Appendix A
Example of RME exemplary lesson materials
Topics:
Linear equation systems
Matrices
Symmetry
Side seeing
Statistics
Linear equations system: Finding Price
Topic: Linear equations system with two variables
Quarter: 2
Grade : Eight, junior secondary school
Title : Finding price
Time : Two or three 45-minute class session
Before teaching
Overview: (what students are going to do?)
Given the prices of combinations of items, students able to determine prices of
single items. Students use strategies such as exchanging, reasoning, and finding
patterns in combination chart to solve shopping problems. Students will discover
how patterns are related to patterns in a succession of equations.
Goals: (What will the students be able to do when they finish this lesson?)
Students will:
• Use pictures, words, or symbols to solve problems;
•
•
•
•
•
•
•
•
•
Use exchanging, substituting and other strategies to solve problems;
Develop an understanding of equation and variable;
Describe one's own solution process and follow the solution process of someone else;
Discover, investigate and extend patterns;
Organize information from problem situations using combination charts and equations;
Interpret a mathematical solution in terms of the problem situation;
Develop reasoning skills to solve equation-like problems;
Recognize similarities in solution strategies
Solve informally problems that involve system of equation
About mathematics: ( What new concepts will be used in this lesson?)
In the previous, students used the value of one item of each kind to find the value of a
combination. In this section, students use the value of the combination of items to find the
value of one item of each kind. Students create new combinations from given ones by
adding, subtracting, or extending patterns.
In each problem context in this section, students are given two linear equations (in picture or
story form) with two unknowns, which are the prices of two items by themselves. As
students solve problems using visual representations of the combinations and a combination
chart, they develop reasoning skills for solving systems of equation.
Materials: (What media or materials will be needed for the teaching activities?)
• Student lesson materials
• Student assessment materials
• Student activity sheets
During Teaching
Introduction: (What is the context? How the students work?)
Introduce this section by discussing with students their own shopping experiences and the
prices of items in familiar store. Divide students in the small group if necessary.
Activities:
1. Students may work on contextual problems 1-3 and 4-7 in a small group or
individually.
2. By moving around find out which students or groups have the ‘clever’ or
intended strategy. This information is important in discussing session.
3. Stimulate the students to compare their solutions.
4. Ask the student or the group of students to present their answer in front of the
class.
5. Guide the students in a class discussion
On-going assessment:
Problem 8-10 can be used to informally assesses student's ability individually.
After Teaching
End-class assessment
Problems 1- 4 in assessment materials can be used to assesses students ability to
solve the shopping problems.
Home work
Problem 11 and 12 in the student materials may be assigned as homework.
Teacher Guide
1. Without knowing the prices of a pair of
glasses
or a calculator, you can
determine which item is more expensive.
Explain how.
2. How many calculators can you buy for $
50?
3. What is the price of one pair of glasses?
Explain your reasoning.
Comments about the Problems.
Encourage students to use exchanging to solve
problems.
1. Tell the students to try to solve problem
without finding the price of each item. If they
do, ask them to try solving the problem in a
different way.
2. Students may solve this problem by imagining a
picture that contains only calculator.
3. Some students may use a guess-and-check
strategy. Other students may double the first
picture to get four pairs of glasses and two
calculators, then exchange two calculators for
one pair of glasses, to end up with five pairs of
glasses that total $ 100.
Hints, comments and solutions
Overview. Given the costs of two
combinations of glasses and calculators,
students use an exchanging strategy to
determine the price of each item.
Solution:
1. Glasses are more expensive than
calculators. Sample explanation:
covering up one pair of glasses
and one calculator from each
picture shows that one pair of
glasses costs the same as two
calculators. So a pair of glasses
costs more than a calculator.
2. You can buy five calculators for $ 50.
Explanations will vary. Sample
explanation:
Since two calculators cost the same as
one pair of glasses, exchange the
glasses for two calculators in either
picture. The result is that five
calculators cost $ 50.
3. One pair of glasses cost $ 20.
Explanations will vary. Sample
strategy:
From 2 is found that five calculators
cost $ 50, so a calculator costs $ 10.
From the second picture a pair of
glasses and three calculators are $ 50,
so a air of glasses is $ 20.
Solutions:
4. Which is more expensive, a cap or an
umbrella? How much more expensive
is it?
