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
