Unit 21
Selesaikan Masalah
Reben merah panjangnya 1 m 35 cm.
Reben biru 85 cm lebih panjang daripada reben merah.
Berapakah jumlah panjang kedua-dua reben itu?
解决问题 = selesaikan masalah；比……长 = lebih panjang daripada；缎带 = reben
这一课学用四个步骤解长度、质量和液体体积的应用题。题目说红缎带长 1 m 35 cm，蓝缎带比红的长 85 cm，问两条一共多长。85 cm 不是蓝缎带的长度，而是“多出来的部分”，所以要两步：先求蓝缎带，再把两条加起来。题目里有 m 也有 cm，算的时候要会换算。
例子：哥哥身高 1 m 40 cm，爸爸比他高 30 cm，爸爸就是 1 m 70 cm。
注意：很多人把 85 cm 直接当成蓝缎带的长度，答案就错了。
solving problems = selesaikan masalah; longer than = lebih panjang daripada; ribbon = reben
In this unit we solve word problems about length, mass and liquid volume in four steps. The red ribbon is 1 m 35 cm long, the blue ribbon is 85 cm longer than the red one, and we need the total length of both. The 85 cm is not the blue ribbon's length but the extra part, so there are two steps: find the blue ribbon first, then add the two. The question mixes m and cm, so we must convert as we work.
Example: a brother is 1 m 40 cm tall and father is 30 cm taller, so father is 1 m 70 cm.
Watch out: many pupils treat the 85 cm as the blue ribbon's length, which gives a wrong answer.
Empat langkah
Diberi → Dicari → Cara → Semak
Untuk masalah panjang, jisim dan isi padu cecair
1. Diberi
nombor dan unit dalam soalan
2. Dicari
apa yang soalan mahu? dalam unit apa?
3. Cara
model bar → ayat matematik → kira
4. Semak
operasi songsang: tambah ↔ tolak, darab ↔ bahagi
| tukar unit |
|---|
| 1 m = 100 cm · 1 kg = 1 000 g · 1 ℓ = 1 000 mℓ |
已知 = Diberi；所求 = Dicari；方法 = Cara；检查 = Semak；换单位 = tukar unit
度量衡应用题也用四个步骤。Diberi：把数字连同单位一起抄下来。Dicari：问的是什么，答案要用什么单位。Cara：画条形模型、写算式、计算；单位不一样时要先换算：1 m = 100 cm，1 kg = 1 000 g，1 ℓ = 1 000 mℓ。Semak：用相反的运算检查。
例子：题目问“几 mℓ”，算出 1 ℓ 500 mℓ 就要再写成 1 500 mℓ。
注意：长度是满 100 进 1，质量和液体体积是满 1 000 进 1，不要混在一起。
given = Diberi; to find = Dicari; method = Cara; check = Semak; converting units = tukar unit
Measurement word problems use the same four steps. Diberi: copy the numbers together with their units. Dicari: what is asked, and which unit the answer should be in. Cara: draw a bar model, write the number sentence and work it out, converting first when the units differ: 1 m = 100 cm, 1 kg = 1 000 g, 1 ℓ = 1 000 mℓ. Semak: check with the opposite operation.
Example: if the question asks how many mℓ, an answer of 1 ℓ 500 mℓ must be rewritten as 1 500 mℓ.
Watch out: length regroups at 100, but mass and liquid volume regroup at 1 000, so do not mix them up.
Diberi dan Dicari
Lukis model bar
Lebih panjang = sama panjang + bahagian lebih
85 cm ialah bahagian lebih, bukan panjang reben biru
条形模型 = model bar；多出来的部分 = bahagian lebih
先写 Diberi：红缎带 1 m 35 cm，蓝缎带比红的长 85 cm。Dicari：两条的总长。画模型：红的画一条；蓝的先画一段跟红的一样长，再接上多出来的 85 cm。看图就知道蓝缎带是 1 m 35 cm + 85 cm = 2 m 20 cm，总长是红条加蓝条。
例子：如果题目说“短 20 cm”，蓝条就画得比红条短，缺的那段标 20 cm。
注意：先画一样长的部分，再画多出来的部分，就不会把 85 cm 当成整条。
bar model = model bar; the extra part = bahagian lebih
Write Diberi first: the red ribbon is 1 m 35 cm and the blue ribbon is 85 cm longer. Dicari: the total length of both. In the model, draw one bar for red; for blue, first draw a part as long as the red bar, then join on the extra 85 cm. The picture shows the blue ribbon is 1 m 35 cm + 85 cm = 2 m 20 cm, and the total is the red bar plus the blue bar.
