Mathematics 7

# Web Quests

## CHAPTER 4

WORKING ON WASTE AT SCHOOL

Students will use tables of values, models, and scatter plots as part of their strategy to solve problems related to a school vermicomposting program.

### GOALS

7m66 identify the relationship between whole numbers and variables

7m67 identify, extend, create, and extend patterns using whole numbers and variables

7m69 apply and discuss patterning strategies in problem-solving situations

7m70 describe patterns in a variety of sequences using the appropriate language and supporting materials

7m71 extend a pattern, complete a table and write words to explain the pattern

7m72 recognize patterns and use them to make predictions

7m75 present solutions to patterning problems and explain the thinking behind the solution process

grid paper

a ruler

coloured pencils

a calculator

### INSTRUCTIONAL PROCESS

FROM STUDENT PAGE

INTRODUCTION

There are many different ways to take care of and protect the environment. What are some of the things you can do to preserve and protect the environment at home and at school?

NOTES FOR TEACHER:

Before each Internet session, it is always a good idea to check links to ensure they are still active.

This Web Quest can be done pairs or in groups of three.

As a class, read the Introduction. Brainstorm the different ways to protect the environment, such as recycling glass and paper, eliminating or reducing packaging, re-using objects, and cutting down on consumption. If students do not offer composting as an example, ask the class if they are familiar with it, and if not, describe what it entails.

Your class has been chosen to be the start-up class for a vermicomposting program at your school. Vermicomposting means composting with worms.

The principal of your school would like your class to do some Internet research on the subject and make a presentation using the data you find. You will need to find out the following:

• general information on vermicomposting
• the quantity of worms and bins you would need for one classroom
• the number of classrooms that will be vermicomposting after one year
• the amount of castings your worms will have produced after 36 weeks and after 90 weeks.

Together, read through the Task section. Ensure that students are clear on what is expected of them.

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

1. Use the Web links below to research and write a brief report on one of the following aspects of vermicomposting. Then present your report to the class.
1. possible building materials for bins
2. types of bedding material and the quantity needed
3. what foods to feed your worms
4. feeding techniques
5. harvesting the compost
6. possible problems and how to solve them

QUESTION 1

Assign each group one of the six areas of focus to research. Stress that they should also have a general understanding of vermicomposting but only need to prepare a short report on the specific point. If groups will be presenting their findings orally, tell them to write the information in point form.

TIP: When you are looking for specific information on a Web page, scan the text instead of reading all of it from start to finish. To begin, do not read every word of the texts but look through them quickly. For example, if you are looking for information on what to feed worms, look at the section headings first and focus on sections that are related to this subject, such as a section titled "Feeding Worms".

Summary of information on Web sites:

• SWRC - Vericomposting

Provides basic info, including bin size and worm chart using kg and cm.

• Compost Action Project: Vermicomposting

Provides basic information, including number of worms in half a pound.

• Featured Themes - Waste

Provides basic information, including diagrams. Source for fact that worms are mature at 2 months.

• Composting with Worms

Less accessible. Encourage students to scan only for relevant information. Source for fact that worms double in number after 2 months.

Encourage students to use the scan technique. Much of the information in these Web sites is repetitive and does not need to be read thoroughly.

1. Use the information on the Web sites to decide on the number of bins and the quantity of worms (in kg) you will need for your class. Be sure to include the size of the bins in your answer. Explain your thinking and show all your work.

Keep the following in mind when making your decision:

• You will be creating waste from only one meal a day and snacks, five days a week. So divide the number of people in your class by 2 since you will be producing about half as much waste as an average person.
• Some students will need to volunteer to take care of the worms at their homes over the holidays and the summer. This means the bins need to be appropriate for an average-sized family.

QUESTION 2

Students may have varying responses for question 2, depending on how they interpret the problem. Students should be able to recognize the benefits of having several smaller boxes opposed to one or more large boxes in the classroom. All the Web sites provide information on the size of box needed based on the food consumption of a family. Students should be able to recognize that they would be producing less waste because they only eat one meal at school and no cooking waste would be going in the box.

Sample question:

"What are some of the advantages of using several smaller boxes in the classroom?"

It will be easier for someone to take the box home over the holidays and have enough food to feed them. If we have troubles with one box we will still have others to use and we won't be risking all our worms. If we have smaller boxes they will probably take up less room than one box.

