## Math Problems

In theory, the Insight method of teaching math can use any problems. In practice, you can't use problems your students remember how to solve. Also, I have developed problems to suit my techniques and to teach concepts I want to teach. Finally, because I teach concepts, the problems can be different.

I regularly add problems to this list.

#### Reverse Arithmetic

Reverse Arithmetic I start with this type of problem. For example, find 3 numbers which add to 100. This teaches number facility, including numbers and operations as tools. It also segues nicely into the problem of expressing a pattern.

#### Expressing Patterns

Expressing Patterns Teaches the concept of a variable and develops facility with their use. Also, what-were-you-thinking problems.

#### Base 10 Operations

• Natural Operations Nothing to do with base-10. Investigating the natural, real-world operations that correspond to addition, subtraction, multiplication, and division.
• Packaging Problems Story problems analogous to the base-10 operations of addition, subtraction, multiplication, and division. Also used to teach other bases, or mixed bases such as yards-feet-inches.
• Exploring the Representation of Number. An exploration of different methods of representing number.

#### Algebra problems

These are all story problems. They can be solved without algebra, but they have algebraic equivalence.
• Loox problems have strange animals in a box. For example, A box contains 3 cats, 4 dogs, and one loox. There are 17 eyes in the box. How many eyes does a loox have?
• Stick problems express an algebra equation using sticks. For example x + 3 = 7 would be two sticks, one unknown length and one length 3, that together are as long as a stick of length 7.
• magic problems. I am thinking of a number....
• Silver & Gold

#### Computer Programming

Computer Programming Someone has built a machine to follow instructions. Be the machine! Be the machinemaster!

#### Other

• Frodo Problems Example: 3 is a blodo. Adding 4 to a blodo makes a new blodo. Make as many blodos as you can. These primarily teach number facility, but they also address recursion and set a foundation for understanding the axiomatization of numbers.
• Numbers. Understanding the different types of numbers.
• Tinkering. The process of improving on a first answer or idea.
• Categories Pattern recognition, but moreso describing/defining categories.
• Rules Teaching students to build mathematical rules (being a mathematician)
• A Mathematical "Magic" Trick Probably teaches some basic concept about being careful in calculations

### Essays:

 Dad: "Son, did you do all of your homework tonight?" Seven-year-old son (admonishingly): "Dad, you know I don't have homework on Sunday night" Dad (with a twinkle in his eye): "But did you do all of your homework tonight?" son: (big smile) "Yes, dad." Mathematician interacting with his son. (Logically, if there was no homework, then the son did all of it.)