1. GUIDED
A rectangular tray of blood samples covers 72 square centimetres. One side measures 9 cm. How long is the other side? What is the perimeter all the way around the tray?
Area = one side × the other side, so 72 ÷ 9 =
So the other side measures cm
Perimeter = 9 + + 9 + = cm
Answer:
Did you know? White blood cells are made inside your bones, in the soft marrow at the centre.
2.
A clinic packs 75 vaccine vials into trays. Each tray holds 8. How many trays go out completely full, and how many vials are left over? Then: how many trays are needed to carry every vial?
SHOW YOUR THINKING
Answer:
Did you know? A vaccine works by showing your immune system a harmless piece of a germ, so it can practise before the real one arrives.
3.
A lab grows 128 cell samples a day for 7 days. Then 94 of them are found spoiled and thrown out. How many good samples are left?
SHOW YOUR THINKING
Answer:
Did you know? Your body makes billions of new white blood cells every single day, and most of them last only a few days.
4.
Two vials of serum sit on the bench. One is 5/8 full. The other is 2/3 full. Which vial holds more? How do you know?
SHOW YOUR THINKING
Answer:
Did you know? Tears and saliva both contain an enzyme that breaks bacteria apart — your eyes and mouth are defending you all day.
5.
A rectangular culture plate has a perimeter of 46 cm. One side measures 14 cm. How long is the other side? What is the area of the plate?
SHOW YOUR THINKING
Answer:
Did you know? Fever is not the germ hurting you — it is your body turning the heat up on purpose, because most germs breed badly when they are too warm.
1. GUIDED
A course of medicine is 8.4 mL in total. So far 3.75 mL has been given. How much is still to be given?
Give 8.4 the same number of decimal places as 3.75:
Line up the decimal points, then subtract:
So the amount still to give is mL
Answer:
Did you know? Antibodies are Y-shaped, and each kind locks onto one specific germ and nothing else — like a key cut for a single door.
2.
A researcher prepares 34 slides, and counts 26 antibodies on each one. How many antibodies is that altogether?
SHOW YOUR THINKING
Answer:
Did you know? Memory cells are why you usually catch chickenpox only once — some of them can still recognise the virus decades later.
3.
A hospital logs 1,347 cell counts and sorts them into batches of 6. How many complete batches are there, and how many counts are left over?
SHOW YOUR THINKING
Answer:
Did you know? Your lymph system has no pump of its own. It only moves when you move, which is one reason walking helps you shake off an illness.
4.
One study covers 3/8 of the samples in a freezer. A second study covers another 1/3 of them. What fraction of the freezer is covered by the two studies together?
SHOW YOUR THINKING
Answer:
Did you know? Most of your immune system sits around your gut — the body puts its defences where the outside world comes in.
5.
Antibody test strips cost $0.35 each. A clinic buys 240 of them and pays with $100. What do the strips cost altogether, and how much change comes back?
SHOW YOUR THINKING
Answer:
Did you know? The thymus, the gland that trains your T-cells, is at its biggest when you are a child and slowly shrinks for the rest of your life.
3rd Grade
1. Other side 8 cm; perimeter 34 cm.
Area = side × side, so 72 ÷ 9 = 8 cm. Perimeter goes all the way round: 9 + 8 + 9 + 8 = 34 cm.
2. 9 full trays, 3 left over — but 10 trays to carry them all.
75 ÷ 8 = 9 remainder 3. Those 3 spare vials still have to travel, so one more tray: 10.
3. 802 samples.
128 × 7 = 896, then 896 − 94 = 802.
4. The 2/3 vial.
Same bottom number — twenty-fourths: 5/8 = 15/24, 2/3 = 16/24. Sixteen beats fifteen, so the smaller-looking fraction wins.
5. Other side 9 cm; area 126 square cm.
Half the perimeter is one of each side: 46 ÷ 2 = 23. Then 23 − 14 = 9 cm. Area = 14 × 9 = 126 square cm.
4th Grade
1. 4.65 mL.
Pad the short one: 8.4 becomes 8.40. Then 8.40 − 3.75 = 4.65 mL. Skipping the padding is what produces 5.65 or 4.75.
2. 884 antibodies.
34 × 26. Split it: (34 × 20) + (34 × 6) = 680 + 204 = 884.
3. 224 complete batches, 3 left over.
1,347 ÷ 6 = 224 remainder 3. Walk it: 13÷6 = 2 r1, bring down 4 → 14÷6 = 2 r2, bring down 7 → 27÷6 = 4 r3. Check: 1,344 + 3 = 1,347. ✓
4. 17/24 of the freezer.
Twenty-fourths work for both. 3/8 = 9/24 and 1/3 = 8/24, so 9/24 + 8/24 = 17/24. Add the tops, keep the bottom.
5. $84 for the strips; $16 change.
240 × $0.35 = (240×0.3) + (240×0.05) = 72 + 12 = $84. Change: $100 − $84 = $16.