We know that:

• there are 30 students in the class.
• We eat only one meal plus snacks and are not there over the weekend
• The boxes must be a convenient size for students to take home over the holidays

We have chosen to have 3 boxes that are designed to be used by 4-6 people because I think this is the size of many families so they will be easy to use over the holidays, and that they are not too big for our classroom. We decided to have three boxes because we predicted that we would be producing about half the average amount of waste because we eat only one meal at school five days a week. We divided the number of students in half, which is fifteen, because it would be more likely we will be producing the waste of 15 people. The boxes are for 4-6 people and five divides easily into fifteen, giving a factor of 3, so we will need 3 boxes.

We will need 6 kilograms of worms.

We know that for a bin for 4-6 people you need between 1.5 and 2 kilograms. We have decided to use the maximum amount of worms in our bins, and since we will have 3 bins we will need 6 kilograms of worms to begin vermicomposting.

1. Worms reproduce at a rapid rate, which is good news because the more worms you have, the more classes you can get vermicomposting.
1. Using the information below, decide how many bins you could set up after one school year (from September to June).

• Worms are able to reproduce at two months old.
• Worms double in number every two months.
• When you have double the number of worms, you need double the number of bins
1. Complete the table of values to display your results.
2. Write the rule for the pattern.
3. How many classrooms will this number of bins supply?

QUESTION 3

For extra support: Have students model problems or parts of problems using concrete materials. For example, provide coloured counters for Step 3, so students may use using a different colour counter to represent each classroom.

For extra challenge: Have students extend their patterns further.

Sample questions:

"How are patterns useful in helping you solve these problems?"

Patterns help me create organized lists, make predictions and generalizations and can save me time when making calculations.

"What is a sequence?"

A sequence is a list of items in a logical order or that follow a pattern.

Sample Anwser:

 Term number Month Number of Bins 1 September/October 3 2 November/December 6 3 January/February 12 4 March/April 24 5 May/June 48

The pattern rule for the sequence is multiply the number by two each time.

1. The castings that the worms produce can be used as fertilizer. 450-600 worms can produce 18 litres of castings in 9 weeks.
1. Click on this link Compost Action Project: Vermicomposting to find out how many worms are in a half a pound.
2. How many litres of castings can 1 pound of worms produce? How many pounds of worms does your class have?
3. Complete the table of values to show the minimum amount of castings your worms could produce in 36 weeks.
4. Write a pattern rule for the number sequence in the table.
5. Write the next four terms in the sequence.
6. Create a scatter plot to predict the minimum amount of castings your worms could produce in 90 weeks.

QUESTION 4

This question requires students to find two pieces of information found on two of the Web sites to solve the problem. Students will be working with an imperial measurement, as it is the only way the information is provided in the Web resources. Because this question involves several steps, most students will benefit from using the scaffolding, which will guide them through the initial steps of the problem.

Sample questions:

"How do you use a scatter plot to make predictions?"

You look at how the coordinates are placed on the graph and determine if there is a pattern. If there is a pattern then you can extend the pattern to make predictions.

"Why do the coordinates in a scatter plot form a line?"

Because the numbers we are using are in a sequence.

For extra support: Provide students with scaffolding for Step 4.

For extra challenge: Have students decide on a size and price for a bag of compost and have them calculate how much money they could generate from the sale of their worms' fertilizer of __ years/months.

Sample questions:

"Do you think there is another strategy for solving this problem?"

"Did you make a plan before you started to make your calculations?"

 LEVEL 1 LEVEL 2 LEVEL 3 LEVEL 4 Understanding of Concepts . attempted solutions demonstrate a limited understanding of concepts . solutions demonstrate some evidence of an understanding of concepts . solutions demonstrate sufficient evidence to show understanding of concepts . detailed solutions demonstrate a thorough understanding of concepts Application of Procedures . makes major errors and/or omissions when extending the patterns and when creating tables and scatter plots . makes several errors and/or omissions when extending the patterns and when creating tables and scatter plots . makes only a few minor errors and/or omissions when extending the patterns and when creating tables and scatter plots . makes almost no errors when extending the patterns and when creating tables and scatter plots Communication . uses very little mathematical vocabulary, and vocabulary used lacks clarity and/or precision   . provides incomplete explanations of how pattern rules work and steps followed to reach answers lack clarity . uses a limited range of mathematical vocabulary with some degree of clarity and precision   . provides partial explanations of how pattern rules work and steps followed to reach answers show some clarity . uses mathematical vocabulary with sufficient clarity and precision to communicate effectively   . provides complete and clear explanations of how pattern rules work and steps followed to reach answers show clarity . uses a broad range of mathematical vocabulary to communicate the pattern rules clearly and precisely . provides thorough, clear, and insightful explanations of how pattern rules work and steps followed to reach answe rs