Cows and Sheep
Problem
In this field we could say, because of the number of animals there, that each cow can see 4 sheep and 3 (other) cows. This could be worded as follows "Each cow can see one more sheep than cows." There are obviously 4 sheep and 4 cows in the field as you see it.
But here are some questions about different fields in which you have to find out how many sheep and cows there are in each field.
In field number 1, each cow can see twice as many sheep as cows; each sheep can see the same number of sheep as cows, so how many cows and sheep are there?
In field number 2, each cow can see three times as many sheep as cows; each sheep can see the same number of sheep as cows, so how many cows and sheep are there?
In field number 3, each cow can see twice as many sheep as cows; each sheep can see one more sheep than cows, so how many cows and sheep are there?
In field number 4, each cow can see twice as many sheep as cows; each sheep can see two more sheep than cows, so how many cows and sheep are there?
In field number 5, each cow can see three times as many sheep as cows; each sheep can see twice as many sheep as cows, so how many cows and sheep are there?
Getting Started
If there was just one cow, how many other cows would it see? How many sheep would the cow see? Does this fit the clues?
If there were two cows, how many would each cow see? How many sheep would each cow see? Does this fit the clues?
How about if there were three cows? Four cows ...?
Student Solutions
Before looking at some solutions that came in we would like to say that we were very pleased with the explanations that came in with many of the solutions - exactly what we would hope to encourage.
Francesca and Alex sent in the first correct solution and they come from Red Hill Field Primary School and so does Sam who sent in another correct solution a week later.
Francesca and Alex wrote:
We had many good replies from Bradon Forest School and here's Samuel's correct solution with some good explanations as to how he went about it.
Rees, who also came from Bradon Forest sent in a Powerpoint presentation and here's his slide for field 1
Well done!
We had 71 replies come in about this problem, They came from far afield - Qatar, Dublin, North Carolina, Australia, New York, Wisconsin and New Zealand as well as the U.K. The problem caused some deep thinking and just 16 replies had the correct answer.
Teachers' Resources
Why do this problem?
Possible approach
- What can you tell me about the number of sheep and cows in the picture?
- How many cows can each sheep see?
- How many cows can each cow see?
- How does the number of sheep a cow can see relate to the number of cows it can see?