Challenge 2 - Pets
Challenge 2 is all about a classroom survey.
Maths teacher Chris Smith and pupils from Grange Academy are here to explain.
The Maths Week Scotland Daily Challenges have been set by the Scottish Mathematical Council.
Mr Smith: Today’s problem is all about a classroom survey.
Mrs McFarlane has 25 children in her primary class. One day she asks them about their pets.
“Put your hand up if you have a dog.” 14 hands go up.
“Put your hand up if you have a cat.” 10 hands go up.
“Now put your hand up if you have a dog and a cat.” 7 hands go up.
How many of the children in Mrs McFarlane’s class don't have either a dog or a cat?
Mr Asif also has 25 children in his primary class.
He too asks them about their pets and has found out that:
3 of them have a parrot. Those who do have a parrot also have a dog.
13 of them don’t have either a parrot or a dog.
How many members of Mr Asif’s class have a dog but no parrot?
Explain your answer.
Pupil: Is there a graph, chart or diagram you can use to organise the information?
Pupil: Remember that some of each class may put their hand up more than once.
Pupil: Don't forget the total number in each class.
Pupil: Have a go at it!
So here's the challenge:
This problem is all about a classroom survey.
Mrs McFarlane has 25 children in her primary class. One day she asks them about their pets:
“Put your hand up if you have a dog.” 14 hands go up.
“Put your hand up if you have a cat.” 10 hands go up.
“Now put your hand up if you have a dog and a cat.” 7 hands go up.
How many of the children in Mrs McFarlane’s class don't have either a dog or a cat?
Need a hint?
- Is there a graph, chart or diagram you can use to organise the information?
- Remember that some of each class may put their hand up more than once.
- Don't forget the total number in each class.
Solution
Worked out the answer? Here's how you can do it.
Did you work out how many pupils in Mrs McFarlane’s class have neither a dog nor a cat?
Let’s look at how we got our answer. One way to work out this challenge is to put the information into a Venn diagram.
So for Mrs McFarlane's class we've got two groups – pupils with a dog, and pupils with a cat, and the area where they overlap shows pupils who have both.
There are seven pupils with a dog and a cat, so we can take this away from the other totals.
14 pupils have a dog.
14 - 7 = 7, so we write a 7 in here.
10 pupils have a cat.
10 - 7 = 3, so we write a 3* in here.
Add the three numbers together, 7 + 7 + 3 = 17
Take this away from the class total, 25 – 17 = 8.
There are eight children who don't have a dog or a cat.
We can use another Venn diagram for Mr Asif's class.
We know that three children have a parrot. And all three of them also have a dog, so the circle for their group fully overlaps the circle showing dog owners.
13 pupils have no pet, so that leaves 12 pupils with a pet, who all have a dog.
The number of pupils who have a dog but no parrot is 12 - 3, which is 9.
If 14 pupils have a dog, 10 have a cat and 7 have both, then the number of pupils with either or both is:
14 + 10 − 7 = 17.
We take the 7 off because otherwise we would be counting some animals twice.Taking this away from the 25 in the class, we now knowL
8 pupils don't have either a dog or a cat.
Well done if you got this one!
Part 1 - Mrs McFarlane's class
Step 1
One way to do this is to put the information into a Venn diagram.
We've got two main groups:
- Pupils with a dog.
- Pupils with a cat.
The area where they overlap shows pupils who have both a dog and a cat.
Step 2
There are 7 pupils with a dog and a cat, so we can take this away from the other totals.
14 pupils have a dog.
- 14 - 7 = 7
- We can write a 7 inside the circle with dogs.
- This shows 7 pupils have a dog but no cat.
10 pupils have a cat.
- 10 - 7 = 3
- We can write a 3 inside the circle with cats.
- This shows 3 pupils have a cat but no dog.
Step 3
Add the three numbers together:
- 7 + 7 + 3 = 17
This shows the total number of pupils with a pet is 17.
Take this away from the class total:
- 25 – 17 = 8
There are 8 children who don't have a dog or a cat.
Part 2 - Mr Asif's class
Step 4
We can use another Venn diagram for Mr Asif's class.
We know that:
- Three children have a parrot.
- All three of them also have a dog.
- The circle for children with a parrot is fully inside the circle showing dog owners.
Step 5
13 pupils have no pet. We can take this away from the total number of pupils:
- 25 -13 = 12
This means there are 12 pupils with a dog.
Take away the number of pupils with a parrpt and a dog to find the the number of pupils with a dog but no parrot
- 12 - 3 = 9
Nine pupils have a dog but no parrot.
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