I have to solve and explain carefully step by step as if I was teaching it to a sixth grader.?

Question

80,000 attend a Patriots game. After the game, the fans are so excited that they decided to organize a party for each day for a year. They decided that, on each day, if it was their birthday, they would return to the stadium at noon to celebrate. Why would at least one party have more than 200 people?
It's a written assignment for a math class that teaches us to teach math but I won't be teaching this type because I'll be teaching early childhood, can you please help me?

I need a detailed step by step explaination and why and how it works

Answer 1

I would start by asking the kids questions.

How many days are in a year?

So, if we have 80,000 people how could we estimate how many people will be at each party? At least 1 kid will be smart enough to tell you to divide it. Be sure that write it on the board as you go.

When you come up with 219 then ask the kids if they really think that the birthdays will be divided equally. If that is true, then if there are 24 kids in your class... there should be 2 birthdays in each month. (Maybe as a starter for the lesson you could have some sort of birthday poster and could quickly write the names of the kids under each month that their birthday falls. You may have some months with 5 birthdays, and others with 1 or none). If they say that they think that the birthdays will be evenly then use your birthday chart and explain that their birthdays are random; that it does not work out to exactly 2 birthdays in each month.

Then you can explain to them that with 80,000 people there are likely to be a few birthdays on more days than others. They will get it; especially when you use their own data to help explain it.

If time allows you could do another problem that is similar, but maybe using something like the day they got their first pet (I don't know; something...) anyway, because some people may have never had a pet you could ask if it is possible that some people never come to celebrate. Or maybe use vet patients for the problem because then we could assume that all patients would qualify.

Answer 2

This is an example of probability. If you have 80,000 people and there are 365 days in the year then you would take 80,000 and divide it by 365. The answer is 219. That shows that the probability of there being a day over 200 is likely.