I always knew mine and my mom's budget. I mean, not at like 5, but once I was around 11 I did. Heck when I was a teenager I handled all our grocery shopping and was often put in charge of paying bills. Not because my mom couldn't, but she worked full time and went to school and often picked up an extra job or extra shifts so we could make it, so she didn't have time to grocery shop or sit down and pay the bills. I also handled our laundry, made us dinners, and after seeing what she spent eating in her work cafeteria every day, started making her lunches. But our family dynamic was different then the average families, it was just the two of us, she had to rely on me to handle some adult things or she would've gone batty. And I liked it, I felt very grown up with my coupons and grocery list (as an adult I feel less grown up with my grocery list and can never remember the dang coupons). And I'll say this, I was much more prepared for adulthood then my friends were. I had to sit most of them down and go "Ok, so this is a budget"....and credit cards are not part of your budget.I would go further. My Cousin C's son wanted an Ipad desperately his 2nd grade year. They helped him compare prices and specs and gave him a flat amount they would contribute. They also let the rest of the family know he was saving up for one, when we asked about birthday and Christmas. He saved his allowance money, school snack money, did extra chores, worked for neighbors, and between July and December saved enough money for his Ipad. You better believe that thing gets treated with great care.
However I think "No, we can't afford that", is a pretty basic standard thing most parents say to kids. "Mom, I want a iPad!", "No", "But why not?", "Because we can't afford an iPad", "But I want one!", "We still can't afford it", seems like a reasonable answer to me.
My kids like to save for "big" things with their allowance (big, in their minds, is stuff like the LEGO sets that are in the $30-80 range). They do pretty well with it, especially as they don't have much chance to spend their money on little stuff. They do need to buy presents for sisters' birthdays, but they still usually manage to save up enough to get a new LEGO set every few months or so. One nice thing about this is that it gives them a really understandable point of comparison. We can point out that a season of soccer costs as much as buying that really awesome LEGO riding camp set that they long for. Or that one month's violin lessons cost the same as the LEGO cafe. Etc. It helps them understand just how much an activity, or clothes, or whatever cost in comparison to other things. They can see that a season of soccer, two months, costs the same as clothes for a kid for an entire season.
When they'd get older, we'd like to give them a very large allowance, but have them responsible for paying for a lot of stuff... their clothes, lessons, any special foods, books and toys, whatever. That way, if they really want those awesome sneakers, they can get them, but then they might have to buy cheaper other clothes, or go without juice, or wait longer to save up for that American Girl doll, whatever.
When my MIL was in high school, she had a teacher who gave this assignment where each kid got a certain amount of money, and they were supposed to use it to outfit their first apartment. My MIL used almost all of it on buying a really great sound system, and bought just the very basics otherwise (a mattress and sheets/blankets/pillow to sleep on the floor, some kitchen stuff). The teacher failed her, saying she needed to learn how to prioritize. My MIL argued that she did know how to prioritize! She could live without a kitchen table, she'd eat on the floor. She could live without a couch, she'd sit on her bed. But she couldn't live without being able to listen to music, and it needed to sound good. I thought that was pretty hilarious, especially as my MIL has a talented eye for decorating and has a beautiful home. And a nice sound system.