Reforming Math, 4

(Continuing from Reforming Math 1, Reforming Math 2, and Reforming Math 3.)

My latest e-mail to the Head of School at Natural Friends:

Here's a list of basic math concepts, with sample questions that all graduating NF kids should be able to do, WITHOUT CALCULATORS. To the best of my knowledge, none of the following is currently being taught at NF. If you have kids who can do all this, ask whether they study math outside of NF, for instance with Kumon, tutoring, or help from their parents.
 
I.) Standard algorithms.

     1.) standard long division algorithm
         try this.) 2226 ÷ 3.

     2.) standard multiplication algorithm
         try this.) 23 x 3560.

     3.) standard subtraction algorithm.
         try this.) 3246 - 1634

     4.) standard algorithm for taking an average
         try this.) what's the average of {10, 100, 36, 84}?

II.) Fractions.

     1.) fractions are a form of division.
         try this.) how can you write 7 ÷ 4 as a fraction?

     2.) general concepts: x/x = 1, x/1 = x, etc.

         try this.) How would you write 4 as a fraction?

         try this.) Complete this sentence: "multiplying by 1/2 is the same as dividing by _."

         try this.) Complete this sentence: "any number divided by itself is _."

         try this.) Complete this sentence: "any number divided by 1 is _."

         try this.) How would you write "one-half of 37" in mathematical notation?

     3.) multiplicative inverse (reciprocal) of a fraction.
         try this.) 5/4 x _ = 1

     4.) how to convert a fraction to a decimal
         try this.) convert 4/7 to a decimal.

     5.) how to divide one fraction by another
         try this.) 4/7 ÷ 2/3

     6.) how to cross-cancel when multiplying fractions
         try this.) 4/5 x 2/3 x 5/4
         try this.) What is one-half of two-thirds of three-fourths of four-fifths of 5?

     7.) multiplying a whole number by a fraction.
         try this.) 4 x 1/2 = _

III.) Decimals.

     6.) how to multiply two decimals
         try this.) .25 x .75

     7.) how to divide two decimals
         try this.) .75 ÷ .25

IV.) Shortcuts with 10.

     8.) how to multiply by multiples of 10
         try this.) 234567 x 100.

     9.) how to divide by multiples of 10
         try this.) 234567 ÷ 100.

Readers -- what math are your kids missing?