6. Use the two pictures above to make a
new combination of umbrellas and caps.
Write down the cost of the combination.
7. Make a group of only caps or only
umbrellas. Then find its price.
8. What is the price of one umbrella? One
cap?
4. The umbrella is more expensive by $ 4. Strategies will vary. Some students may cover up a
cap and an umbrella in each row. This leaves one umbrella and one cap, with a $ 4 difference
between their costs.
5. Answers will vary. Some students may double the first or second combination to get four
umbrellas and four caps, totaling $ 160, or two umbrellas and four caps, totaling $ 152.
Other students may add the two combinations: three caps and three umbrellas
cost $ 80 + $ 76, or $ 156.
6. Answers will vary. Sample student strategies:
Strategy 1
Some students will exchange a cap for an umbrella or vice versa in either picture.
• Since an umbrella is $ 4 more than a cap, trade the cap in the first picture for an umbrella and
add $ 4 to $ 80. So, three umbrellas cost $ 84.
• Since an umbrella is $ 4 more than a cap, trade the umbrella in the second picture for a cap. So,
three caps cost $ 72.
Strategy 2
Some students may extend the strategy in problem 5 and look for patterns in an organized list as
pictured below.
$ 152
$ 156
$ 160
•
Reading down, as the umbrellas increase by one, the caps decrease by one and the amount
•
increases by $ 4. In two more moves, there will be six umbrellas and no caps for $ 168
Reading up, as the umbrellas decrease by one, the caps increase by one and the amount decreases
by $ 4. In two more moves, there will be no umbrellas and six caps for $ 144.
7. One cap costs $ 24 and one umbrella costs $ 28.
Solution:
8. One jacket cost $ 14 and one T-shirt cost
$ 8. Explanations will vary. Sample
explanation:
2 T-shirts + 1 jean = $ 30
1 T-shirts + 2 jean = $ 36
0 T-shirts + 3 jean = $ 42
1 jean = $ 14 ( divide by 3)
Because a jean is $ 6 more than a T-shirt,
A T-shirt costs $ 8.
This method can be used in reverse by
repeatedly exchanging a jean and
subtracting $ 6 each time.
9. No, this is not a fair exchange. The two pictures
show that adding two pencils and eliminating a
clipboard decreases the price by $ 1. To be fair, B
should pay A $ 1.
10. One pencil costs $ 0.25, and one clipboard costs $
1.50.
Explanations will vary. Sample students
strategies:
Strategy 1. Some students will repeat the exchange of
one clipboard for two pencils and total cost is decreased
for $ 1 until only pencils are left. At the end 16 pencils
equal to $4, so a pencil cost $ 0.25
Strategy 2. Some students may calculate the price of a
clipboard by repeatedly trading two pencils for one
clipboard and adding one dollar to the total cost. At the
end only 8 clipboards left costs for $12. So , one
clipboard
costs for $ 1.50
Summary
11.Shopping problems and explanations will vary.
8. Austin bought two T-shirts and
one jacket for a total of $30.
When he got home, he regretted
his purchase. He decided to
exchange one T-shirts for another
jacket. Austin was able to do this
, but he had to pay $6 more
because the jacket was more
expensive than the T-shirt. What
was the price of each item?
Explain your reasoning.
A spent $ 8 to buy four clipboards
and eight pencils. B spent $ 7 to
buy three clipboard and 10 pencils.
B wants to trade A two pencils for
a clipboard
9. Is that a fair exchange? If
not, who has to pay the
difference, and how much
is it?
10. What is the price of pencil?
What is the price of a
clipboard?
Explain your reasoning.
11. Create your own shopping
problems. Be sure you
can solve the problem, then
ask someone else to solve it.
Have the person explain to
you how he or she found the
solution.
Shopping problems can be solved using the method of exchange. Identifying a pattern in a
picture or combination chart can make it possible to find the cost of one item. Extending a
pattern or combining information can also help you find the cost of one item.
12. Summary question
Find the cost of one item using exchange strategy and combination chart (use this chart below)
Cost of Combinations ( in dollars)
#'s
b
a
s
k
e
t
b
Comments:
a
l
Students use combination
charts to solve two of the
5
shopping problems they
answered earlier in this
4
section. The combination
3
73
chart can be used to solve
problems about only two
2
34
kinds of items. The same
reasoning used in problems
1
1-11 can be used in
0
completing
the
combination
chart.
