Answer key (for a parent)Week 04 · younger son1 / 4
Answers and reasoning
A review week. Question 1 is still handed over already worked
Fri 25 Sept — mixed review
4428 ÷ 5 = 85 remainder 3 (5x85+3 = 428 ✓)
8905 ÷ 7 = 129 remainder 2 (7 x 129 + 2 = 905 ✓)
9A billion is 1,000,000,000 and ten million is 10,000,000 → 100 times
12174 ÷ 8 = 21 people, 6 stickers left over
extra42 | 000 | 000 → 42 million
Sun 27 Sept — round-up
3100 ÷ 7 = 14 remainder 2 → 14 each, 2 left
7204,000,000. The zero in the middle is the part to watch.
9620 ÷ 9 = 68 remainder 8 (9 x 68 + 8 = 620 ✓)
116,000,000,000,000 → twelve zeros
Stretch answers (for a parent)Week 04 · younger son · stretch3 / 4
Stretch: answers and how to mark them
Nothing is recorded. Praise it as "how many stages he got through"
For a parentThe stretch is handed over as a "level up". Do not mark ticks and crosses; put into words how far he got — "you reached stage 2". Stopping at 20 minutes is the rule. If he says "we haven't learnt this", do not argue; skipping is fine. Each stage hides one unneeded number (18 schools, 18 °C, 36 trucks, distance from the sea). Circling it is worth praising too.
Stage 1 · Water (social studies × big numbers, ÷ 1 digit)
What it tests (PISA): choosing the needed numbers from a table → dividing in "blocks of ten million" = employ → judging the size of an answer = interpret.
2560 million is 56 blocks of ten million. 56 ÷ 7 = 8 → 80 million L
33 billion is 300 blocks of ten million. 300 ÷ 8 = 37 r 4 → just over 37 days → B (about 40 days)
Full: B + a division or estimate. Partial: B alone, or 37 found but another letter chosen. None: A or C with no working.
Stage 2 · Rainwater (science × ÷ 1 digit, graph)
What it tests (PISA): reading a graph = employ → dividing to find "per drain" → checking every hour against the 6,000 L limit = interpret / evaluate.
6Only 63,000 is more than 9 × 6,000 = 54,000 L → hour 3 only (hour 4: 45,000 ÷ 9 = 5,000 L, fine).
Full: 3 only. Partial: 3 and 4 (took 45,000 as too much). None: 3 missing.
Stage 3 · Rubbish (social studies × ten times, a tenth, working back)
What it tests (PISA): turning sentences into calculations (a tenth, □) = formulate → ten times, a tenth, dividing in blocks = employ. Question 9 uses the answer to 7; if 7 was wrong but 9 is done correctly from it, give partial credit.
7A tenth of 600 million → 60 million kg
870 million × 10 = 700 million kg (undoing a tenth is ten times)
9420 million is 42 blocks of ten million, 60 million is 6. 42 ÷ 6 = 7 years
Stage 4 · Shelters (social studies × ÷ 1 digit, what a remainder means)
What it tests (PISA): deciding what the remainder means here (round up) = interpret → a two-step plan that finds "one day's water" first = formulate. Question 11 previews October's "what a remainder means".
1195 ÷ 8 = 11 r 7. The 7 left over need a room too → 12 rooms
Full: 12. Partial: "11 r 7" (the division is right). None: anything else.
12One day: 480 × 3 = 1,440 L. 1,440 → 2,880 → 4,320 is three lots → B (3 days)
Full: B + a reason, e.g. "they need 1,440 L a day, so 3 days is 4,320 L".
Partial: B alone, or got as far as 1,440.
None: C (4,320 ÷ 480 = 9 is litres per person, not days — worth looking at together).