Mathematics 7

# Web Quests

## NEIGHOURHOOD IN BLOOM PROJECT

In this Web Quest, students will use their knowledge of multiples and information they find on an on-line garden catalogue to choose an appropriate number of flower bulbs to plant in a designated green space. Students will then determine what a specified pattern of flowers will look like using their knowledge of factors.

### GOALS

7m1 Compare, order and represent [decimals, integers,] multiples, factors [and square roots].

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

7m11 Generate multiples and factors of given numbers.

7m24 Explain the process used and conclusions reached in problem solving and investigations.

### MATERIALS

paper and pencil (for recording calculations and explaining strategy)

calculator (optional)

### FROM STUDENT PAGE

NOTES FOR TEACHER:

As a group, read the Introduction. Discuss with students the advantages of having more green space in your community. For example, green spaces make areas more beautiful, they decrease air pollution, and provide habitat and food for birds and insects.

This Web Quest can be done individually or in pairs.

##### 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 TEACHER:

Together, read through the Task section. Ensure that students are clear on what is expected of them. Students should choose only plants that are appropriate for their growing zone. Explain to students that not all plants are hardy (strong) enough to grow in all growing zones of Canada.

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 TEACHER:

To provide extra support, suggest students choose a type of bulb that comes in packages of 5 and another type of bulb that comes in packages of 15. Finding common multiples will be easier with these numbers.

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 TEAHCER:

To provide extra support, lower the number of bulbs needed to about 75 for each type of bulb.

To provide extra challenge, ask students to find 3 different types of bulbs, instead of 2, and tell them that they need 125 of each type of bulb.

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

Sample questions:

"What is a multiple?"

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?"

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?"

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?"

The common multiple closest to 100 could be greater than 100

To provide extra challenge for students, pose the following question:

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

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

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 TEACHER:

If students are having trouble finding a procedure to find the common factors, suggest that they 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 students are working, interview and/or observe them to see how they are interpreting and carrying out the task.

Sample question:

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.

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 students, 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?"

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

### ASSESSMENT

 LEVEL 1 LEVEL 2 LEVEL 3 LEVEL 4 Understanding of Concepts •demonstrates a superficial or inaccurate understanding of multiples and factors •demonstrates a partial understanding of multiples and factors •demonstrates a grade-appropriate   understanding of multiples and factors •demonstrates an in-depth understanding of multiples and factors Application of Procedures •  selects an inappropriate procedure for finding common multiples and common factors   •  makes major errors and/or omissions when applying procedure •  selects a simple or partially appropriate procedure for finding common multiples and common factors •  makes several errors and/or omissions when applying procedure •  selects an appropriate procedure for finding common multiples and common factors   •  makes only a few minor errors and/or omissions when applying procedure •  selects the most efficient procedure for finding common multiples and common factors   •  makes almost no errors and/or omissions when applying procedure Communication •  provides an incomplete explanation of their solution that lacks clarity •  provides a partial explanation of their solution that shows some clarity •  provides a complete and clear explanation of their solution •  provides a thorough, clear, and insightful explanation of their solution