0
1
2
3
4
5
Number of footballs
Solution
12. Explanations will vary.
By exchange the sample strategy as follows:
• Divide the first picture by two (one of each for $ 17)
• Than multiply by three to find the price of three basket ball and three football ($
51)
• Than compare to the second pictures
• Subtract to find the price of two footballs ($ 22)
• The price of one football is $ 11.
• Substitute the price of one football into the first line to calculate $ 17- $ 11= $ 6
Using the combination chart strategy will vary but produce the same result.
Student's materials
Finding Price
In this section you will use the strategy of exchanging to solve problems involving money.
1. Without knowing the prices of a pair of glasses or a calculator, you can determine which
item is more expensive. Explain how.
2. How many calculators can you buy for $ 50?
3. What is the price of one pair of glasses? Explain your reasoning.
Which is more expensive, a cap or an umbrella? How much more expensive is it?
5. Use the two pictures above to make a new combination of umbrellas and caps. Write
down the cost of the combination.
6. Make a group of only caps or only umbrellas. Then find its price.
7. What is the price of one umbrella? One cap?
8. Austin bought two T-shirts and one jacket for a total of $30. When he got home, he
regretted his purchase. He decided to exchange one T-shirts for another jacket. Austin
was able to do this , but he had to pay $6 more because the jacket was more expensive
than the T-shirt. What was the price of each item? Explain your reasoning.
A spent $ 8 to buy four clipboards and eight pencils. B spent $ 7 to buy three clipboard
and 10 pencils. B wants to trade A two pencils for a clipboard.
9. Is that a fair exchange?
If not, who has to pay
the difference, and how
much is it?
10. What is the price of
pencil? What is the
price of a clipboard?
Explain your
reasoning.
11. Create your own shopping problems. Be sure you can solve the problem, then ask
someone else to solve it. Have the person explain to you how he or she found the
solution.
Summary
Shopping problems can be solved using the method of exchange. Identifying a pattern in a
picture or combination chart can make it possible to find the cost of one item. Extending a
pattern or combining information can also help you find the cost of one item.
12. Summary question
Find the cost of one item using exchange strategy and combination chart.
#'s
b
a
s
k
e
t
b
a
l
Cost of Combinations (in dollars)
5
4
3
73
2
34
1
0
0
1
2
3
4
5
Number of footballs
Assessment
1. Use additional paper if needed
2. Use additional paper if needed
3. Nina and Sita earn money baby-sitting. One day Sita worked four hours and Nina
worked three hours. They earned $ 18 together. Another day Sita worked six hours and
Nina worked seven hours. That day they earned $ 34 together. Do Nina and Sita earn
the same amount of money per hour? Explain your answer. On a third day, they both
worked six hours. How much money did they earn together on that day?
4.
Suppose you have two equations:
3 P + 7 T = 98
4 P + 2 T = 50
Find the value for P and T that make both equations true.
Linear equations system: Shopping equations
Topic: Linear equations system with two variables
Title: Shopping equations
Grade: Eight, junior secondary school
Time: Two or three 45-minute class sessions
Before Teaching
Overview: (what students are going to do?)
Students are introduced to the context of shopping. They find the prices of individual
items when they know the total price of a combination of items.
Goal: (what will the students be able to do when they finish this lesson?)
Students will:
•
•
•
•
•
•
•
•
•
•
•
Use pictures, words, or symbols to solve problems;
Use exchanging, substituting and other strategies to solve problems;
Interpret and use combination charts, notebook notation and equation;
Develop an understanding of equation and variable;
Describe one's own solution process and follow the solution process of
someone else;
Discover, investigate and extend patterns;
Organize information from problem situations using combination charts,
notebook notation and equations;
Interpret a mathematical solution in terms of the problem situation;
Develop reasoning skills to solve equation-like problems;
Recognize similarities in solution strategies
Solve informally problems that involve system of equations
About mathematics: (what new concepts will be used in this lesson?)
The mathematics in this section the same as in the section finding price. Students
find possible prices of a combination of two items based on the total price of a
combination of two items. Some student may use a guess-and-check method to
find one solution.
Materials: (what media or materials will be needed for teaching activities?)
