Dice (get a variety of dice...up to a 20 sided dye and those with numbers and those with dots representing the number)
Preschoolers and role a simple six sided die and tell you the number.
Preschoolers can role a simply six sided die and then use counting bears to count out the number.
Elementary students and roll two die and add them, multiply, them, divide them or subtract them.
Use dice of different colors and have each color represent a place value. Roll all the dice and then have your child determine which number is in the ones, tens, hundreds, and then write it out properly.
Elementary students can use a die with math operations on it and two numbered die to do some quick equations.
Use one die as the numerator and one as the denominator and roll to get your fraction. Then you can add, reduce, subtract, etc. all from that point.
Whatever task requires numbers, you can throw a die to get the number you need. I have had my children roll two dice and add that number, then roll two more dice and add that number then multiply the two numbers they came up with. Have fun with it!
Strange Animal or Monster Math on a Roll
Here's a cute way to reinforce math and have fun drawing at the same time. Get out paper and crayons, markers, or colored pencils. Then roll a die and tell your child that is how many eyes your creature has or how many ears or mouths and so on until their strange creature is complete.
Preschooler Art and Math Mix Up
Have your preschooler roll a die and then draw that many flowers, happy faces, stars, etc. For more of a challenge, have her roll the die and draw the number in happy faces then roll again and "add" that many happy faces to her previous set. Then ask how many happy faces are all together. You can also have her cross out that number of happy faces for subtraction but be aware you may find yourself in negative numbers if she rolls twice. Roll once and then you tell her the number to cross out and ask how many are left.