math
Zeroth power
Summary:
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. Down to Grade/Age:
5th Grade
Up thru Grade/Age:
Middle School

How many days in your week? (or, modulo arithmetic..)
Summary:
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 Zeroday and continuing as Oneday, Twoday (which conveniently becomes Tuesday if Sunday is Zeroday), etc. Start with simple questions like "So if your week has 5 days, and today is Threeday, 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 Zeroday, what day will it be in 4 days? 8 days? 16 days?" 
Middle School Math Assessments
Summary:
Standardized tests are part of the reality of modern schools, and although justifiably criticized they can also be a useful teaching tool. Ask your kids to take the test for their grade levels, without help, explaining that this is just a way to see what they might need help with and what they already understand. Tell them not to guess, but just circle any problem they don't understand. After the test is complete, make a list of all the problems each child missed or circled. If they missed more than 2 or 3 problems, plan to work on a few at a time over a period of several days. For each missed problem, do NOT tell the child how to do it  you want them to retake the test on their own later and figure it out for themselves. Instead, make several similar problems, including some with easier numbers, and have them work on the similar problems, with help if necessary, until they can work the problems independently. Down to Grade/Age:
Middle School
Up thru Grade/Age:
Middle School

Question by Question: Mental word problems
Summary:
Anytime, anywhere, anything can turn into math. In the car, take turns asking each other problems (let the kids pose problems too!). Start with concrete scenarios: "So, if we baked 100 cookies, and there were 5 of us, how many cookies would we each get?". Or if the kids are into fractions, make it 17 cookies. It is easy to ask a hard problem, as you may find out when your kids take a turn to ask you! Try to ask problems that are a little bit hard for your kids, but not way above their level. Then, if the don't get the answer right, DON'T TELL them how to do it. Ask an easier or more concrete question instead, until they can get it right. Try to ask related questions that may help with the first one. 
How many arithmetic problems can you answer in 60 seconds?
Summary:
Free online speed test will tell you the answer. This is a free javascript math quiz from the Argonne National Laboratory. See http://bteaching.com/arithmattack.htm Drill in arithmetic is sometimes underrated, but fluency in math is just like fluency in reading. Its much easier to see the beauty in poetry when you can read easily, and it is much easier to appreciate the beauty in algebra and calculus when calculating isn't painful! Down to Grade/Age:
Kindergarten
Up thru Grade/Age:
Middle School

Half of a Onesided Paper = ?
Summary:
What do you get when you cut a Mobius strip in half lengthwise? The answer may surprise you! This is a simple exercise but may be both motivating and confounding. For children who have not played with Mobius strips before, start by introducing the idea of the strip  here are a few ways: 1) ask the child, 'is there a way to make this strip of paper have only one side?' or 2) make one without explanation by simply cutting a strip of paper, twisting it, and taping the ends. Ask your child to draw a line along the shape as far as they can. Down to Grade/Age:
PreK
Up thru Grade/Age:
Adult

How Many Questions?
Summary:
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 openended 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?" Down to Grade/Age:
Kindergarten
Up thru Grade/Age:
High School
