs of corresponding sides are equal- they course a proportion. The base of operations of the small triangle corresponds to the base of the big triangle and the height of the minor triangle corresponds to the tiptop of the large triangle. Therefore, the following proportion could be gear up up:

4 cm / 6 cm = 3 cm / x

Once the proportion itself is set upward, the students should have no problem solving it. Inside this category, I take broken the problems into several groups. There will be problems that deal with switching around the same variable in a given situation. For case if problem J beneath, you could be given the elevation of the Eiffel belfry and not the height of the person. One time a student has an understanding of setting upward proportions, it will be easier for them to switch variables around depending on what is given in the trouble. Also, there will exist problems that will be fabricated more than difficult through the use of fractions and decimals. In each of the problems the students volition be expected to depict a motion picture in order to visually see the sides that correspond with each other. The proportion will then be prepare based on the similar figures. The following are examples of either similar figure or scale drawing/model problems.

J. On a sunny day, the Eiffel Tower casts a shadow that is 328 feet long. A 6-human foot-tall person standing next to the tower casts a 2-foot-long shadow. How tall is the Eiffel Tower?

The following proportion would exist prepare up to solve the missing pinnacle of the Eiffel Tower:

328 ft / 2 feet = 10 ft / vi ft —> x = 984

K. Rachelle's school photo package includes 1 big photo and several smaller photos. The large photo is similar to the small photo. The minor photo is two inches long and 1.5 inches broad. If the height of the large photograph is x inches, what is the width?

The post-obit proportion would be gear up to solve the problem:

ten in / ii in = 10 in / 1.v in —> x = 7.v

The two problems above show the exact process of how students would solve this type of problem. They would first have to sketch a drawing of the problem itself and label the lengths that they know. From there, the proportion could be set upwardly. (Encounter Appendix A, numbers 19 - 25 for additional bug.)

Solving proportions is a broad topic. With this unit, I have been able to analyze the types of issues and separate them into dissimilar groups in order to categorize them. The unit itself will permit students to have a much clearer picture show of how to set proportions from word problems. Having the students focus on all of the different dimensions will enable them to successfully solve proportion discussion problems.

Classroom Activities

Earlier I begin the lessons with the students, there are a few prerequisites that I would be sure to comprehend to be confident that my students understand the topics. Defining a proportion as two ratios set equal to each other would be the first thought that I go over with them. Also, I would be certain that my students know how to cross multiply to solve a proportion. Some of this would have been covered earlier in the yr or the previous twelvemonth for most of my students. I would spend some time reviewing and making certain that they felt comfortable with the topics.

Prior to the first lesson, the students will be introduced to what a unit charge per unit is. They volition be able to correctly set them up and solve them focusing on the units that are attached with the numbers as I take explained in my strategies above.

Lesson 1

Objective

Students will be able to prepare and solve proportions. They will also be able to solve word problems based on unit rates.

Warm-upward

"Your mom needs to get to the grocery store and she asks yous to go shopping with her. When you go to the store, you lot really want cereal merely you lot are having trouble figuring out what kind to get, you cannot decide between the Fruity O'south and the Circles of Fruit. Your mom told you that you lot demand to get the cheapest cereal per ounce. The problem is the boxes are 12 and 16 ounces. Draw, without using numbers, how y'all would figure out what cereal was cheaper per ounce."

Procedure

To be sure students had a strong understanding of unit of measurement rates; I would do an action with them based on the warm-upwardly. There would be viii to x stations set up upward with different products found in a grocery store such as paper towels, cereal, canned soups, toilet paper, etc.

Each station would accept ii similar products such as a 12 ounce box of proper name brand cereal and a twenty ounce box of generic brand cereal. I would give the students the cost of each of the boxes of cereal. The students would and so work in groups to come across which ane was the better buy. They would essentially have to find the unit rate of each of the unlike products and and so compare the two. The students would rotate effectually to each of the stations comparison all of the items and identifying unit of measurement rates. Once completed, we would have a class discussion nearly the importance of the activeness. The post-obit questions could be asked:

How tin this be used in somebody's every day life?

Can you explain in your own words the importance of finding unit rates?