Example: if the question said 20 cm shorter, the blue bar would be drawn shorter than the red one, with the missing piece marked 20 cm.
Watch out: draw the equal part first and the extra part second, and you will never mistake the 85 cm for the whole bar.
Cara dan Semak
Dua langkah pengiraan
Langkah 1: panjang reben biru · Langkah 2: jumlah
Langkah 1 · biru
| m | cm | |
|---|---|---|
| 1 | ||
| 1 | 35 | |
| + | 85 | |
| 2 | 20 |
Langkah 2 · jumlah
| m | cm | |
|---|---|---|
| 1 | 35 | |
| + | 2 | 20 |
| 3 | 55 |
35 + 85 = 120 cm = 1 m 20 cm → tulis 20, bawa 1
Semak: 3 m 55 cm − 2 m 20 cm = 1 m 35 cm ✓
第一步 = langkah 1；第二步 = langkah 2；进位 = kumpul semula
第一步求蓝缎带：1 m 35 cm + 85 cm，cm 栏 35 + 85 = 120 cm，120 cm 就是 1 m 20 cm，所以 cm 栏写 20，进 1 到 m 栏，m 栏 1 + 1 = 2，蓝缎带 2 m 20 cm。第二步求总长：1 m 35 cm + 2 m 20 cm，cm 栏 55，m 栏 3，总长 3 m 55 cm。检查：3 m 55 cm − 2 m 20 cm = 1 m 35 cm，回到红缎带的长度。
例子：2 m 70 cm + 50 cm → 120 cm → 写 20 进 1 → 3 m 20 cm。
注意：cm 满 100 才进 1 m，不是满 10，也不是满 1 000。
step 1 = langkah 1; step 2 = langkah 2; regrouping = kumpul semula
Step one finds the blue ribbon: 1 m 35 cm + 85 cm. In the cm column 35 + 85 = 120 cm, which is 1 m 20 cm, so write 20 there and carry 1 to the m column, where 1 + 1 = 2; the blue ribbon is 2 m 20 cm. Step two finds the total: 1 m 35 cm + 2 m 20 cm gives 55 in the cm column and 3 in the m column, so 3 m 55 cm. Check: 3 m 55 cm − 2 m 20 cm = 1 m 35 cm, the red ribbon again.
Example: 2 m 70 cm + 50 cm → 120 cm → write 20, carry 1 → 3 m 20 cm.
Watch out: carry 1 m only when the centimetres reach 100, not 10 and not 1 000.
Cuba
Tali A panjangnya 2 m 60 cm. Tali B 95 cm lebih pendek daripada tali A. Berapakah jumlah panjang kedua-dua tali?
比……短 = lebih pendek daripada；两步 = dua langkah
第一步求绳子 B：比 A 短 95 cm，所以用减法，2 m 60 cm = 260 cm，260 − 95 = 165 cm = 1 m 65 cm。第二步求总长：2 m 60 cm + 1 m 65 cm，cm 栏 60 + 65 = 125，写 25 进 1，m 栏 2 + 1 + 1 = 4，答案 4 m 25 cm。1 m 65 cm 只做了第一步；6 m 15 cm 是把“短”当成“长”来加。
例子：A 1 m 50 cm，B 比 A 短 30 cm，B 是 1 m 20 cm，两条共 2 m 70 cm。
注意：lebih pendek 用减法求 B，最后问 jumlah 还要再加一次。
shorter than = lebih pendek daripada; two steps = dua langkah
Step one finds rope B: it is 95 cm shorter than A, so subtract; 2 m 60 cm = 260 cm and 260 − 95 = 165 cm = 1 m 65 cm. Step two finds the total: 2 m 60 cm + 1 m 65 cm gives 60 + 65 = 125 in the cm column, so write 25 and carry 1, and 2 + 1 + 1 = 4 in the m column; the answer is 4 m 25 cm. 1 m 65 cm stops after step one, and 6 m 15 cm treats shorter as longer.
Example: A is 1 m 50 cm and B is 30 cm shorter, so B is 1 m 20 cm and both make 2 m 70 cm.
Watch out: lebih pendek means subtracting to find B, and jumlah means adding once more at the end.
