Kidstuff

This variation on Twenty Questions teaches kids a bit of information theory and lets them take a different approach to powers of 2.

First, the kids should be familiar with the regular game of Twenty Questions.

Then, ask as an open-ended question: "Suppose instead of the whole world. you were only allowed to think of certain objects. How many questions would it take to find the right one? What if the questions had to have only yes/no answers?"

Here is another opportunity for discovery: one-third. For kids who have learned how to divide and get decimals (or show a child briefly who has learned long division and knows what decimals are). Ask simply, what is one-third in decimal?

The discovery that 1/3 = .33333333... the repeating decimal, is surprising enough on its own for a child who has never seen an infinite series before. What usually will tweak their curiousity, though, is to continue - ok, what is 2/3? Then wait a moment, and see if they think of 3/3 by themselves. The idea that 3/3 = .999999999... may get the child saying, wait a minute - 3/3 = 1!

They have just proved that an infinite series can equal a whole number; if your child doesn't want to accept it, that is ok. Just assure them that if the series stops anywhere, it is less than one, it only equals one if it is really infinite.

The fun thing is, this can be done by a 4th grader.

For kids who have been introduced to exponents but haven't been taught specifically about what it means to take 'N to the zero power', this is an opportunity for a small 'Aha!' moment.

If a child already knows what is ten to the 2 (10^2 = 10 * 10 = 100) and 10^1 = 10, ask them what is 10^0.

Let them think a bit. Many kids will answer 'zero'. Ask, well, then what is zero times 10? If its not 10^1, then that can't be right.

Explain that 10^0 must be the thing that you multiply by 10 to get 10^1. This should be enough of a clue that they realize that 10 to the zero is 1.

Then, without any other explanation, ask something that sounds hard - "what is eighty-seven to the zeroth power?" With a bit of thought, your child may be able to come to the sudden realization that everything to the zeroth power is 1!

(This only works if they haven't already been taught this fact in school - it is fun to discover things that no one has told you. So don't be afraid to try this somewhat early, before

Here is a fun way to introduce kids to the concept of modulus (without ever saying the word): ask, why does a week have 7 days? Suppose you could change it - how many days would you put in the week? Then ask some questions about 'in X days, what day would it be?'

It helps to ask the child to consider the days as being named by number at first, to look at the patterns, starting with Zero-day and continuing as One-day, Two-day (which conveniently becomes Tuesday if Sunday is Zero-day), etc.

Start with simple questions like "So if your week has 5 days, and today is Three-day, what day will it be in 6 days?"

Make sure to ask several with the modulus "If your week has 4 days, and today is Zero-day, what day will it be in 4 days? 8 days? 16 days?"

Once they realize that it always goes back to the same day every time the number is a multiple of the days in the week, kids can have fun answering what sound like 'hard' questions: "So your week has 9 days, today is Seven-day, what day will it be in 80 days?