Does this activeness change the manner that yous retrieve about grocery shopping? If and then, in what ways has it changed the way you think? (There would be a word on different methods of finding unit rates by not setting up proportions.)

When the class discussion is completed the students would work with a partner on an in-class project. The students would demand to accept the information they accept from the previous activity and begin amalgam discussion problems. The students will have to prepare them in different means using the data that they collected and a scenario to go along with information technology. Each pair of students would create five discussion problems on their own.

Assessment

For homework that night, the students would have to take their word problems dwelling house and teach their parents how to solve them. They will need to take them through the steps of how to fix and solve each proportion. The parent would so demand to write a note stating that their child taught them how to solve bug involving unit rates. This will start up a skilful discussion with students and their parents because more likely, their parents figure out the "better purchase" or unit of measurement rate regularly.

Lesson ii

Prior to Lesson 2, the students would become through the strategies with me for setting up and solving percent proportions as listed in the strategies portion of my unit. We would use the issues in the text itself and too apply sample problems from the Appendix. By the fourth dimension the lesson is taught, the students would empathise how to correctly set a percent proportion to solve.

Objective

Students will be able to solve word problems by setting upwardly and solving pct proportions.

Warm-up

"Describe where and how percents are used in our lives everyday. Exist certain to include at least three examples, and then explicate the importance of them."

Procedure

There would be a give-and-take of the warm-upwards focusing on where percents are used in our daily lives. I would exist certain to focus on topics such as discounts when shopping, leaving a tip at a eating house and revenue enhancement on purchases.

The students would be given menus from an surface area restaurant. I find it easier to laminate them so that they will final longer than simply newspaper menus. The students and so are put into groups at different 'tables' as if they are coming to the restaurant for dinner. There will exist i server for each table of guests. The students will lodge meals, including a drink and dessert. They will then take to figure out the price of their own meal with a given revenue enhancement and tip percent. I will change the tax rate and tip amount each time. The server will and then be the i that figures out the price for everyone at the table. The guests and server will share and discuss their answers.

The students volition then take to accept the menus and brand 3 word problems based on the menu. Each individual student will write these based on the prices but using percents such as; how much is a certain entrée with a coupon for fifteen% off? There would be a discussion about as a customer, the tip is based on the original cost, non the discounted price.

Assessment

The students would then merchandise with each other and respond the problems. They would then give the answered issues back to the person who synthetic the problem. At this betoken, the students would cheque their peers work and discuss with them issues in ways that they were solved.

Lesson iii

Objective

Students volition be able to construct and solve word problems containing proportions. They will besides be able to solve problems that are made by their peers into the course of board games.

Warm-upwards

"Describe the correct procedure of how to prepare a proportion and solve information technology using the following trouble: Joey needed to get to the store. He looked on the map and saw that it was 5 inches from his hotel. The scale was ii inches: 0.75 miles. How many miles did he walk to get to the store?"

Process

At that place would be a discussion nigh the warm-up. Students would share their responses and give an explanation as to how it works.

A project would be introduced to the students as a cumulative project based on proportions. The students would be put in groups of two to three students. In their groups they would accept to make a board game. The game has to satisfy certain criteria. Each game has to have at to the lowest degree 20 word bug (either taken from books or made up on their own), with at least six of the types: percents, similar figures and scaling and unit rates. There also needs to be an answer key so that when other students play the game, they tin bank check their work and answers. The students are expected to be artistic on the type of game they produce. Information technology can comprise any type of subject area or topic, just as long equally there are the given amounts of give-and-take issues that can exist solved by setting up a proportion.

Assessment

After completing the game board, the students would be graded on their project both individually and on the terminal product equally a group grade. Nosotros would and so spend some time assuasive the students to play each other's games. Every game that the students play, they will fill up out an evaluation canvas on the game they played. Those evaluations will too get averaged into the terminal grade.

Appendix A

1a. For a read-a-thon, a 7th grade course read 243 books in 4.5 weeks. If they read the aforementioned number of books every calendar week, how many books were read per week?

243 books / 4.5 weeks = x books / ane week

1b. For a read-a-thon, a seventh grade class read 243 books full. If they averaged 54 books per week, how many weeks did it take them to read all of them?

