Twins

03/26/2010

Here is the problem that we did not have time to complete today. We asked children to take it as their homework. Next time when we meet I would like kids to explain how to resolve the problem.

In the second grade there are 4 pairs of twins among other children. On Halloween party each child in that class brought dad and mom and they are all in the gym. No other people are in the gym. There are 85 people all together. How many kids in that second grade?

If you help solving this problem then you can use the following directions. It is how I started to explain to my group of kids.

First I asked them a question: We have 4 pairs of twins, how many children is it? 4 x 2 = 8. Correct.
How many parents each pair of twins have? 2: mom and dad.
How many parents those 8 kids have? 4 pair x 2 = 8. Correct.
How many children and parents for those 4 pairs of twins. 8 children + 8 parents = 16 people.
We know that there are 85 people in the gym. It includes children who are twins and their parents AND children who are not twins and their parents.
We already know that there are 16 people (twins and their parents). How many people you need to add to 16 in order to get 85? This way we will find number of children who are not twins and their parents.
16 + ? = 85, where '?' is number of children who are not twins and their parents.
? = 69 Correct. So now we know that number of children who are not twins and their parents is equal to 69.
It is where our group stopped.

To continue the thought process we can do the following.
There 69 people who are children (who are not twins) and their parents. We know that each such child has 2 parents. So we have (1 child + 2 parents) x ? = 69. In other words we have a family of 3 people (1 child + 2 parents). How many such families we have in order to get to 69 people? The answer is 23.
So we have 23 families with 1 child in each of them . So how many children we have in those families all together? The answer is 23.
So we have 4 pair of twins = 8 children + 23 children (who are not twins) = 31.
It means that number of children in the class is 31.

Let's now verify that we solved the problem correctly.
4 pairs of twins => 4x2 children + 8 parents + 23 (children who are not twins) + 23 x 2 (parents for children who are not twins) = 8 + 8 + 23 + 46 = 85. So we got 85 people all together.