# Web Quests

## CHAPTER 1

## 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)

### HELPING YOUR CHILD THROUGH THE TASK

**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

- 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.

- 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

- 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.