Module 3
The Translation Table.
直訳表 （Chokuyaku-hyō）
帰国子女・インターナショナルスクール生のための、デジタルSAT 数学の無料教材。独学で進められます。
Word problems are not puzzles. They are sentences written in a code that maps, phrase by phrase, onto symbols. Memorise the table below and most sentences convert mechanically.
One exception, and it matters more than the rule. Translating strictly left to right works for +, × and =, but it is wrong for the subtraction phrases in Module 1 — "six less than 2x" is 2x − 6, not 6 − 2x. Convert in order, then check whether any reversal phrase appeared.
| English | Symbol | 日本語 |
|---|---|---|
| is, are, was, will be, equals | = | 〜は〜である |
| a number, what number | x | ある数 |
| sum, more than, increased by, added to | + | 和・増加 |
| difference, less than, decreased by, fewer than | − | 差・減少 |
| product, times, twice, of (with a fraction or percent) | × | 積・〜倍 |
| quotient, per, divided by, ratio of | ÷ | 商・〜あたり |
Translate in order. "Three more than twice a number is 17."
three more than → + 3 · twice a number → 2x · is → = · 17 → 17
Result: 2x + 3 = 17
日本人がハマる理由
日本語は助詞で文法上の役割を示します。「ある数に3を足す」なら、語順を入れ替えても、何に何を足すのかは変わりません。英語にはこれに当たる助詞がなく、語順だけが情報です。語順ではなく意味で読む帰国生は、たいてい違う式を立て、その式には正しく答えてしまいます。文の意味を考える前に、前から順に、機械的に記号へ置き換えてください。
練習問題
難易度は出題者による目安です。College Board の判定ではありません。
Three more than twice a number is 17. What is the number?
Correct Answer: B
Explanation: 2x + 3 = 17 → 2x = 14 → x = 7.
- (A) 5: This is
(17 − 2) ÷ 3— the 2 and the 3 have swapped roles. "Twice" multiplies; "three more" adds. - (C) 10: This is
(17 + 3) ÷ 2. The 3 was added instead of subtracted when undoing the equation. - (D) 34: This is
2 × 17— the operation was applied to the answer rather than undone.
Difficulty Justification
Rated Easy: a two-step translation with small integers. It is here to set the mechanical habit that the reversal phrases in Module 1 ("less than", "subtracted from") try to break.
The sum of a number and 8 is equal to three times the number. What is the number?
Correct Answer: B
Explanation: x + 8 = 3x → 8 = 2x → x = 4.
- (A) 2: From
8 = 4x: thexwas moved to the right side with the wrong sign (3x + xinstead of3x − x). - (C) 8: The number given in the sentence, copied out. It is a quantity in the problem, not the answer.
- (D) 12: This is
3 × 4— the correct value of "three times the number", but the question asked for the number. See Module 8.
Difficulty Justification
Rated Easy, but choice D is deliberately the correct answer to a question that was not asked — the habit Module 8 is about.
One-third of a number, increased by 6, is 14. What is the number?
Correct Answer: C
Explanation: "One-third of a number" → x/3. So x/3 + 6 = 14 → x/3 = 8 → x = 24.
- (A) 8: This is
x/3, notx— the intermediate value, one step short. - (B) 18: From
x/3 = 6→x = 18: the 6 was taken as the value of one-third of the number and the 14 was dropped. "Increased by 6" means 6 is added tox/3. - (D) 60: From
x/3 = 14 + 6 = 20→x = 60: the 6 was added instead of subtracted when undoing "increased by 6".
Difficulty Justification
Rated Medium: the comma after "number" carries the grouping. English uses punctuation where Japanese would use a particle, so this is precisely where a returnee's instinct gives no help.