Do you know that an increasing demand for paper contributes
to the destruction of trees from which papers are made? If waste papers were
recycled regularly, it would help prevent the cutting down of trees, global
warming and other adverse effects that would destroy the environment. Paper recycling does not only save the earth
but also contributes to the economy of the country and to the increase in
income of some individuals. This is one situation where questions such as “Will a decrease in production of paper con- tribute
to the decrease in the number of trees being cut?” can be answered using the
concepts of variations. There are
several relationships of quantities that you will encounter in this
situation. You will learn how a change
in one quantity could correspond to a predictable change in the other.
Activity
Please write your answer in the comment box.
Let’s
Recycle!
The Supreme Student Governance launches a recycling campaign
of waste materials to schools in order to raise students’ awareness of
environmental protection and the effects of climate change. Every kilogram of
waste materials earns points that can be exchanged for school supplies and
grocery items. Paper, which is the number one waste collected, earns 5 points
for every kilo.
The table below shows the points earned by a Grade 9 class
for every number of kilograms of waste paper collected.
Number of kilogram (n)
|
1
|
2
|
3
|
4
|
5
|
6
|
Points
|
5
|
10
|
15
|
20
|
25
|
30
|
Questions:
1. What happens to the number of points when the number of
kilograms of paper is doubled? tripled?
2. How many kilograms of paper will the Grade 9 class have to
gather in order to raise 500 points? Write a mathematical statement that will
relate the two quantities involved.
3. In what way are you able to help clean the environment by
collecting these waste papers?
4. What items can be made out of these papers
Discussion
There is direct variation whenever a situation produces pairs
of numbers in which their ratio is constant. The statements: “y varies directly as x” “y is directly proportional to x” and “y is proportional to x” may be translated mathematically as y = kx,
where k is the constant of variation. For two quantities, x and y, an increase
in x causes an increase in y as well.
Similarly, a decrease in x causes a decrease in y.
http://www.purplemath.com/modules/variatn.htm
http://www.math-only-math.com/what-is-variation.html
http://www.shelovesmath.com/algebra/beginning-algebra/direct-inverse-and-joint-variation/
http://www.purplemath.com/modules/variatn.htm
http://www.math-only-math.com/what-is-variation.html
http://www.shelovesmath.com/algebra/beginning-algebra/direct-inverse-and-joint-variation/
Review
We CANS
Please write your answer in the comment box.
Tin cans of beverages are collected for recycling purposes in
many places in the Philippines.
Junk shops pay Php 15.00 for every kilo of tin cans bought
from collectors. In the following table, c is the cost in peso and n is the
number of kilos of tin cans:
n
|
1
|
2
|
3
|
4
|
5
|
6
|
c
|
15
|
30
|
45
|
60
|
75
|
90
|
a. Write a mathematical statement that relates the two
quantities n and c.
b. What is the constant of variation? Formulate the
mathematical equation.
c. Observe the values of c and n in the table. What happens
to the cost c when the number n of kilos of paper is doubled? Tripled?
d. Graph the relation.
e. How much would 20 kilos of tin cans cost if at the end of
month, the cost for every kilo of tin cans will increase by 5 pesos?
f. What items can be made out of these tin cans?
please put your answer here
ReplyDelete1. The points also increased or doubled/tripled when the number of kilogram increased or doubled/tripled.
ReplyDelete2. One kilogram of recycled paper is equivalent to 5 points, so if you have 100 kilograms of papers you will have 500 points.
3. You can save trees by recycling paper.
4. Cans, Bottles, Tires, etc.
a. C= 15n
b. K= c/n
c. it also increased
d. no graph
e. 400 pesos
f. You can used tin cans and making a flower vase.
1. Points will also increase ufthe number of kilogram will be increased
ReplyDelete2. 1 kilo of recycled paper is equal to 5 points, so if you have 100 kilo of paper you will have 500 points.
3. we will save trees if everyone will recycle paper
4. paperbags, scrapbooks, etc.
a. C= 15n
b. K= c/n
c. it will increase also
d. there is no graph
e. 400 pesos
f. tables, chairs, even wheelchairs
1. Points will also increase ufthe number of kilogram will be increased
ReplyDelete2. 1 kilo of recycled paper is equal to 5 points, so if you have 100 kilo of paper you will have 500 points.
3. we will save trees if everyone will recycle paper
4. paperbags, scrapbooks, etc.
a. C= 15n
b. K= c/n
c. it will increase also
d. there is no graph
e. 400 pesos
f. tables, chairs, even wheelchairs
1. The number of points will also be doubled or tripled.
ReplyDelete2. 500=5x
3. By collecting these waste papers, these can be sold in a junk shop, then the junk shop can sell these waste paper in a factory where paper is recycled. That way, the cutting of trees can be decreased.
4. We can make crafts out of waste paper like paper mache, paper mat, etc.
a. c=15n
Deleteb. 15
c. The cost is also doubled or tripled.
d. I can not draw the graph here but the appearance of the graph is a slanting straight line, facing the right side of the Cartesian Coordinate plane.
e. Php 400
f. Tabo, dust pan, water sprinkler, pen holder, decorations, etc.
1. The number of points will also be doubled or tripled.
ReplyDelete2. 500 points is equvalent to 100 kg of paper
3. The collected waste paper can be recyled and use again in making new papers.
4. Bags, new papers and scrap books
a. c=15n
ReplyDeleteb. 15
c. The cost is also doubled or tripled.
d. No graph
e. Php 400
f. Tabo, vase crafts
1. Points will also increase dependent on the increase in kilo
ReplyDelete2. 100 kilo of paper you will have 500 points.
3. we can save papers and save the environment
4. paperbags, scrapbooks, etc.
a. C= 15n
b. K= c/n
c. it will increase also
d. can't do the graph
e. Php 400.00
f. pail.vase.container