How do I teach my kid the value of money?

Not by explaining it. The value of money is not a concept somebody can be told, it is a thing that gets learned by handling some and finding out what it costs to get.

The gap most families never cross is between money that arrives and money that was earned from a stranger. Allowance teaches budgeting, which is useful, and it teaches nothing about worth, because the amount was not connected to anything the kid did. Payment for chores is closer and still inside the house, where the rate is set by somebody who loves them.

What changes a kid is somebody with no obligation to them handing over money in exchange for work. That is the moment forty dollars stops being a number and becomes four hours of raking.

Three things do the actual teaching once that has happened.

Spending it badly. This is not a failure of the lesson, it is the lesson. A kid who blows eighty dollars on something ridiculous has learned something at the cheapest price it will ever be available. Imposing a savings rule on their money quietly converts it back into your money with conditions, and the ownership was the point.

Seeing costs. A kid who never pays for fuel or supplies believes the whole price is profit. Once the business pays for what it uses, thirty dollars in and four dollars out becomes visible, and that is the beginning of understanding margin.

The trade against time. The most useful sentence available at this age is this costs three lawns. Once a kid prices things in their own work, they have a conversion rate for the rest of their life.

The question that does more than any lecture: what is this money for? Most kids have never been asked and the answer is usually more interesting than expected.