1. GUIDED
A mason loads 59 stones onto carts. Each cart holds 7. How many carts go out completely full, and how many stones are left over? Then: how many carts does he need to move every stone?
59 ÷ 7 = remainder
Carts that go out completely full:
The leftover stones still need a cart, so carts needed:
Answer:
Did you know? Masons carved a personal mark into each stone they cut, because they were paid by the stone.
2.
94 archers are posted to the towers. Each tower holds 8 archers. How many towers are needed so that every archer has a place?
SHOW YOUR THINKING
Answer:
Did you know? An arrow slit is narrow on the outside and wide on the inside, so the archer can swing his aim while staying a tiny target.
3.
A wall crew lays 136 bricks a day for 6 days. Then 87 bricks are found cracked and pulled back out. How many bricks are left in the wall?
SHOW YOUR THINKING
Answer:
Did you know? Many castle walls were whitewashed. The Tower of London's keep is called the White Tower for exactly that reason.
4.
Two water barrels stand in the courtyard. One is 5/6 full. The other is 3/4 full. Which barrel holds more water? How do you know?
SHOW YOUR THINKING
Answer:
Did you know? Most castle moats were dry. A ditch was there to stop attackers tunnelling under the wall, not to hold water.
5.
A rectangular courtyard covers 96 square metres. One side measures 8 m. How long is the other side? What is the perimeter all the way around?
SHOW YOUR THINKING
Answer:
Did you know? The base of a castle wall was often built sloping outward, so a stone dropped from above bounced off it into the attackers.
1. GUIDED
A cistern is filled in two goes. In the morning 2/5 of it is filled. In the afternoon another 1/3 is filled. How much of the cistern is full?
A common bottom number for 5 and 3 is
2/5 = /15 and 1/3 = /15
Now add the top numbers only, keep the bottom:
Answer:
Did you know? A castle under siege lost to thirst long before hunger, so the well was usually the first thing dug.
2.
A grain store is 5/6 full. Over the winter, 2/9 of the store is eaten. How much grain is left?
SHOW YOUR THINKING
Answer:
Did you know? Grain was stored high up and dry, because damp grain rots and a rotten store could end a siege on its own.
3.
One quarry sends 5/6 of a cartload of lime. Another sends 3/4 of a cartload. How much lime arrives altogether? Give your answer as a mixed number.
SHOW YOUR THINKING
Answer:
Did you know? Lime mortar sets slowly and keeps hardening for years, which is why 900-year-old walls are still standing.
4.
A castle has 47 arrow slits. Each one is stocked with 36 arrows. How many arrows is that altogether?
SHOW YOUR THINKING
Answer:
Did you know? A trained longbowman could loose about ten arrows a minute, so a well-stocked slit emptied fast.
5.
A workshop makes 288 arrowheads in 6 days, working at a steady rate. At that same rate, how many would it make in 11 days? If 37 of those fail inspection, how many good arrowheads are there?
SHOW YOUR THINKING
Answer:
Did you know? A portcullis was dropped, not lowered — its own weight was the whole point, and winching it back up took several people.
3rd Grade
1. 8 full carts, 3 left over — but 9 carts to move them all.
59 ÷ 7 = 8 remainder 3. Those 3 spare stones still have to travel, so one more cart: 9.
2. 12 towers.
94 ÷ 8 = 11 remainder 6. Eleven towers leaves 6 archers standing in the yard, so the answer is 12, not 11.
3. 729 bricks.
136 × 6 = 816, then 816 − 87 = 729.
4. The 5/6 barrel.
Give them the same bottom number. Twelfths work: 5/6 = 10/12 and 3/4 = 9/12. Ten twelfths beats nine.
5. Other side 12 m; perimeter 40 m.
Area = side × side, so 96 ÷ 8 = 12 m. Perimeter = 8 + 12 + 8 + 12 = 40 m.
4th Grade
1. 11/15 of the cistern.
Fifteenths work for both. 2/5 = 6/15 and 1/3 = 5/15, so 6/15 + 5/15 = 11/15. Add the tops, keep the bottom.
2. 11/18 of the store.
Eighteenths: 5/6 = 15/18 and 2/9 = 4/18. 15/18 − 4/18 = 11/18.
3. 1 7/12 cartloads (that is 19/12).
Twelfths: 5/6 = 10/12 and 3/4 = 9/12. 10/12 + 9/12 = 19/12, which is more than a whole, so 1 7/12.
4. 1,692 arrows.
47 × 36. Split it: (47 × 30) + (47 × 6) = 1,410 + 282 = 1,692.
5. 528 arrowheads, 491 of them good.
Find the one-day rate first: 288 ÷ 6 = 48 a day. Then 48 × 11 = 528. Finally 528 − 37 = 491 good ones.