Mathematics 7

Web Quests

NEIGHOURHOOD IN BLOOM PROJECT

TASK CONTEXT

In this chapter, your child has been learning about number relationships, such as multiples, factors, divisibility, powers, and square roots. In this Web Quest, your child will focus on working with multiples and factors to solve problems. Using information gathered on an on-line garden catalogue, your child will choose an appropriate number of flower bulbs to plant in a designated green space. He or she will then use factors to figure out how to plant the bulbs to create a pattern.

GOALS

• Generate multiples and factors of numbers
• Compare, order, and describe multiples and factors
• Explain the strategies used to reach solutions to problems

MATERIALS

paper and pencil (for recording calculations and explaining strategies)

calculator (optional)

counters, beads, or pennies (optional)

VOCABULARY

Your child should be familiar with the following vocabulary:

multiple - The product of a whole number when multiplied by any other whole number (e.g., when you multiply 10 by the whole numbers 0 to 4, you get the multiples 0, 10, 20, 30, 40)

common multiple - A number that is a multiple of two or more given numbers (e.g., 12, 24, and 36 are common multiples of 4 and 6)

least common multiple (LCM) - The least whole number that has two or more given numbers as factors (e.g., 12 is the least common multiple of 4 and 6)

factor - One of the numbers you multiply by in a multiplication operation

common factor - A number that divides into two more other numbers with no remainders

greatest common factor (GCF) - The greatest whole number that divides into two or more other whole numbers with no remainder (e.g., 4 is the greatest common factor of 8 and 12)

FROM STUDENT PAGE

NOTES FOR PARENTS:

Before beginning, have your child tell you about some of the concepts that were covered in Chapter 1 and review the vocabulary listed above.

Read the Introduction with your child. Discuss the advantages of having more green space in your community. For example, green spaces make areas more beautiful, decrease air pollution, and provide habitat and food for birds and insects.

INTRODUCTION

A volunteer group has planned a Neighbourhood in Bloom project to create more green space in your neighbourhood. Teams of volunteers will be planting flower bulbs in unused areas. Your class has volunteered to help out.

NOTES FOR PARENTS:

Together, read through the Task section. Ensure that your child is clear on what is expected of him or her. Your child must choose only plants that are appropriate for your growing zone. Explain to your child that not all plants are hardy (strong) enough to grow in all zones of Canada. The map on the Web site that you will be using will tell you what growing zone you live in.

TASK

You are put in charge of choosing the flowers for an area of green space. Once you have chosen which type of flowers to plant, decide how many packages of each type of bulb you will need to buy. Then figure out how to plant the bulbs to create a pattern.

PART A
1. Choose the types of flowers you would like to plant.
• You must choose 2 different types of flowers.
• Each type of flower you choose must come in packages that have a different number of bulbs than the packages of the other type of flower you choose.

NOTES FOR PARENTS:

To give your child extra support, suggest that he or she choose bulbs that come in packages of 5 and 15. Finding common multiples of these numbers will be easier.

Not all flowers can grow in every part of Canada, so before choosing, find out which growing zone you live in. Click on this link for McConnell Nurseries to begin. Once you are at the Web site, click the zone map link and then select your province from the drop-down list to find out which growing zone you live in.

To choose flowers, click the shop online link and then click the Bulbs link. When you find a flower that you want to plant, click the INFO link below the picture of the flower to find out how many bulbs come in each package. Pay attention to the coldest zone listed for the types of flowers you choose and make sure you do not live in a colder zone.

1. When buying the flower bulbs, you must keep in mind the volunteer group's requirements:
• The volunteer group thinks you will need about 100 bulbs of one type of flower and about 100 bulbs of another type of flower.
• You must have an equal number of each type of flower.

How many packages of bulbs do you need to buy so that you have an equal number of each type of flower and you do not buy any extra bulbs?

Use your knowledge of multiples to answer the question. Keep in mind how many bulbs come in the packages for each type of flower.

NOTES FOR PARENTS:

Discuss with your child what strategy he or she plans to use to solve the problems.

While your child is working, you may want to ask him or her some of the following questions:

"What is a multiple?"

Sample answer:

A multiple is the number you get when you multiply one number by another. For example, 15 is a multiple of 5 because when you multiply 5 by 3, you get 15.

"How can you calculate the number of bulbs in 1, 2, 3, 4, 5, . packages for each type of flower you chose?"

Sample answer:

You multiply the number of bulbs in one package by the number of packages. This is the same as making a list of multiples for the number of bulbs in a package.

"How does making a list of multiples help you find the number of packages you need?"

