Mathematics 7

# Web Quests

## PLANNING A TRIP

This Web Quest allows students to practise working with fractions, percents, decimals, rates, and ratios to solve problems in a real-life context. The Web Quest's focus on travelling and buying tickets will help students see the importance of proportional thinking in everyday life.

### GOALS

7m6 solve and explain multi-step problems involving simple fractions, decimals, and percents

7m7 explain, in writing, the process of problem solving using appropriate mathematical language

7m8 use a calculator to solve number questions that are beyond the proficiency expectations for operations using pencil and paper

7m12 explain numerical information in their own words and respond to numerical information in a variety of media

7m24 explain the process used and any conclusions reached in problem solving and investigations

7m27 solve problems that involve converting between fractions, decimals, and percents

paper and pencil

calculator

### FROM STUDENT PAGE

NOTES FOR TEACHER:

As a group, read the Introduction. Brainstorm about things you need to do to plan a trip.

Divide students into pairs. This Web Quest can also be done individually.

### INTRODUCTION

Going on a trip is a lot of fun, but it also takes a lot of planning. What are some of the things you need to decide before going on a trip?

NOTES FOR TEACHER:

Have students read through the Task section. Ensure that they are clear on what is expected of them. Stress that there are several parts to each question, so they will need to follow the steps carefully.

To provide extra support, allow students who have difficulty expressing their thoughts in writing to explain their steps orally to you in an interview format.

Your friend's parents are thinking of taking you and your friend on a trip to Orlando, Florida over the holidays. Before they make their final decision, they would like you and your friend to do some Internet research. They have given you this list of things to research:

• The distance to Orlando, Florida by car in kilometres
• The amount of time the drive will take
• Some of the attractions you could visit and how much they will cost.

1. Click on this link MapQuest: Driving Directions to find out the distance between where you live and Orlando, Florida. The Web site will also tell you how long the drive will take.
1. Enter your home address under Enter a starting address. If you are not sure about your exact address, enter your town or city and your province in the appropriate boxes. Then under Enter a destination address, enter "Orlando" in the City box and "FL" in the State/Prov. box. Then click the Get Directions button.
2. The MapQuest Web site gives you the total distance in miles. Using your knowledge of ratios, calculate the distance of the trip in kilometres. (Hint: There are 1.6 kilometres in a mile.)

NOTES FOR TEACHER:

You may want to give your students the abbreviation for their province. You may also want to ask students to use the address for your school, so they are all starting from the same point.

While students are working, observe and/or interview students to see how they are interpreting and carrying out the task.

If students are having trouble converting miles to kilometres, hint that they need to create two equivalent ratios. If they need more help, tell them they need to find a scale factor.

The distance from Markdale, Ontario to Orlando, Florida is 1352.21 miles and it would take 22 hours and 33 minutes.

I know that 1 kilometre is equal to1.6 miles. I can express this as a ratio 1:1.6.

I know the distance is 1352.21 miles. I want to know the distance in kilometres, so I wrote the second ratio as 1352.18:___ .

I wrote a proportion with a missing term for the distance in kilometres.

1:1.6 = 1352.18 : ___

The ratios must be equivalent. Since 1 x 1352.21 = 1352.21, the scale factor is 1352.21.

I multiplied 1.6 by 1352.21 to get the missing term, which is 2163.54.

The distance from Markdale, Ontario to Orlando, Florida must be 2163.54 km.

1. What is the average rate in kilometres per hour you would be driving? Show your work and explain your thinking. (Hint: The MapQuest Web site gives you the time your trip will take in hours and minutes. Before you make your calculations, convert the minutes into hours. Keep in mind there are 60 minutes in an hour. Express the number of hours as a decimal.)

I know the trip will take 22 hours and 33 minutes and there are 60 minutes in an hour. 60 minutes is 100% of an hour. To figure out what percent of an hour 33 minutes is, I wrote a proportion with a missing term for the percentage of an hour.

