For a parent. These are the answers (4 A4 sheets). They are in nothing the child is given.

Answer key (for a parent)October week 1 · younger son1 / 4

Answers and reasoning

A new unit. If he says he has not learnt it, go back to the worked question 1

Fri 2 Oct — rounding

(printed) 2,700

tens digit 6 → up → 5,200

tens digit 4 → down → 8,300. Watch for 8,400 from looking at the 9.

hundreds digit 4 → down → 38,000. Watch for 39,000 from looking at the 9.

tens digit 5 → up; 69 hundreds becomes 70 → 7,000

hundreds digit 4 → 24,000. Watch for rounding twice (→ 24,500 → 25,000).

third digit 8 → up → 48,000

smallest 75, largest 84

at least 550 and less than 650. 650 itself rounds to 700, hence "less than".

A and B (2,950 → 3,000; 3,049 → 3,000). C is 2,900, D is 3,100.

200 + 300 + 500 = about 1,000 yen (really 999)

300 + 400 + 200 = 900 → enough (really 790). 305 → 400 is rounding up (ordinary rounding would give 300). Even an over-estimate is under 1,000, so it is certainly enough. Saying that is the full answer.

50 x 20 = about 1,000 yen (really 1,008)

Answer key (for a parent)October week 1 · younger son2 / 4

Answers and reasoning

Sun 4 Oct — costume, corrections, puzzle

1-1

42 ÷ 6 = 7

1-2

80 ÷ 4 = about 20

1-3

20+20+30+30+10 = about 110 (really 111)

2-1

300 ÷ 6 = 50 yen

2-2

400 ÷ 8 = about 50 yen

2-3

A: 300 ÷ 5 = 60, B: 450 ÷ 9 = 50 → B is cheaper. The cheaper packet (A) is not the cheaper biscuit.

tens digit 4 → 7,600

45 to 54 (at least 45, less than 55)

50 x 40 = about 2,000 yen (really 1,976)

Check against the notebook.

30 ÷ 5 = 6 gaps; both ends planted, so 6 + 1 = 7 trees. If he says 6, count the trees in his drawing together. Gaps and trees are off by one.

hundreds digit 4 → 3,000 (not 4,000)

Stretch answers (for a parent)Stretch · younger son3 / 4

Stretch — answers and how to mark them

Not recorded. One sheet, or half of one, is fine — praise what got done

1 · Sunny day and rainy day

What it tests

Scientific context × a line graph — the familiar way in. PISA: retrieve (1, 2) → interpret & evaluate (3). The key skill is the scale. The 15 mm of rain is not needed. Links to the science fact that sunny days swing more.

(printed) 20 °C

Sunny: highest 26 °C (2 pm), lowest 14 °C (6 am)
Rainy: highest 19 °C, lowest 17 °C

Not right. Sunny 26 − 14 = 12 °C, rainy 19 − 17 = 2 °C. The sunny day changes more.
Full credit: both gaps (12 and 2) and "not right".
Partial: correct but no numbers, e.g. "the sunny line goes up and down more".
No credit: "right", or looking only at one temperature.

2 · Water used at home

What it tests

Societal context × rounding, estimating, ÷ one digit, big numbers. PISA: employ (4, 5) → formulate and evaluate (6). The 4,800-yen bill is not needed.

Toilet 200 L, washing 100 L

200 + 200 + 100 + 100 + 100 = about 700 L. Exactly 720 L (20 L apart).

Not right. Per person 720 ÷ 4 = 180 L. 180 × 50,000 = 9,000,000 L — far less than 100,000,000 (about a tenth).
Full credit: reaches 9 million L and says "not more".
Partial: 180 L correct, or 9 million reached but not compared with 100 million.
No credit: "right, the numbers are big" with no working.

Stretch answers (for a parent)Stretch · younger son4 / 4

Stretch — answers and how to mark them

3 · Ready for a disaster

What it tests

Personal/societal context × multiplying, dividing and estimating. PISA: formulate (7) → employ (8) → evaluate (9). If every price rounds down, the estimate falls short. The 1,980-yen radio is not needed.

3 × 4 × 3 = 36 L. 36 ÷ 12 = 3 boxes.

400 + 300 + 200 = about 900 yen

Not enough. 448 + 348 + 249 = 1,045 yen, over 1,000. All three had a 4 in the tens and rounded down, so the estimate came out low.
Full credit: 1,045 yen and "not enough" — or "all three were rounded down, so the real cost is more than 900" and "it may not be enough".
It is the mirror image of Friday's Q12 (round up when you need to be sure it is enough).
Partial: "not enough" with a wrong sum, or the right sum with no conclusion.
No credit: "enough, because 900 is less than 1,000".

4 · Comparing prefectures

What it tests

Societal context × rounding big numbers and "how many times". PISA: employ (10, 11) → evaluate (12). The areas are not needed.

2,400,000

2 + 1 + 5 + 1 million = about 9 million (exactly 9,322,024)

Right. 680 thousand × 7 = 4,760 thousand, less than Sky's 5,050 thousand (exactly 682,045 × 7 = 4,774,315 < 5,049,760).
Full credit: works out 7 times Peach, compares with Sky, says "right".
Partial: 7 times worked out but not compared, or stops at "about 7 times".
No credit: decides with no calculation.