Sample answer:

Once you make a list of multiples for each type of flower, you can look for the multiples that are the same. The pair of multiples that are the same and closest to 100 tell you the number of packages you should buy so you don't buy any extra bulbs.

"Why would you want to find multiples higher than 100 to solve this problem?"

Sample answer:

The common multiple closest to 100 could be greater than 100.

To provide extra challenge for your child, ask the following question:

"How could you solve the problem knowing only the lowest common multiple (LCM)?"

Sample answer:

I could take the LCM and triple it. 35 x 3 gives me 105, which is the common multiple closest to 100.

PART A SAMPLE ANSWER:

White Emperor Tulip (package of 7)

7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112

Fancy Frills Tulip (package of 5)

5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110

I made a list of multiples of 7 and 5 up to around 100 because that is the approximate number of each type of bulb I need.

I circled all the numbers that were the same. This tells me the number of bulbs I need to buy of each type of flower to have an equal number of bulbs.

The common multiple closest to 100 is 105. So if I bought 105 of each type of bulb, I would have an equal number of the two types of flowers without buying any extra.

To find out how many packages of White Emperor Tulips I need to buy, I divide 105 by 7 (which equals 15).

To find out how many packages of Fancy Frill Tulips I need to buy, I divide 105 by 5 (which equals 21).

So, I would buy 15 packages of White Emperor Tulips and 21 packages of Fancy Frill Tulips.

PART B
1. Now that you have bought the bulbs, you can start planting them. Your teacher challenges you to make a pattern with two different colours of flowers. The pattern must meet the following criteria:
• The pattern is made up of a row of alternating purple and yellow rectangles.
• Each rectangle of purple flowers must include 28 evenly spaced bulbs.
• Each rectangle of yellow flowers must include 36 evenly spaced bulbs.

How can you plant the bulbs in the shape of rectangles so that the purple and yellow rectangles have the same number of rows? For each combination of purple and yellow rectangles, describe how many rows and how many columns of bulbs would be in the purple rectangle and in the yellow rectangle.

Use your knowledge of factors to solve the problem. Show your work and explain the strategy that you used to solve the problem.

NOTES FOR PARENTS:

If your child is having trouble finding a procedure to solve the problem in Part B, suggest that he or she try one of the following methods:

•  Make a factor rainbow for each number and then circle the common factors.

•  Use 28 counters (you can substitute beads or pennies for counters) and rearrange the counters to make all the possible rectangles. Each time you create a rectangle, write down how many rows and columns are in that rectangle. Repeat this process with 36 counters. The number of rows and columns for all the rectangles you made tell you the factors of each number. Write down the factors for each number in order and circle the common factors.

•  Draw all the possible rectangles that have an area of 28 units, and then draw all the possible rectangles that have an area of 36 units. (The side lengths must be whole numbers.) Then determine which purple rectangle sides match the yellow ones.

While you child is working, you may want to ask the following question:

"How can common factors help you solve this problem?"

Sample answer:

I can look for factors that are common to both 28 and 36. These common factors will tell me how many rows to put in my rectangles so that the purple and yellow rectangles have the same side lengths.

PART B SAMPLE ANSWER:

Factors of 28 (purple): 1, 2, 4, 7, 14, 28

Factors of 36 (yellow): 1, 2, 3, 4, 6, 9, 12, 18, 36

I listed all the factors of 28. For each factor, I listed its partner, such as 1 and 28. I found the partner by dividing 28 by the first factor. I stopped when there were no more factors.

I connected the factor pairs to create a factor rainbow. This helped me make sure I knew which factors are pairs.

I did the exact same thing with the factors of 36.

Then I circled all the factors of 28 and 36 that are common. The common factors tell me that if I make a purple rectangle with 1, 2, or 4 rows, I can match that rectangle to a yellow rectangle with 1, 2, or 4 rows.

The factor rainbow tells me the partner of each of the common factors, so I know that my pattern can be 3 different possible combinations:

1) A purple rectangle with 1 row and 28 columns combined with a yellow rectangle with 1 row and 36 columns.

2) A purple rectangle with 2 rows and 14 columns combined with a yellow rectangle of 2 rows and 18 columns.

3) A purple rectangle with 4 rows and 7 columns combined with a yellow rectangle of 4 rows and 9 columns.

To provide extra challenge for your child, pose this question:

"Describe how many rows and columns each rectangle would have if you used the greatest common factor (GCF) as the number of rows in each rectangle?"

Sample answer:

The purple triangle would have 4 rows and 7 columns and the yellow rectangle would have 4 rows and 9 columns.