1.
A lab hallway has 7 doors in a row, evenly spaced. It is 48 metres from the first door to the last. How far apart are two doors next to each other? Careful — count the gaps, not the doors.
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Answer:
Did you know? Germs are far too small to see. A dot the size of this full stop could hold thousands of bacteria.
2.
On a balance, 3 test tubes weigh exactly the same as 1 beaker. A beaker and a test tube together weigh 32 grams. How much does one test tube weigh? How much does the beaker weigh?
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Answer:
Did you know? Not all germs are harmful. Your gut is home to trillions of helpful bacteria that help you digest your food.
3.
A lab test starts at 9:40 am. It runs for 1 hour 50 minutes, waits 25 minutes, then runs for 40 minutes more. At what time does it finish?
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Answer:
Did you know? Bacteria can split in two in about 20 minutes. One becomes two, two become four — that is how a few turn into millions.
4.
A tray holds 15 sample cups in a row. Every 2nd cup gets a blue dot. Every 3rd cup gets a red dot. How many cups have both dots? How many have no dot at all?
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Answer:
Did you know? A virus is not quite alive on its own. It can only make copies of itself once it gets inside a living cell.
1.
A lab has a 5-litre jug, a 3-litre jug, and a tap. Neither jug has any marks on it. Using only these, how can you measure out exactly 4 litres? Write the steps.
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Answer:
Did you know? Lab work uses exact amounts on purpose. A test can give the wrong answer if a measure is off by even a little.
2.
At a science meeting, 6 scientists each shake hands once with every other scientist. How many handshakes happen in total? Hint: two people share one handshake, so don't count it twice.
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Answer:
Did you know? Handshakes spread germs, which is why hospitals now use gel and elbow-bumps during an outbreak.
3.
Four labs — P, Q, R, and S — are ranked by how many tests they ran. Q ran more than P. S ran fewer than P. R ran more than Q. List the four labs in order, from most tests to fewest.
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Answer:
Did you know? Scientists check each other's work before it is trusted. That review is a big part of how science stays honest.
4.
Two taps fill a sample tank. On its own, tap A fills the tank in 6 hours. Tap B fills the same tank in 4 hours. With both taps running together, how long does the tank take to fill? Think about how much of the tank each tap fills in one hour.
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Answer:
Did you know? Your kidneys are a filter tank of their own. They clean your entire blood supply about 40 times a day.
3rd Grade
1. 8 metres apart.
7 doors in a row have only 6 gaps between them, not 7. So 48 ÷ 6 = 8 metres. Dividing by 7 gives 6.86 — the fencepost trap in reverse. Draw the 7 doors and count the spaces.
2. A test tube is 8 g; the beaker is 24 g.
The beaker weighs the same as 3 test tubes, so a beaker plus a tube is really 4 test tubes. 32 ÷ 4 = 8 g each, and the beaker is 3 × 8 = 24 g. Check: 24 + 8 = 32. ✓
3. 12:35 pm.
9:40 + 1 h 50 min = 11:30. Then + 25 min = 11:55. Then + 40 min = 12:35 pm. Crossing noon is the tricky part — 11:55 + 40 goes past 12:00.
4. 2 cups have both dots; 5 cups have none.
Blue cups: 2, 4, 6, 8, 10, 12, 14 — that is 7. Red cups: 3, 6, 9, 12, 15 — that is 5. Cups 6 and 12 are on both lists, so 2 have both. Marked cups altogether: 7 + 5 − 2 = 10, so 15 − 10 = 5 are bare.
4th Grade
1. Fill the 5, pour into the 3, and 2 is left; empty the 3, move the 2 across, refill the 5, top up the 3 — 4 litres stay in the big jug.
Fill the 5-L jug. Pour it into the 3-L jug until full — that leaves 2 L in the big jug. Empty the 3-L jug, pour the 2 L into it. Fill the 5-L jug again, then top up the 3-L jug — it only needs 1 L more, so 4 L remain in the 5-L jug. There is a longer route too; any that ends at exactly 4 is right.
2. 15 handshakes.
Each of the 6 shakes hands with the other 5, which counts 6 × 5 = 30 — but that counts every handshake twice (once from each side). So 30 ÷ 2 = 15. Answering 30 means he forgot to halve; 36 means he counted people shaking their own hand.
3. R, Q, P, S — most to fewest.
R > Q (R ran more than Q). Q > P. P > S (S ran fewer than P). Chain them: R > Q > P > S. Building the chain one link at a time beats trying to hold all four in mind at once.
4. 2 hours 24 minutes.
In one hour tap A fills 1/6 of the tank and tap B fills 1/4. Together: 1/6 + 1/4. Twelfths: 2/12 + 3/12 = 5/12 of the tank each hour. So the whole tank takes 12/5 hours = 2 2/5 hours = 2 h 24 min. Note it is faster than either tap alone — the sanity check.