• Teacher guide
• Student lesson materials
• Student assessment material
During Teaching
Introduction
Introduce this section by discussing with students, their own shopping
experiences and the prices of items in familiar store. Students can work in pairs
of small groups if necessary.
Activities
• Give the students contextual problems (problems 1-5 and 6-10) and they can
be work in a small group or individually.
• By moving around find out which students or groups have the ‘clever’ or
intended strategy. This information is important in discussing session.
• Stimulate the students to compare their solutions.
• Ask the student or the group of students to present their answer in front of the
class.
• Guide the students in a class discussion
They can retry these activities by working on problems 6,7, 8, 9 and 10.
On-going assessment
Problem 11, 12 and 13 may be assigned for practicing until the end of class
After Teaching
End-class assessment
Students may be asked to do the problems in the assessment materials.
Home work
Problem 14,15, 16, an 17 may be assigned as homework.
Student materials: Shopping Equations
Austin and Udin are friends. Their favorite store, which sells only Jeans and T-shirts, is
having a gigantic sale. Austin and Udin have saved some money, and they are ready to shop!
For this sale, all T-shirts have one price and all jeans have one price.
Austin buys two jeans and five T-shirts for $ 154
1 a. Find a possible per-item price for jeans and for T-shirts.
b. Are other prices possible? Explain your answer.
Is it possible that the price of a T-shirt is $ 32? Explain why or why not.
2a. What is the cost of four pairs of jeans and ten T-shirts?
What are some other purchases for which you know the cost?
You can write a "shopping equation" for Austin's purchase. If J stands for the jeans price
and T for the T-shirt price, you can write:
2J + 5 T = 154
This shopping equation is an example of an equation with two unknowns.
3. What shopping equation describes the price of four pairs of jeans and ten Tshirt? How is it related to the original shopping equation?
The equation 2J + 5 T = 154 is true for many values for J and T.
4. Check that the number pair J = 52 and T = 10 makes the equation true.
Find three other number pairs that work.
5. Another number pair that works for the equation is J = 8 and T = -2.
Explain why these values do not make sense for this problem.
Describe the ranges of values for J and T that make sense for this equation.
Values for J and T that make the equation true are called solutions to the equation.
6. Udin buys three pairs of jeans and four T-shirts. The total cost is $ 182.
a. Write a shopping equation for Udin's purchase.
b. Find three solutions without considering Austin's purchase.
7. Look back at the information you have for Austin's and Udin's purchase.
Using that information, find the prices for one T-shirt and one pair of jeans.
TABLES
In the previous unit: 'Comparing quantities', you developed several strategies to solve similar
shopping problems. For one strategy, called "notebook notation", information is organized
in a table.
Hannah solved problem 7
using the notebook notation
method, as shown on the right.
8. Explain Hannah's solution
9. Copy Hannah's table and
write and equation for each
row in the table.
J
T
Price
----------------------------------------------------------Austin's purchase
2
5
154
Udin's purchase
3
4
182
----------------------------------------------------------6
15
462
6
8
364
---------------------------------0
7
98
0
1
14
0
5
70
2
0
84
1
0
42
Selena discovered her own way to solve problem 7.
Austin
|
Udin
----------------------------------------------------------------------J
T
Price
|
J
T
Price
----------------------------------------------------------------------2
5
154
|
3
4
182
4
10 308
|
6
8
364
6
15 462
|
9
12
546
8
20 616
|
12 16
728
10
25
770
|
15 20
910
---------------------------------------------------------------------J
T
Price
------------------------------------6
15
462
subtract
6 8
364
divide by 7
0
7
98
0
1
14
-------------------------------------The value of T is 14
10.
a. Explain Selena's strategy
Describe how you can find the
value of J
11. Gramedia's book store is having a sale on paperback books and pencil. All
the books on sale are one price, and all the audio pencil on sale are one
price. Ani buys two books and five pencils for $ 46. Bety buys six books
and three pencils for $ 42. Find the price of one book and the price of one
pencil.
12. The Dial Shop has one price for any watch and one price for any radio.
Five watches and four radios cost $ 134. Four watches and five radios cost
$ 127. Find the prices of one watch and the price of one radio.
Below is another way to look at Selena's strategy in the previous page. While it uses
equations, it is still the same strategy.