Masalah jisim
Darab dahulu, kemudian tambah
3 bungkus beras dan sebungkus gula
Langkah 1 · beras
| kg | g | |
|---|---|---|
| 1 | ||
| 1 | 500 | |
| × | 3 | |
| 4 | 500 |
Langkah 2 · jumlah
| kg | g | |
|---|---|---|
| 1 | ||
| 4 | 500 | |
| + | 800 | |
| 5 | 300 |
先乘后加 = darab dahulu, kemudian tambah；米 = beras；糖 = gula
3 包米一样重，用乘法：1 kg 500 g × 3。g 栏 500 × 3 = 1 500 g，1 500 g 是 1 kg 500 g，写 500 进 1；kg 栏 1 × 3 + 1 = 4，米共 4 kg 500 g。第二步加上那包糖：4 kg 500 g + 800 g，g 栏 500 + 800 = 1 300，写 300 进 1，kg 栏 5，总共 5 kg 300 g。检查：5 kg 300 g − 800 g = 4 kg 500 g，再 ÷ 3 = 1 kg 500 g。
例子：2 包面粉各 1 kg 200 g，加 1 包 600 g 的盐，共 3 kg。
注意：g 满 1 000 才进 1 kg，不是满 100。
multiply first, then add = darab dahulu, kemudian tambah; rice = beras; sugar = gula
The 3 bags of rice weigh the same, so multiply: 1 kg 500 g × 3. In the g column 500 × 3 = 1 500 g, which is 1 kg 500 g, so write 500 and carry 1; in the kg column 1 × 3 + 1 = 4, so the rice is 4 kg 500 g. Step two adds the sugar: 4 kg 500 g + 800 g gives 500 + 800 = 1 300 in the g column, so write 300 and carry 1, making 5 kg 300 g. Check: 5 kg 300 g − 800 g = 4 kg 500 g, and ÷ 3 gives 1 kg 500 g.
Example: 2 bags of flour at 1 kg 200 g each plus a 600 g packet of salt make 3 kg.
Watch out: grams carry 1 kg only when they reach 1 000, not 100.
Cuba
Jisim beg Amir 3 kg 200 g. Beg Bala 650 g lebih ringan daripada beg Amir. Berapakah jumlah jisim kedua-dua beg?
比……轻 = lebih ringan daripada；书包 = beg
第一步求 Bala 的书包：比 Amir 的轻 650 g，用减法。3 kg 200 g = 3 200 g，3 200 − 650 = 2 550 g = 2 kg 550 g。第二步求总质量：3 kg 200 g + 2 kg 550 g = 5 kg 750 g。2 kg 550 g 只做了第一步；7 kg 50 g 是把“轻”当成“重”，先加了 650 g。
例子：西瓜 2 kg，菠萝比它轻 800 g，菠萝 1 kg 200 g，两个共 3 kg 200 g。
注意：200 g 减 650 g 不够，要向 kg 借 1，借来的是 1 000 g，不是 100 g。
lighter than = lebih ringan daripada; bag = beg
Step one finds Bala's bag: it is 650 g lighter than Amir's, so subtract. 3 kg 200 g = 3 200 g, and 3 200 − 650 = 2 550 g = 2 kg 550 g. Step two finds the total mass: 3 kg 200 g + 2 kg 550 g = 5 kg 750 g. 2 kg 550 g stops after step one, and 7 kg 50 g treats lighter as heavier and adds the 650 g first.
Example: a watermelon is 2 kg and a pineapple is 800 g lighter, 1 kg 200 g, so both are 3 kg 200 g.
Watch out: 200 g minus 650 g will not go, so borrow 1 kg, which is 1 000 g, not 100 g.
Masalah isi padu cecair
Darab dahulu, kemudian bahagi
4 jag jus dituang sama banyak ke dalam 8 botol
Langkah 1 · jumlah jus
| ℓ | mℓ | |
|---|---|---|
| 1 | ||
| 1 | 250 | |
| × | 4 | |
| 5 | 0 |
Langkah 2 · setiap botol
| 6 | 2 | 5 | ||
| 8) | 5 | 0 | 0 | 0 |
5 ℓ = 5 000 mℓ · 5 000 mℓ ÷ 8 = 625 mℓ
Semak: 625 mℓ × 8 = 5 000 mℓ = 5 ℓ ✓
先乘后除 = darab dahulu, kemudian bahagi；橙汁 = jus oren；瓶 = botol
第一步求全部果汁：4 壶一样多，1 ℓ 250 mℓ × 4。mℓ 栏 250 × 4 = 1 000 mℓ，刚好 1 ℓ，写 0 进 1；ℓ 栏 1 × 4 + 1 = 5，共 5 ℓ。第二步平均倒进 8 个瓶子，题目问几 mℓ，先换成 5 000 mℓ，再 5 000 ÷ 8 = 625 mℓ。检查：625 × 8 = 5 000 mℓ，就是 5 ℓ。
例子：3 瓶各 1 ℓ 的水平均倒进 4 个杯子，3 000 ÷ 4 = 750 mℓ。
注意：5 ℓ ÷ 8 不够除，要先换成 mℓ 再除。
multiply first, then divide = darab dahulu, kemudian bahagi; orange juice = jus oren; bottle = botol
Step one finds all the juice: the 4 jugs hold the same amount, so 1 ℓ 250 mℓ × 4. In the mℓ column 250 × 4 = 1 000 mℓ, exactly 1 ℓ, so write 0 and carry 1; in the ℓ column 1 × 4 + 1 = 5, giving 5 ℓ. Step two pours it equally into 8 bottles, and the question asks for mℓ, so change 5 ℓ to 5 000 mℓ first, then 5 000 ÷ 8 = 625 mℓ. Check: 625 × 8 = 5 000 mℓ, which is 5 ℓ.
