Mathematics 7

# Web Quests

## PLANNING A TRIP

For this Web Quest, your child will be researching a trip to Orlando, Florida using the Internet. Your child will continue their work with ratios, rates, fractions, percent, and decimals in a real-life context. This Web Quest helps demonstrate the importance of proportional thinking in everyday life.

### GOALS

• solve multi-step problems involving fractions, decimals, percent, ratios, and rates
• explain the process of problem solving and any conclusions reached in their own words while using appropriate mathematical language

paper and pencil

calculator

### VOCABULARY

Your child should be familiar with the following vocabulary:

equivalent rates - rates that represent the same comparison (e.g., 90 km/ 2 h and 45 km/h)

equivalent ratios - two or more ratios that represent the same comparison (e.g., 1:4, 2:8, and 3:12 area all equivalent ratios)

proportion - a number sentence that shows two equivalent ratios (e.g., 1:4 = 2:8 or 1/4 = 2/8)

rate - a comparison of two quantities measured in different types of units; unlike ratios, rates include units

scale factor - a number that you can multiply or divide each term in a ratio by to get the equivalent terms in another ratio; can be a whole number or a decimal

term - the number that represents a quantity in a ratio

### FROM STUDENT PAGE

NOTES FOR PARENTS:

Ask your child to tell you a bit about what he or she has learned in Chapter 2. Review any new vocabulary.

Read the Introduction with your child. Discuss things you need to do to plan a trip.

### 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 PARENTS:

Read through the Task section together. Make sure your child understands what he or she has to do.

Encourage your child to do as many questions as he or she can without a calculator.

If your child has difficulty expressing his or her thoughts in writing, have him or her explain the steps orally to you.

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 PARENTS:

You may want to give your child the abbreviation for your province.

If your child is having trouble converting miles to kilometres, hint that he or she needs to create two equivalent ratios. If he or she needs more help, hint that he or she needs 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 352.21.

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 PARENTS:

If your child is having trouble finding attractions on the Web site, suggest that he or she 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 PARENTS:

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.

Tip: When you write a percent, think "per hundred".

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.