Austin
|
Udin
---------------------------------------------------------------------2J + 5T = 154 |
3J + 4T = 182
4J + 10T = 308 |
6J + 8T = 364
6J + 15T = 462 |
9J + 12T = 546
8J + 20T = 616 |
12J + 16T = 728
10J + 25T = 770 |
15J + 20T = 910
-------------------------------------------------------------------------------------------------------6J + 15T = 462
subtract
6J + 8T = 364
divide by 7
7T = 98
1T = 14
-------------------------------------The value of T is 14
13. a. You can find the value
of J by combining the
equations:
8J + 20 T = 616
and
15 J + 20 T = 910.
Show how
b. Once you know that T =
14, there is another way to
find the value of J.
Show how.
In problem 13, you found a pair of values that satisfies both equations. The pair of values is
called a common solution for the two equations.
14. a. Find a common solution for the two equations X + 2 Y = 95
and the X + Y = 55. Is there more than one common solution?
b. Do the equations X + 2 Y = 95 and 3 X + 6 Y = 290 have a common
solution?
c. Is there a common solution for these three equations: X + 2 Y = 95,
X + Y = 55 and 3 X + Y = 110? Explain your answer.
d. Sandy thinks three equations can never have a common solution.
Explain why you agree or disagree with Sandy.
15. A bill for two glasses of apple juice and three glasses of orange juice is
$ 5.20. Another bill for four glasses of apple juice and sic glasses of
orange juice is $ 10.40.
Explain why it is not possible to find the price of one glass of apple juice.
Suppose the price of one glass of orange juice is 40 cents more than the price of one glass of
apple juice. What is the price of one glass of apple juice?
Summary
In this lesson, you solved shopping problems. You used both a table
(notebook notation) and equations to solve the problems.
The equation 2X + 5Y = 100 has two unknowns, so it has many solutions.
When a pair of values satisfies two equations with two unknowns, that pair of
values is a common solution.
Summary Questions
Here are two equations with two unknowns:
2 X + 5 Y = 100
3 X + 8 Y = 156
This pair of equations has one common solution. Find it using a method discussed in this
section.
Does every pair of equations with two unknowns have one common solution?
examples to justify your answer.
Give
Assessment materials
1. The price of one banana and two apples is $ 1.85. The price of three bananas and four
apples is $ 4.45.
How much the price of:
•
•
•
•
•
•
2.
six bananas and eight apples ?
four bananas and six apples ?
two bananas and two apples ?
one banana and one apple ?
one banana?
one apple?
The following is data in a taxi company. Fill in the table.
--------------------------------------------------------Driver
liter diesel liter oil
price
--------------------------------------------------------A
45
3
81
B
25
1
42
C
20
2
….
D
50
2
…
E
70
4
….
F
10
0
….
3. From the following equations:
4a + 8 b = 36 (1)
2a + 3b = 16 (2)
Two time of (2) = ……… …….… (3)
(3) subtract by (1) = ……………
b =?
a=?
check whether your answer is true or not by substitute the value of a and b into (1) and (2) .
4. Try this equation system
4 L + 3 M = 96
L + M = 27
Find the value of L and the value of M
Make up a story to fit these equations
Use additional paper if needed
Matrices
Cihampelas
Cihampelas is a famous market in Bandung. Here, in a number of stores, people
can buy various of jeans and t-shirts. One of the stores is Toko Rambo. In this
store, 36 trousers Wrangler with different sizes and types are available with the
following specifications:
28" (long 28 inches)= 6
30" = 12
32" = 12
34" = 6
Other types of jeans are also available with size and quantities as follows:
Levis : 6, 12, 12, and 6
Cardinal : 3, 7, 6 and 3
Esperite : 6, 6, 6 and 3
Darwin : 3, 6, 6 and 3
Problems:
1. All this information can be written down well-ordered in matrix-form. Write
the matrix.
2. How many trousers fit with your sizes? Explain!
3. In a month, the number of trousers has been sold can be seen on the following
matrix. Write down the number of trousers which has not been sold?
4. The average profit per pair of Wrangler jeans is Rp. 3000,-; Levis Rp. 3500,-;
Cardinal Rp. 4000,-; Esperite Rp. 2500,- and Darwin Rp. 4000,-. What is the
total Profit on the small size?
