Answer key (for a parent)Week 04 · elder son1 / 4
Answers and reasoning
A review week. Watch whether he can name the unit, more than whether he got it right
Fri 25 Sept — mixed review
1Over 20 → 15⁄20 ＋ 8⁄20 = 23⁄20 = 13⁄20
2Factors of 18: 1,2,3,6,9,18 / of 27: 1,3,9,27 → 9
5Over 24 → 20⁄24 − 9⁄24 = 11⁄24
6GCD of 30 and 45 is 15 → side 15 cm, (30÷15)x(45÷15) = 2x3 = 6 squares
7Over 24 → 9⁄24 against 10⁄24 → 5⁄12 is larger
8Over 30 → 21⁄30, 20⁄30, 18⁄30 → 7⁄10 > 2⁄3 > 3⁄5
91 common denominator / 2 factors / 3 cancelling / 4 multiples / 5 common denominator / 6 factors / 7 and 8 common denominator.
Saying 'cancelling uses the GCD, a common denominator uses the LCM' is enough. The naming matters more than the sorting.
Sun 27 Sept — round-up
4LCM of 15 and 20 → 60 seconds
5Over 45 → 36⁄45 against 35⁄45 → 4⁄5 is larger
62560÷320 = 8, 1600÷320 = 5 → 8 : 5
7LCM of 15 and 20 → 60 teeth
94Al ＋ 3O₂ → 2Al₂O₃. O needs the LCM of 2 and 3, which is 6 → three O₂ and two Al₂O₃. That gives 4 Al on the right, so 4 on the left.
Stretch answers (for a parent)Week 04 · elder son · stretch3 / 4
Stretch: answers and how to mark them
Nothing is recorded. The partial-credit notes are for seeing how far the thinking got
1 · Weather club (science × common multiples)
What this story tests (PISA): seeing "recorded together" as a common multiple = formulate → working out the LCM = employ → judging what changes when a condition changes = interpret / evaluate. The 1.5 m is not needed.
1LCM of 20, 30 and 45 is 180 minutes → three hours later, 12:00.
2LCM of 20 and 30 is 60 → every hour: 9, 10 … 17 o'clock, 9 times.
Partial credit: 8 (forgot to count 9:00; the idea is right).
Note: 3 (9:00, 12:00, 15:00) is when all three line up, photo included; this asks only about temperature and rainfall.
310, 12 and 15 minutes — each gives an LCM of 60 with 20 and 30. 25 gives 300 and 40 gives 120, so they do not work.
Full: exactly those three. Partial: two of the three, or all three plus one wrong. None: anything else.
4Not right. The LCM of 10, 20 and 45 is also 180 minutes, so they still line up at 12:00. Every 20-minute time is also a 10-minute time, so only 20 and 45 decide it.
Full: "not right" + why the LCM does not change, e.g. "10 goes into 20, so it stays the LCM of 20 and 45, which is 180", "the LCM of 10, 20, 45 is still 180".
Partial: "not right" alone, or 180 found with no sentence.
None: "right", or "10 minutes is shorter so it comes sooner".
2 · Two islands (social studies × fractions)
What this story tests (PISA): reading fractions off the drawing = employ → noticing a bigger share is not always a bigger area = interpret / evaluate → turning a plan into a calculation = formulate. The populations are not needed.
5Over 24: 1 − 15⁄24 − 4⁄24 − 2⁄24 = 3⁄24 = 1⁄8
Partial: 3⁄24 (not in lowest terms).
6Not right. Island A farmland 48 ÷ 6 = 8 km²; Island B farmland 72 ÷ 8 = 9 km². B has more. The islands are different sizes, so the shares alone cannot compare the areas.
Full: 8 and 9 found, "not right" + reason, e.g. "the islands are different sizes, B has 1 km² more".
Partial: 8 and 9 right but no conclusion or reason; or no calculation but "the wholes are different, so you can't tell".
None: "right" (compared the fractions only).
71 − 1⁄4 − 1⁄12 − 1⁄8 = 24⁄24 − 6⁄24 − 2⁄24 − 3⁄24 = 13⁄24 (forest falls from 15⁄24 by 2⁄24; as area, 26 km²)
3 · Releasing young fish (social studies × common factors, odd & even)
What this story tests (PISA): seeing "the same number each, none left" as a common factor = formulate → the GCD and listing common factors = employ → using odd / even to say "impossible" when the numbers change = interpret / evaluate. The lengths and the 3 boats are not needed (if he used "3 boats", talk about that).
8GCD of 84 and 60 → 12 points, each with 7 bags of flounder and 5 of sea bream.
9Common factors 1, 2, 3, 4, 6, 12; the even ones → 2, 4, 6, 12 points.
Partial: only 12, or 1 or 3 mixed in.
10(1) No. 65 is odd — it does not divide by 2 — so it cannot be shared equally over an even number of points. (84 and 65 have only 1 as a common factor → just 1 point.)
Full: "no" + either reason (odd / only common factor 1). Partial: "no" alone. None: "yes".
(2) 1 bag (66 bags: the GCD of 84 and 66 is 6). Going down to 64 only allows 4.
For a parentNo score. Look at the one-sentence answers in 4, 6 and 10 (1) — whether he could write a reason is the heart of the stretch, even when the sum is right. Missed items do not go into the corrections notebook; the same shape comes back in next month's stretch.