Logical reasoning, Assumption and adjustment
The Chicken and Rabbit Puzzle
Turn a heads-and-legs puzzle into a clear strategy: make a simple assumption, then account for the difference.
THE KEY IDEA
Start with a simpler situation.
Chickens have two legs and rabbits have four. Imagine every animal is a chicken first. This gives a starting total of two legs per animal.
Compare that total with the actual number of legs. Each rabbit contributes two extra legs compared with a chicken, so divide the extra legs by two to find the number of rabbits.
Subtract the rabbits from the total number of animals to find the chickens. Always check both the number of animals and the number of legs.
YOUR TURN
Try it yourself
A new challenge: a pen contains 12 animals, all chickens or rabbits. There are 34 legs altogether.
How many chickens and how many rabbits are there?
Need a hint?
If all 12 animals were chickens, how many legs would there be? How many extra legs does each rabbit contribute?
Show the worked answer
Twelve chickens would have 12 x 2 = 24 legs.
There are 34 - 24 = 10 extra legs. Each rabbit adds 2 extra legs, so there are 10 / 2 = 5 rabbits and 12 - 5 = 7 chickens.
Check: 7 + 5 = 12 animals, and 7 x 2 + 5 x 4 = 34 legs.
A SHARED TEACHING REFERENCE
Teaching with this video
Use the video as a common starting point, then ask students to explain the structure in their own words.
Discussion prompts & teaching notes
Notice: Which quantity stays fixed when a chicken is replaced with a rabbit?
Explain: Why do we divide the extra legs by two, not four?
Check: Does the answer satisfy both totals?
Extend: Start by imagining all 12 animals are rabbits instead. There would be 48 legs, an excess of 14. Replacing seven rabbits with chickens removes 14 legs.
Shared vocabulary: assumption, difference, adjustment, total, check.