5. Compute in the same way the profit on size 30". And in total?
SIMETRI
Asli
Hasil
Mesin photo kopi
1. Jelaskan secara tertulis bagaimana perbedaan antara ukuran kertas asli dengan hasil
kopian.
2. Manusia atau hewan adalah contoh yang bagus dalam belajar simetri. Contoh, gambar
kupu-kupu di bawah yang merupakan hasil kerjaan temanmu. Berapakah banyaknya
sumbu simteri pada kupu-kupu? Gambarkan satu contoh lain binatang yang mempunyai
sumbu simetri?
Gambar berikut disebut bilangan Arab
1 2 3 4 5 6 7 8 9 0
3. Bilangan yang mana yang mempunyai sumbu simetri? Gambar sumbu simterinya!
A B C D E F G H I J K L M N
O P Q R S T U V W X Y Z
4. Huruf mana yang mempunyai satu sumbu simetri ? lebih dari satu ?
5. Gambarkan huruf yang dapat dirotasikan sejauh 180° dan masih terlihat
kongruen?
6.
O
O O
O
Menggunakan empat lingkaran kecil
tentukanlah lokasi sumbu simetri sehingga
jumlah lingkaran kecil bersama sama
bayangannya menjadi:
a. 2
b. 4
c. 6
d. 7
Jelaskan alasan anda!
7. Desainlah segitiga yang memiliki satu, dua dan tiga sumbu simetri. Jelaskan
karakteristik setiap segitiga.
8. Gambarlah satu persegi panjang, jajaran genjang dan bujur sangkar.
Gambarlah sumbu simetri masing-masing. Jelaskan perbedaan sumbu
simetrinya.?
9. Berilah satu contoh dengan gambar manusia menggunakan translasi.
10. Cerminkanlah secara berturutan sebuah segitiga terhadap dua garis yang saling tegak
lurus. Jelaskan hubungan antara segitiga pertama dengan segitiga hasil refleksi.
11. Sama seperti soal nomor 10, jika kedua garis tidak saling tegak lurus.
12. Buatlah satu desain bebas seperti orang membuat atik yang menggunakan konsep
refleksi, rotasi atau translasi.
13. Apakah ada setuju jika salah seorang teman berkata bahwa dia dapat melipat jajaran
genjang ditengahnya sehingga kedua bagian tepat saling menutupi? Jelaskan Mengapa?
SIDE SEEING
1. Gambar berikut adalah top view dari suatu bangunan
1.
2.
Sketsalah bangunan tersebut dengan jumlah kubus minimal. Berapa banyak blok yang
kamu pakai?
3.
Apakah kamu kira semua temanmu di kelas membuat bangunan yang sama dengan
bangunan kamu. Mengapa atau mengapa tidak?
4.
Sekarang buat bangunan yang lain yang sama 'top view' nya. Apakah kamu kira
semua temanmu di kelas membuat bangunan yang sama dengan bangunan kamu.
Mengapa atau mengapa tidak?
5.
Gambar berikut adalah gambar dari suatu gedung.
a. Berapa banyak kubus yang dipakai?
b. Gambarkan top view dari gedung.
c. Gambarkan side view dari depan, kiri dan kanan.
6. Gambarkan satu top view dan satu side view dari gedung yang menggunakan 10
kubus.
7. Gambar di atas adalah suatu kota dengan empat gedung utama a, b, c dan d
a. Hitunglah jumlah kubus pada setiap gedung?
b. Gambar top view setiap gedung.
Pada gambar di sebelah kanan, angka pada
setiap bujur sangkar disebut angka tinggi atau
height number. Angka tinggi menunjukkan
berapa banyak kubus ditumpukkan pada
bujursangkar itu.
8. Berapa banyak kubus yang diperlukan
untuk membuat bangunan di sebelah
kanan ini?
9.
Berapa banyak kubus yang kamu
butuhkan untuk lantai paling atas
bangunan ini? Mengapa?
1
2
2
1
2
4
3
2
2
5
4
2
1
2
2
1
10. Gambarkan dua side view berbeda dari bangunan di bawah ini:
1
2
3
4
11. Gambar berikut ditemukan di internet. Buatlah cerita menggunakan beberapa kalimat
tentang gambar berikut.