243 books / x weeks = 54 books / ane week

1c. For a read-a-thon, a seventh class grade read books. They read 54 books per calendar week and they did it for 4.v weeks. How many books did they read full?

243 books / 4.5 weeks = x books / ane week

2a. David read 45 pages of a book in l minutes. How many pages should he be able to read in 80 minutes?

45 pages / 50 min = x pages / 80 min

2b. David reads 45 pages of a book. If he tin read 72 pages in lxxx minutes, how long did information technology take him to read the 45 pages of the book?

45 pages / x min = 72 pages / lxxx min

2c. David reads a book for 50 minutes. If he can read 72 pages in 80 minutes, how many pages will he read in the fifty minutes?

x pages / l min = 72 pages / lxxx min

3. Jim constitute out that later on working for 9 months he had earned vi days of vacation time. How many days will he take earned after working for two years?

9 months / 6 days = 24 months / x days —> x = 16

4. Mary baked a batch of 3 dozen cookies for 40 women at the women'due south club. Next calendar month the women's club is expecting sixty women to attend the monthly meeting, how many cookies should Mary bake?

iii dozen / 40 women = x dozen / 60 women —> ten = 45

5. Last week, Amy worked seven hours each day Monday through Th, and eight hours on Saturday. She earned a total of $333. If her hourly rate was constant find the corporeality of money that Amy earned for each hour of work?

36 hrs / $333 = 1hr / ten dollars —> x= $9.25

half dozen. Store-A-Lot Market is advertisement 3 pounds of bananas for $2.37. Food Farm is advertizement 2 pounds of bananas for $i.70. Which supermarket is advertising the lower price per pound for bananas?

iii lbs / $ 2.37 = 1 lb / x dollars and 2 lbs / $ 1.lxx = 1 lb / 10 dollars —> Food Farm is cheaper.

vii. Mr. Scrub offers three means to pay for carwashes: a book of six car wash coupons for $33.00, a special offer of 2 washes for $11.50, or one was for $5.95. Which pick offers the least expensive unit toll for ane motorcar wash?

6 coupons / $ 33.00 = i coupon / 10 dollars and 2 coupons / $ eleven.50 = i coupon / x dollars and 1 coupon / $ 5.95 = ane coupon / x dollars —>6 coupons

8. For a read-a-thon, a fifth class form read 243 books in four.v weeks. At this rate, how many books were read per calendar week?

243 books / 4.5 weeks = 10 books / 1 week —> 10 = 54

9. It is 600 miles from San Diego to Napa Valley. Duane drove up to Napa on Tuesday. He averaged fifty mph. What was his travel fourth dimension?

threescore miles / x hours = l miles / i hour —> x = 12

ten. Jim plant out that after working for 9 months he had earned 6 days of vacation time. How many days will he have earned after working for two years?

9 months / 6 days = 24 months / x days —> x = 16

xi. If iv grapefruits sell for 79 cents, how much will 6 grapefruits cost?

4 grapefruits / $ 0.79 = 6 grapefruits / x dollars —> x = i.nineteen

12. Kelly takes inventory of her closet and discovers that she has 8 shirts for every 5 pairs of jeans. If she has 40 shirts, how many pairs of jeans does she accept?

8 shirts / 5 jeans = forty shirts / x jeans —> x = 25

xiii. David read twoscore pages of a volume in 50 minutes. How many pages should he be able to read in 80 minutes?

40 pages / fifty min = 10 pages / lxxx min —> x = 64

14. Mr. Green has a garden. Of the 40 seeds he planted, 35% were vegetable seeds. How many vegetable seeds were planted?

x / 40 = 35% / 100 —> ten = 14

xv. Shelley ordered a painting. She paid thirty% of the full price when she ordered it, and she will pay the remaining amount when information technology is delivered. If she has paid $fifteen, how much more than does she owe?

xv / x = 30% / 100 —> x = 50 —> 50 - fifteen = 35

16. Glucose is a type of sugar. A glucose molecule is composed of 24 atoms. Hydrogen atoms make up 50% of the atoms in the molecule, carbon atoms brand upward 25% of the molecule, and oxygen atoms make up the other 25 %. How many atoms of hydrogen are in a molecule of glucose?

x / 24 = 50% / 100 —> x = 12

17. Kylie usually makes 85% of her shots in basketball game. If she shoots xx shots, how many will she likely make?

x / 20 = 85% / 100 —> ten = 17

eighteen. In a high schoolhouse survey, it was plant that 240 of 600 students walk to schoolhouse. What per centum of the students walk to school?

