Packaging Problems

I use these problems to make the operations of base-10 arithmetic meaningful.

Essentially, these problems suppose that there are 10 apples in each box of apples and 10 boxes of applies in each crate of apples. Students then perform tasks using apples. These tasks are then analogs to base-10 operations. For example, in subtration, opening a box of applies is equivalent to borrowing.

More sophisticated Concepts

For older children, the exact same problems can be used to teach other bases.

If there are 12 kumquats in a box of kumquats and 3 boxes of kumquats in a crate of kumquats, you have a "mixed-base" problem, which corresponds to the inch-foot-yard method of measuring length (or more generally, any of our non-base-10 methods of measurement).


You should probably first do the "Natural Operations" problems. These problems pretty much assume those skills.

Ode to Algebra

Thrust into this dingy classroom
we die like lampless moths
locked into the desolation of
fluorescent lights and metal desks.
Ten minutes until the bell rings.
What use is the quadratic formula in our daily lives?
Can we use it to unlock the secrets in the hearts of those we love?
Five minutes until the bell rings.
Cruel Algebra teacher,
Won't you let us go?

From "The Princess Diaries", by Meg Cabot.