12. Ceritakan pada teman sebelah anda apa yang kamu ketahui tentang gambar berikut.
13. Di bawah ini adalah gambar salah satu orang siswa temanmu. Gambarkan side view
dan top view dari objek tersebut. Kemudian gambarkanlah suatu objek yang ada di
rumahmu. Usahakan objeknya berbeda dengan temanmu.
Statistik
Populasi dan Sampel
Populasi adalah semua group yang kamu tertarik untuk menemukan sesuatu.
Sample adalah bagian dari populasi
1. Berikan satu contoh populasi dan sampel yang
kamu ketahui. Jelaskan.
Populasi Indonesia
Daerah
Sumatra
Jawa
Kalimantan
Sulawesi
Bali and Nusa Tenggara
Maluku
Irian Jaya
1980
28,016,160
91,269,528
6,705,086
10,409,533
8,487,110
1,411,006
1,173,875
1990
36,506,703
107,581,306
9,099,874
12,520,711
10,163,854
1,857,790
1,648,708
2. Berapa persen kenaikan populasi dari '80 to '90?
3. Jika populasi naik seperti 10 tahun terakhir berapa populasi Indonesia pada tahun 2000?
4. Bandingkan populasi pada tabel dengan daerah pada peta. Buatlah gambar atau grafik
pada setiap daerah. Apa kesimpulan anda? Apa implikasi dari kesimpulan itu?
Reprinted from BPS Homepage
Luas daerah di Indonesia
Daerah
Sumatra
Jawa
Kalimantan
Sulawesi
Bali and Nusa Tenggara
Maluku
Irian Jaya
Luas (km2)
473,481
132,186
548,006
189,216
88,488
74,505
421,981
Sampah
Apakah kamu tahu berapa banyak sampah yang dihasilkan oleh seseorang dalam satu
minggu? Untuk mendapatkan ide kamu dapat menghitung jumlah bungkus sampah setiap
minggu di rumahmu.
5. Asumsikan rata-rata penduduk Indonesia membuang sampah 2 kg sehari.
a. Berapa banyak total sampah rata-rata penduduk Indonesia setahun?
b. Berapa banyak setiap orang menghasilkan sampah dalam setahun?
6. Aktivitas:
Buat data jumlah anggota keluarga setiap siswa.
Tabulasikan data tersebut
Hitung Range, Rata-rata, Modus, dan Median
Hitung jumlah sampah yang dihasilkan oleh seluruh keluarga kelas itu bila dihubungkan
dengan soal 1.
Air
Aktivitas
Investigasilah rata-rata air yang digunakan oleh kalian setiap hari. Buatlah dan
estimasilah jumlah air yang dipakai dalam liter. Bandingkanlah hasilmu dengan
teman sebelah, diskusikanlah dan jika perlu koreksi setiap kesalahan. Kemudian
hitunglah rata-rata kelas untuk penggunaan air dalam sehari atau 24 jam.
Energy Listrik
Listrik diukur dengan satuan Watts. Namun, karena banyak alat elektronik
menggunakan ukuran unit yang besar yaitu kilowatt. Satu kilowatt sama dengan
1000 watts. Jika sesuatu menggunakan satu kilowatt listrik selama satu jam maka
satu kilowatt-hour (kWh) listrik digunakan.
Table di sebelah adalah standard penggunaan listrik
untuk barang elektronik.
7. Berapa banyak energi yang dihemat jika kamu
menggunakan bola lampu 60-watt dari pada
100-watt?
8. Buatlah tabel yang berisikan data pemakaian
listrik di rumahmu. Kemudian buatlah grafik
sederhana.
9. Berdasarkan data dan grafik yang kamu buat,
bagaimana kamu menyimpulkan menjadi
informasi penggunaan listrik di rumahmu dan
kaitkan dengan rekening bulanan yang dibayar.?
Appliances
Kilowatts
Pemanas Air
Kompor gas
Kulkas
AC
Pembeku es
Pengering
TV Color
Radio-Tape
Mesin cuci piring
Setrika
Bola Lampu 100Watt
Bola lampu 60Watt
Mesin Cuci
Pemanas Air
Pembakar roti
4.5
12.2
0.6
1.5
0.34
4.8
0.33
0.1
1.2
1.2
0.1
0.06
0.5
0.9
1.2