Unit 12
Selesaikan Masalah
Masalah matematik boleh diselesaikan dengan 4 langkah: ① Fahami soalan ② Rancang cara ③ Selesaikan ④ Semak jawapan.
解决问题 = selesaikan masalah
解题有四个步骤：先读懂题目（fahami），想好方法（rancang），计算或推理（selesaikan），最后检查答案（semak）。常用的方法有：做表格、画图找规律、用数线倒推。
例子：比较两个人的步数或游戏得分时，可以先把数目放进数位表，再逐位比较。
注意：答案写完要回到题目检查一次，看看有没有回答题目真正问的东西。
solve problems = selesaikan masalah
There are four steps: understand the question (fahami), plan a method (rancang), solve (selesaikan) and check the answer (semak). Useful methods include making a table, drawing a diagram to see a pattern and working backwards on a number line.
Example: to compare two step counts or two game scores, put the numbers in a place value table and compare place by place.
Watch out: after answering, go back to the question and check that you answered what it really asked.
Cara 1: Buat jadual
Langkah Aina 3 507, langkah Boon 3 570
| ribu | ratus | puluh | sa | |
|---|---|---|---|---|
| Aina | 3 | 5 | 0 | 7 |
| Boon | 3 | 5 | 7 | 0 |
Digit sama nilai: 3 (ribu) dan 5 (ratus)
3 507 lebih kecil daripada 3 570 → langkah Aina lebih sedikit
做表格 = buat jadual；数值相同 = sama nilai
把两个数目按数位放进表格，上下对齐。上下一样的数字，就是“数值相同的数字”；第一个不一样的数位决定谁大谁小。
例子：4 128 和 4 182 → 4 和 1 数值相同；十位 2 比 8 小 → 4 128 比较小。
注意：7 在个位和 7 在十位，数值不同。
make a table = buat jadual, same value = sama nilai
Put both numbers into a place value table, lined up. Digits that match in the same place have the same value; the first place that differs decides which is greater.
Example: 4 128 and 4 182 → 4 and 1 have the same value; tens 2 is less than 8 → 4 128 is smaller.
Watch out: a 7 in the ones place and a 7 in the tens place have different values.
Cuba
Langkah Dina 6 473 dan langkah Hafiz 6 437. Siapakah berjalan lebih banyak langkah?
谁的步数比较多 = siapa lebih banyak langkah
把 6 473 和 6 437 放进数位表，逐位比较：千位、百位相同时看十位。
例子：思考方法像这样：7 341 和 7 314 → 十位 4 比 1 大。
注意：两个数的数字一样，只是十位和个位对调了。
who walked more steps = siapa lebih banyak langkah
Put 6 473 and 6 437 in a place value table and compare place by place: when the thousands and hundreds match, look at the tens.
Example: think like this: 7 341 and 7 314 → tens 4 is more than 1.
Watch out: the numbers use the same digits with the tens and ones swapped.
Fikir lagi
3 507 dan 3 570 menjadi 4 000 apabila dibundarkan kepada ______ terdekat.
约到哪一位 = bundar kepada tempat apa
把两个数分别约到十、约到百、约到千，看看哪一种结果两个都是 4 000。约到十、约到百时，十位和个位还会留下不同的数字。
例子：7 346 和 7 352 约到十都是 7 350（约到百是 7 300、7 400）。
注意：结果最后三位都是 0，这是一个提示：约到千才会让百、十、个位都变成 0。
round to which place = bundar kepada tempat apa
Round both numbers to the nearest ten, hundred and thousand, and see which one gives 4 000 for both. Rounding to tens or hundreds still leaves different digits.
Example: 7 346 and 7 352 both round to 7 350 at the nearest ten (to the nearest hundred they are 7 300 and 7 400).
Watch out: the result ends in three zeros; that is a clue that only rounding to the thousand makes the hundreds, tens and ones all 0.
