STRATEGY 3: GUESS AND CHECK
Often when presented with a problem, you are encouraged to guess the answer. For example, "What's the largest city in the world? Take a guess." You guess Istanbul. "No, it's Tokyo," you are told. "How many people live in Tokyo? Take a guess." You say you don't know. "Go on, take a guess," you're told again. You guess 15 million. "No, 34 million!"
Guessing often produces the wrong answer. But the strategy called "Guess and Check" often produces the right answer. It should probably be called "Guess and Check and Guess Again," because the process of checking the accuracy of each guess and then making another, more informed guess is an essential part of the strategy.
For example, here is a problem:
Busra went to her grandfather's farm. Her grandfather has chickens and goats on his farm. She asked him how many chickens and how many goats. Because her grandfather likes mathematical puzzles, he told her that his animals had 26 heads and 68 legs and from that information she could calculate the number of chickens and the number of goats. If you were Busra, how would you solve the problem?
To use the Guess and Check strategy, you think about the problem and start by making a guess. You expect your first guess to be wrong, but it will give you some information to help you make a better guess next time. You could start by guessing 13 chickens and 13 goats. It's a good idea to keep a record of your guesses, like this:
Guess

Chickens 
Goats 
Number of heads 
Number
of legs 
1 
13 
13 
26 
78 










You see that the number of legs you guessed is too high, because Busra's grandfather said that there are 68 legs. So you guess againyou have to add more chickens and subtract some goats.
Guess

Chickens 
Goats 
Number of heads 
Number
of legs 
1 
13 
13 
26 
78 
2 
20 
6 
26 
64 





Now you have 64 legs and you need four more. But you can't add any more heads, since 26 is the correct number of heads. So you take away two chickens (two heads and four legs) and add two goats (two heads and eight legs).
Guess

Chickens 
Goats 
Number of heads 
Number
of legs 
1 
13 
13 
26 
78 
2 
20 
6 
26 
64 
3 
18 
8 
26 
68 
Now you have the correct answer: 18 chickens and 8 goats.
* Thanks to Highline Council P.S.T.A. for this problem: http://home.blarg.net/~math/
