# teaching machines

## Seven Digit Study

My son and I are on our way to school. It’s just the two of us. These drives should be a great opportunity for some genuine father-son talk, but it rarely happens. My mind is usually anxious about the day ahead, the traffic around us, and the hazards of winter. Even when we do talk, […]

## Apathetic Numbers

My son is 11, and he likes to think about numbers. In this time of working and learning from home, I’ve had him reading Isaac Asimov’s Realm of Numbers. The other day my son stumbled upon this numerical curiosity: $$3 \times 1.5 = 3 + 1.5$$ How fascinating that the numbers don’t care whether they […]

## The Law of Doubled Digit Transposition Over Multiplication

My son is learning long division at school. He was intimidated by it, so we started practicing for just a few minutes every day after school. The format is simple: I generate two numbers, a big dividend and a small divisor, and he divides them. One day I wanted the quotient to be 99 because […]

## Five through Fifteen

On our walks home from school, my 8-year-old son has been telling me of a math problem that he has not been able to solve. Yesterday, after a week of not finding a solution, he wrote down the problem on paper for us to investigate together. Here is the task in my own words: Distribute […]