Example: 3 bottles of 1 ℓ of water poured equally into 4 cups give 3 000 ÷ 4 = 750 mℓ each.
Watch out: 5 ℓ cannot be shared by 8 in whole litres, so change it to mℓ before dividing.
Cuba
Sebotol sirap berisi 2 ℓ. Ibu menggunakan 350 mℓ sirap setiap hari selama 4 hari. Berapakah baki sirap itu?
先乘后减 = darab dahulu, kemudian tolak；糖浆 = sirap
第一步求 4 天共用了多少：350 mℓ × 4 = 1 400 mℓ。第二步求剩下：2 ℓ = 2 000 mℓ，2 000 − 1 400 = 600 mℓ。1 ℓ 650 mℓ 是只减了一天；1 ℓ 400 mℓ 是 4 天用掉的量，题目问的是剩下的。检查：600 + 1 400 = 2 000 mℓ。
例子：一瓶 1 ℓ 的牛奶，每天喝 200 mℓ，喝 3 天，剩 400 mℓ。
注意：每天都用，要先乘天数，再从整瓶减掉。
multiply first, then subtract = darab dahulu, kemudian tolak; syrup = sirap
Step one finds how much is used in 4 days: 350 mℓ × 4 = 1 400 mℓ. Step two finds what is left: 2 ℓ = 2 000 mℓ, and 2 000 − 1 400 = 600 mℓ. 1 ℓ 650 mℓ takes away only one day, and 1 ℓ 400 mℓ is the amount used, while the question asks what remains. Check: 600 + 1 400 = 2 000 mℓ.
Example: a 1 ℓ bottle of milk with 200 mℓ drunk each day for 3 days has 400 mℓ left.
Watch out: the syrup is used every day, so multiply by the days first, then subtract from the whole bottle.
Padankan
Masalah dan ayat matematik
题目配算式 = padankan masalah dengan ayat matematik
“长 40 cm”用加法：1 m 50 cm + 40 cm = 1 m 90 cm。“轻 600 g”用减法：4 kg − 600 g = 3 kg 400 g。“3 瓶一样，每瓶 1 ℓ 200 mℓ”用乘法：3 ℓ 600 mℓ。“平均分进 5 包”用除法：2 kg = 2 000 g，÷ 5 = 400 g。先找关键词，再决定运算。
例子：看到 lebih berat（比较重）就用加法求另一个的质量。
注意：lebih panjang、lebih berat 是加；lebih pendek、lebih ringan 是减。
matching problems to number sentences = padankan masalah dengan ayat matematik
40 cm longer means adding: 1 m 50 cm + 40 cm = 1 m 90 cm. 600 g lighter means subtracting: 4 kg − 600 g = 3 kg 400 g. 3 identical bottles of 1 ℓ 200 mℓ each means multiplying: 3 ℓ 600 mℓ. Shared equally into 5 packets means dividing: 2 kg = 2 000 g, and ÷ 5 gives 400 g. Find the key words first, then choose the operation.
Example: lebih berat (heavier) tells you to add to find the other mass.
Watch out: lebih panjang and lebih berat mean add, while lebih pendek and lebih ringan mean subtract.
Ringkasan
Syabas!
Diberi → Dicari → Cara → Semak
Tulis nombor dengan unit. Lukis model bar: lebih = tambah, kurang = tolak. Masalah dua langkah: siapkan kedua-dua langkah. Tukar unit: 1 m = 100 cm, 1 kg = 1 000 g, 1 ℓ = 1 000 mℓ. Semak dengan operasi songsang.
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