Cara 2: Lukis gambar rajah
Cari nombor gerai ke-7
ke-12 405ke-22 410ke-32 415ke-4?ke-5?ke-6?ke-72 435
+5 setiap gerai → 2 420, 2 425, 2 430, 2 435
画图 = lukis gambar rajah；第 n 个 = yang ke-n
题目给了前面几个数，要求第几个数时，先画出够数的格子，把已知的数写进去，找出每次加几，再一格一格推下去，直到要找的那一格。
例子：座位号码 1 506、1 509、1 512 → 每次加 3 → 第 6 个是 1 521。
注意：第 7 个数只比第 1 个数多加 6 次，不是 7 次；画格子可以避免多算或少算。
draw a diagram = lukis gambar rajah, the nth one = yang ke-n
When you know the first few numbers and need a later one, draw enough boxes, fill in what you know, find the step, and continue box by box until you reach the one you need.
Example: seat numbers 1 506, 1 509, 1 512 → add 3 each time → the 6th seat is 1 521.
Watch out: the 7th number is the 1st number plus 6 steps, not 7; drawing boxes stops you counting one too many or too few.
Cuba
Loker murid dinomborkan menurun empat-empat. Loker pertama bernombor 5 210. Apakah nombor loker kelima?
第五个 = yang kelima
画五个格子，第一格写 5 210，然后每一格减 4，一直写到第五格。
例子：从 6 245 按 5 递减 → 6 245、6 240、6 235、6 230，第四个是 6 230。
注意：从第一格到第五格只减 4 次，减 5 次会得到第六格。
the fifth one = yang kelima
Draw five boxes. Write 5 210 in the first box, then subtract 4 for each box until you reach the fifth.
Example: counting down in fives from 6 245 → 6 245, 6 240, 6 235, 6 230, so the fourth is 6 230.
Watch out: from the first box to the fifth there are only 4 subtractions; 5 subtractions would give the sixth box.
Cuba
Tujuh gerai tadi (2 405 hingga 2 435) disusun semula dalam tertib menurun. Gerai 2 415 berada di kedudukan ke berapa?
递减排列后的位置 = kedudukan dalam tertib menurun
由大到小重新排：先写最大的 2 435，再写 2 430、2 425……一边写一边数位置，找到 2 415 在第几个。
例子：4 715、4 725、4 735、4 745 由大到小排 → 4 725 在第 3 个。
注意：由小到大时 2 415 是第 3 个，由大到小时变成第 5 个，位置变了，所以一定要重新数，不能照抄原来的位置。
position in descending order = kedudukan dalam tertib menurun
Reorder from greatest to smallest: write the greatest, 2 435, then 2 430, 2 425 and so on, counting the positions until you reach 2 415.
Example: 4 715, 4 725, 4 735, 4 745 in descending order → 4 725 is in the 3rd place.
Watch out: in ascending order 2 415 is 3rd, but in descending order it becomes 5th, so always count again instead of copying the old position.
Cara 3: Bekerja ke belakang
Garis nombor
2 290
2 295
2 300
2 305
2 310
Puluh terdekat → 2 300
2 295 hingga 2 304
倒推 = bekerja ke belakang
题目只告诉你约好的结果，要找出原来可能是哪些数。在数线上找出会约成这个结果的范围：比它小 5 到比它大 4。
例子：约到十是 4 860 → 原来的数是 4 855 到 4 864。
注意：4 865 约到十会变成 4 870，所以不在范围内；4 855 却在范围内。
work backwards = bekerja ke belakang
The question only gives the rounded result, and you must find what the original number could be. On a number line, find the range that rounds to it: from 5 below to 4 above.
Example: rounded to the nearest ten it is 4 860 → the original is 4 855 to 4 864.
Watch out: 4 865 would round to 4 870, so it is not in the range, but 4 855 is.
Cuba
Bilangan murid dibundarkan kepada puluh terdekat menjadi 1 250. Nombor manakah mungkin?
可能 = mungkin
把每个选项约到十，看看哪一个会变成 1 250。也可以先算出范围：1 245 到 1 254。
例子：约成 3 480 的数在 3 475 到 3 484 之间。
注意：个位 5 以上要进位。
possible = mungkin
Round each option to the nearest ten and see which becomes 1 250. You can also find the range first: 1 245 to 1 254.
Example: numbers that round to 3 480 lie from 3 475 to 3 484.
Watch out: a ones digit of 5 or more rounds up.
Ringkasan
Syabas!
Fahami · Rancang · Selesaikan · Semak
Gunakan jadual, gambar rajah atau garis nombor untuk menyelesaikan masalah.
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