Costume 2 · chemistry + correctionsSun 20 September1 / 4
Balancing equations, and this week's corrections
A puzzle about making counts match. You do not need to know any chemistry
Name Date
Think about thisPut numbers in the boxes so that each kind of ball appears the same number of times on the left and on the right.
□H₂ ＋ O₂ → □H₂O
H₂ is two H balls, O₂ is two O balls, H₂O is two H and one O.
Start by counting the O balls.
1Fill in the boxes above.
The left has 2 O. Each H₂O on the right has 1.
It looks like chemistry, but all you are doing is making two counts match — the same shape as this week's common denominators.
Now you
2Fill in CH₄ ＋ □O₂ → CO₂ ＋ □H₂O
Count C, then H, then O, and you will not get lost.
3Fill in □N₂ ＋ □H₂ → □NH₃
4Fill in □Fe ＋ □O₂ → □Fe₂O₃
O comes in 2s on the left and 3s on the right. Think about the lowest common multiple of 2 and 3.
5Explain in words why a lowest common multiple turns up in question 4.
This week's corrections
6Pick two questions you got wrong this week and do them again.
Solve them again — do not copy the answer across.
Classic problem — planting trees
7Trees are planted along a straight road every 4 m, from one end to the other. The road is 60 m long. How many trees are needed?
60 ÷ 4 = 15, but 15 is not the answer. Draw it.
More of it — a straight road, and a closed loop
8Along the same 60 m road, trees every 5 m. How many trees?
9Round a circular pond, trees every 4 m. If the perimeter is 60 m, how many trees?
10Question 7 and question 9 are both 60 m at 4 m intervals, and the answers differ by one. Why? Explain in words.
The important question today.
11Along both sides of a 48 m road, trees every 6 m. How many altogether?
12Of the whole numbers 1 to 100, how many are multiples of neither 3 nor 4?
Counting multiples of 3 and of 4 counts the multiples of 12 twice.
Extra · you may skip thisTo plant 21 trees along that same 60 m road, how far apart should they be?