Answer key (for a parent)October week 1 · elder son1 / 4
Answers and reasoning
Friday is an introduction. Check for the diagram before checking the answer
Fri 2 Oct — dividing by a decimal
136 ÷ 4 = 9. 0.9 means only the divisor was multiplied by 10.
3Both times 100 → 450 ÷ 5 = 90. Watch for stopping at times 10 (45 ÷ 0.5).
5Both times 100 → 210 ÷ 35 = 6. Read 2.1 as 2.10, so 210.
6A and D (divisor below 1). B gets smaller, C stays 8. D (0.99) is the one usually missed — even slightly below 1 makes the answer bigger.
7Diagram: top (price) 0 · 150 · ?, bottom (length) 0 · 0.6 · 1. 150 ÷ 0.6 = 1,500 ÷ 6 = 250 yen
82.8 ÷ 0.4 = 28 ÷ 4 = 7 cups
92.4 ÷ 0.8 = 24 ÷ 8 = 3 kg
1053 ÷ 7 = 7 remainder 4 → 7 pieces, 0.4 m left. "4 m left" is the classic mistake. Check: 0.7 x 7 + 0.4 = 5.3.
117.2 ÷ 2.4 = 72 ÷ 24 = 3 m
12(1) 180 x 0.6 = 108 yen (2) 108 ÷ 0.6 = 180 yen
In (1) the price of 1 m is known → multiply; in (2) it is what we want → divide. If he can say whether the ? sits above the 1 or above the 0.6, that is enough.
1342 ÷ 3.5 = 420 ÷ 35 = 12 km per litre. 60 ÷ 12 = 5 L
extra4. Four 25-yen amounts make 100 yen; four 0.25s make 1.
Sun 4 Oct — batting averages, points per game, corrections, puzzle
22 wari 7 bu 5 rin; 0.314
326 ÷ 80 = 0.325 = 3 wari 2 bu 5 rin
47 ÷ 24 = 0.2916… → the fourth place is 6, so round up → 0.292 (2 wari 9 bu 2 rin)
5A: 16 ÷ 50 = 0.320, B: 18 ÷ 60 = 0.300 → A. Comparing per at bat, not total hits, is the point of the day.
7(3+1+0+2+4) ÷ 5 = 10 ÷ 5 = 2 goals. Watch for 10 ÷ 4 — leaving out the 0 game.
88-game total 64.5 x 8 = 516; needed for 9 games 65 x 9 = 585 → 585 − 516 = 69 points. As with batting average: can he run "average x count = total" backwards?
9Check against the notebook. Solved the second time means finished.
10All 2-pointers would be 24. 29 − 24 = 5 short. Each swap to a 3-pointer adds 1 → 5 three-pointers (7 two-pointers). Check: 3x5 + 2x7 = 29.
Stretch answers (for a parent)Stretch · elder son3 / 4
Stretch — answers and how to mark them
Not recorded. For the explain items (3, 6, 9, 12) ask for the reason, not only the answer
1 · A night of heavy rain
What it testsScientific context × adding decimals and evening out (a preview of the mean). PISA: retrieve (1) → employ (2) → interpret & evaluate (3). A mean hides the peaks. The air pressure is not needed.
212.5 + 18 + 31.5 + 42 + 24.5 + 9.5 = 138, 138 ÷ 6 = 23 mm
3Not right. 5–6 pm (31.5 mm) and 6–7 pm (42 mm) were both 30 mm or more. 23 mm mixes wet hours with dry ones, so the peak disappears.
Full: "not right" plus an hour of 30 mm or more, with its number.
Partial: "not right" with no number, or only "because it is an average".
None: "right, 23 is less than 30".
2 · Water on a river bend
What it testsScientific context × decimal ÷ decimal and "how many times". PISA: formulate (4) → employ (5) → interpret (6). The water temperature is not needed. Faster water on the outside wears the bank away — the textbook result, backed by numbers.
4Outside 12.6 ÷ 4.2 = 3 m, inside 7.2 ÷ 4.8 = 1.5 m (times ten: 126 ÷ 42, 72 ÷ 48)
6The outside. It moves 3 m a second, twice as fast as the inside (1.5 m). Faster water wears the bank away harder.
Full: "outside" with the speeds (3 m and 1.5 m, or twice) as the reason.
Partial: "outside, because it is faster" with no numbers.
None: "inside", or no reason.
3 · What seeds need to sprout
What it testsScientific context × a rate (as in batting average) and common denominators. PISA: retrieve (7) → employ (8) → evaluate (9). More ≠ a higher rate. "7 days" is not needed.
7A (34). This one deliberately asks only for the count.
8A 34 ÷ 40 = 0.85, B 22 ÷ 25 = 0.88 → B (17⁄20 = 85⁄100, 22⁄25 = 88⁄100)
9Not right. A and B differ only in light. Dark B (0.88) is higher than bright A (0.85). A has more because more seeds were sown (40 against 25). Seeds sprout without light.
Full: notices the numbers sown differ, compares rates, "they sprout in the dark too".
Partial: only "B sprouted in the dark" (no numbers), or rates with no conclusion.
None: "right, A had 34, the most" — or "not right, B only had 22" (right verdict, wrong comparison).
4 · Two fishing boats
What it testsOccupational context × decimal ÷ decimal. PISA: formulate (10, 11 — divide by what?) → evaluate (12). The winner depends on "per what". Crew size is not needed.
10A 378 ÷ 31.5 = 12 kg, B 280 ÷ 17.5 = 16 kg
11A 378 ÷ 4.5 = 84 kg, B 280 ÷ 3.5 = 80 kg
12It depends. Per litre of fuel, B (16 against 12); per hour, A (84 against 80).
Full: uses both "per one" figures and says the verdict changes with the measure (e.g. "if fuel costs matter, B").
Partial: decides on one measure only.
None: "A, it caught 378 kg, more", or no reason.
For a parent. Items 3, 9 and 12 are three faces of one idea — never decide from one number: set the evened-out figure against each hour, the total against the "per one". A reason for any one of them is enough.