The Rock Pool
Find strategies for investigating number problems.
At one level this problem is very much like Pigs and Ducks, Level 2 but here we have three creatures and three body parts rather than the two of each in that problem. The methods used in Pigs and Ducks though can be used here. Guess and check, make a table will all work.
If this problem was posed at Level 6, then the students there could tackle it by setting up some equations. However, there is no need for that sort of heavy machinery here. There are a few clever ways to solve this one just as there were with Pigs and Ducks.
This suggests a general problem solving strategy. That is, try a simple approach first. Sometimes heavy machinery can get in the way. But it’s important that the class writes up their solution so that they can be sure that it worked.
Some octopuses, some fish and a few mermaids were happily frolicking in a rock pool. Altogether there were 38 arms, 24 eyes and 8 tails all swimming in the pool.
How many mermaids were there?
- State the problem. Get the class to think about it. Ask
What are the key numbers?
What is the key information?
How will you use the fact that there are octopuses? mermaids? fish?
- After some discussion, let the class go into their groups to tackle the problem.
- Help groups that need it.
Tell me the information that you are using. Write it down in some way.
What information can you get from these facts?
For the quicker groups, encourage them to try the Extension.
- Let a few groups report back to the whole class. As there are a number of ways of doing this question try to choose groups that have done things differently.
- Leave time for students to write up their solutions (or let them do this as homework).
Extension to the problem
Write a problem like this one that has three types of creature and three body parts. Or be more original and try something other than creatures.
Let’s first of all write down the information we have. Fish don’t have arms so the arms come from the octopuses and the mermaids. All of the creatures have two eyes and since there are 24 eyes there must be 12 creatures. Octopuses don’t have tails so there are 8 fish and mermaids.
Ah! That seems to be the first break through. 12 creatures, 8 of which are fish and mermaids, so there are 12 – 8 = 4 octopuses.
Now the octopuses contribute 4 x 8 = 32 arms. That leaves 38 – 32 = 6 arms for the mermaids. There must be 3 mermaids.
This problem can also be done using a diagram – draw all the arms, eyes and tails and enclose them in a shape to represent the creatures; or a table – using guess and check. If a group decides on guess and check and gets the right answer, you might like to suggest that they try to find another way.