Question by Question: Mental word problems
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.
To help kids develop their meta-cognition: when they get a difficult problem right, ask with genuine interest "wow, how did you figure that out?" and listen carefully to the answer. Ask questions and avoid telling them the 'right way' to do it - if they are consistently able to get the right answer, then their way is a right way.
Some examples:
Example:Kids love big numbers, but they can also seem intimidating. If you ask your child, 'how much is 100x100' and they guess '1000', don't say 'wrong!'. Without saying right or wrong, ask, 'hm, how much is 10 times 100?' Or back up and ask 'how much are two hundreds? (easy, two hundreds is 200). How much are three hundreds?' and so on.
If they truly don't know that after 900 comes 1000, then you do need to tell them that: 'we call ten hundreds one thousand, that is what one thousand means'. But you are simply telling them the meaning of the word, not how to do the calculation; they should be able to figure out the meaning of 'ten thousand' by themselves once they know what one thousand means!
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Here is a funny example of correcting by questioning: I had asked a third-grader to figure out what is 11 squared, or 11x11. (Ok, this wasn't very concrete. But as the kids get more used to it, you can sneak in more abstract problems.) No idea. Asked, 'what are ten elevens (11x10)?' She calculated this correctly, 110, and realized that she needed to add another 11. But, she made a mental misstep and then concluded the answer to the original problem was 131 instead of 121.
Here it is tempting to say 'wrong! you added wrong, check your work' - but that would lose a golden opportunity to let the child self-correct. Instead of correcting, I asked her 'ok, so what is 110 plus 10? (logically, she answered 130) What is 110 plus 9?' She kept subtracting one from the number 131 until we reached 110 plus zero equals 120 and she burst out laughing. From there she was able to see where she had gone wrong, and figure out the original answer.
Obviously this method takes much longer than drill and memorization, but what it teaches is much more than just the answer to 11x11. It can also be done anywhere, without a book, paper or pencil.
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Throwing odd-sounding questions can be fun as well. "What is one third of six-sevenths?" can sound hard at first.
So ask instead, "If you had six oranges and three kids, how many oranges would each kid get, assuming each kid liked oranges?" Most will answer correctly, 2 oranges.
Then ask, "If you had six sevenths and three kids, how many sevenths would each kid get, assuming each kid liked sevenths?" Most will at least smile at this thought, and also clearly see the correct answer.