33/60 = ___ /100

To calculate the missing term, I divided 60 by 100 to get a scale factor of 1.6. Then I divided the number of minutes (33) by 1.6 to get the missing term, which is 55. I now know that 33 minutes is 55% of an hour and I can express this as a decimal: 0.55. So I know that the total amount of time the trip takes is 22.55 hours.

I wrote the distance in kilometres and the time in hours as a rate. To find the kilometres per hour, I wrote a proportion:

2163.54 km / 22.55 h =   ___ km / 1 h

The scale factor is 22.55 because 22.55 divided by 1 equals 22.55. So I divided 2163.54 by 22.55, which equals 95.9.

The average rate of the car would be 95.9 km/h.

1. Click on this link http://www.orlandoinfo.com/attractions to find out about some of the attractions you could visit in Orlando. Your friend's parents think they may be able to save some money if they buy tickets over the Internet. Choose 3 interesting attractions that offer discount tickets on the Web.

NOTES FOR TEACHER:

If students are having trouble finding attractions on the Web site, suggest that they click on the Discount Orlando Attraction Tickets button.

1. Round each of the regular ticket prices and the discount ticket prices to the nearest whole number.
2. Calculate the savings, expressed as percentages, for one adult discount ticket for each of the 3 attractions you chose.
3. List the attractions in order from the greatest discounted ticket to the least.

NOTES FOR TEACHER:

Sample question:

"Why would you convert the savings to percentages? "

It is easy to figure out what percent is higher or lower because all percents are out of 100.

a) The full-price adult ticket is \$19.95 and the discount ticket is \$15.95. I rounded the price of each type of ticket to whole numbers.

Full-price ticket: \$20

Discount ticket: \$16

b) To calculate the percent of savings for each ticket, I expressed the price of a discount ticket and the price of full-price ticket as a ratio.

16

20

To find the percent, I wrote a proportion that includes a ratio with 100 (since percent means out of 100) and a missing term.

16   =     __

20        100

I divided 20 by 100 to determine the scale factor of 0.2. I divided 16 by the scale factor to calculate the missing term, which is 80.

I now know that the discount ticket is 80% of the price of the full-price ticket. If I subtract 80 from 100, I get 20. So I save 20% buying the discount ticket.

To provide extra challenge to students, suggest the following:

•  Have students calculate the price of admission tickets in Canadian dollars. Have students answer the following question:

(You can use this link to an Online Conversion Web site to find out the current conversion rate.)

•  Have students calculate the percentage of savings on admission tickets without rounding the prices to whole numbers.

### ASSESSMENT

 LEVEL 1 LEVEL 2 LEVEL 3 LEVEL 4 Understanding of Concepts •  attempted solutions demonstrate limited understanding of concepts •  solutions demonstrate some evidence of understanding of concepts •  solutions demonstrate sufficient evidence of understanding of concepts •  detailed solutions demonstrate thorough understanding of concepts Application of Procedures •  use of procedures to determine rates of travel, distance in kilometres, and percentage of savings    include major errors and/or omissions •  use of procedures to determine rates of travel, distance in kilometres, and percentage of savings    include several errors and/or omissions •  use of procedures to determine rates of travel, distance in kilometres, and percentage of savings is mostly correct, but there may be a few minor errors and/or omissions •  use of procedures to determine rates of travel, distance in kilometres, and percentage of savings    includes almost no errors or omissions Communication •  few mathematical conventions, words, or symbols are used   •  provides incomplete or inaccurate explanations/ justifications that lack clarity and logical thought •  some mathematical conventions, words, or symbols are used correctly •  provides partial explanations/ justifications that are relatively clear and show some logical thought •  most mathematical conventions, words, and symbols are used correctly •  provides complete, clear, and logical explanations/ justifications •  a range of mathematical conventions, words, and symbols are used correctly •  provides thorough, clear, and insightful explanations/ justifications Problem Solving •  uses a strategy and attempts to solve the problems but does not arrive at   answers •  uses a strategy that is somewhat appropriate and develops partial and/or incorrect solutions •  uses appropriate and effective strategies and solves the problems •  shows   flexibility and insight when carrying out the plan by trying and adapting one or more strategies to solve the problems