240 / 600 = x % / 100 —> ten = 40

xix. A statue casts a shadow that is 360m long. At the same time, a person who is 2 m alpine casts a shadow that is 6 m long. How tall is the statue?

x / 360 m = 2 m / half dozen m —> x = 120

20. Paul swims in a pool that is similar to an Olympic-sized pool. Paul's pool is 30m long by 8 one thousand wide. The length of an Olympic-sized pool is fifty g. To the nearest meter, what is the width of an Olympic-sized pool?

8 one thousand (width) / 30 thou (length) = x m (width) / 50 1000 (length) —> x = thirteen.iii

21. A blueprint for a house states that ii.v inches equals ten feet. If the length of a wall is 12 feet, how long is the wall in the blueprint?

two.5 in / x ft = x in / 12 ft —> x = 3

22. A collector'due south model truck is scaled so that 1 inch on the model equals 6 ¼ feet on the actual truck. If the model is ii.3 inch high, how high is the bodily truck?

one in / half-dozen.25 ft = ii.iii in / x ft —> x = 14.38 ft

23. Truss bridges use triangles in their support beams. Mark plans to make a model of a truss bridge in the scale 1 inch=12 feet. If the height of the triangles on the bodily bridge is 40 anxiety, what volition the height be on the model?

ane in / 12 ft = x in / 40 ft —> ten = 3.33

24. On a map, every ii inches represents an actual distance of 100 miles. Find the actual distance between two towns if the map distance is 5 inches.

ii in / 100 mi = v in / 10 mi —> ten = 250

25. Tater and Abby are trying to determine the distance between two detail cities by using a map. The map key indicates that four.v cm is equivalent to 75 km. If the cities are 12.vii cm apart on the map, what is the actual altitude between the cities?

4.5 cm / 75 km = 12.7 cm / x km —> x = 212

Annotated Bibliography

Abramson, Marcie (2001). Painless Math Word Issues. Hauppauge, NY: Barron's Educational Series, Inc.

The book shows several techniques for solving give-and-take problems. Also gives helpful websites in back of book.

Aharoni, Ron (2007). Arithmetic for Parents. El Cerrito, CA: Sumizdat.

This book discusses ways that parents can work with their child to solve dissimilar types of math problems.

Bennett, J, Chard, David, Jackson, A, & Milgram, J (2004). Math Class 1. Austin: Holt, Rinehart and Winston.

This is a text book for sixth course math students in the state of North Carolina.

Bluman, Allan G. (2005). Math Discussion Problems Demystified. New York, NY: McGraw Hill.

This book shows students and teachers alike how to break downwards word issues to arrive easier for them to solve.

Burns, Marilyn (1998). Math: Facing an American Phobia. U.S.: Math Solutions Publications.

This volume discusses ways of dealing with the math in a manner that addresses it equally a 'phobia'.

Holliday, M., Cuevas, D., Moore-Harris, M., & Carter, M. (2004). Algebra 1. Columbus, OH: Glencoe/McGraw-Hill.

Algebra i text book for the state of Due north Carolina.

Salvadori, Mario (1998). Math Games for Center School. Chicago, IL: Chicago Rev. Printing.

This book gives many unlike types of games for middle school students.

Steddin, Maureen (2000). Get Wise! Mastering Math Word Bug. Canada: Peterson'south Thompson.

This book gives ways that students can 'master' word problems. It is written on a student level.

Sterling, Mary Jane (2001). Algebra for Dummies. New York, NY: Hungry Minds.

This is a volume just like the other in the series to break down means to successfully learn Algebra.

Source: https://teachers.yale.edu/curriculum/viewer/initiative_07.06.08_u

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