Everyone says it: One year for a dog equals seven years for a human. But like a lot of things everyone says, it’s wrong.

Dogs do have life stages a lot like humans’, but the math isn’t that straightforward. To start, a 1-year-old dog isn’t equivalent to a 7-year-old human.

“If you look at a 1-year-old dog, he’s sexually mature,” says veterinarian Dr. Marty Becker. “They still have a little filling out to do, and they’re not completely mentally mature, but they’re full adult size and capable of reproducing.”

Veterinary behaviorist Dr. Lisa Radosta suggests thinking of a 1-year-old dog as roughly mentally equivalent to a 13-year-old human. This means that a lot of development is packed into your puppy’s first year.

“If I keep my human baby home for the first year of her life, it doesn’t matter. I have a lot of time before she gets to kindergarten age at 5,” Radosta says. “But if you wait with a dog, you now have a teenager on your hands — a teenager who’s never seen a UPS truck, never seen a man in a hat, never seen a dog who barks at him.”

That’s why it’s critical for puppies to get out and learn about the world during that first year. Within the first four or five months, they go through distinct periods when they are most open to different kinds of experiences and new people. Positive exposure in that period lays a sound foundation, but you also need to look out for a second stage, usually somewhere between 4 and 8 months, when dogs can develop new fears.

“Your dog might be perfectly fabulous with men with hats, and then at 6 months old he says no, they’re frightening,” Radosta says. “You have to work through it.”

Trainers also want you to know that dogs go through a stage much like human adolescence.

“It’s a stage when a lot of relationships with dogs break down,” says Patricia McConnell, a trainer and certified applied animal behaviorist. “And it’s understandable: Your puppy sat whenever you asked for four months, and now he looks at you like he’s never heard that word before.”

When a dog will go through this stage differs by breed and individual, but it’s less upsetting if you understand that it’s a normal part of maturation.

“Dogs seem to go through a period between usually 6 to 10 or 11 months in which a lot of their impulse control falls apart, a lot of their training falls apart, a lot of their interest in paying attention to you and doing what you ask falls apart,” says McConnell.

Take a deep breath, take a couple of steps backs in your training and help them do it right. And remember, this stage will pass.

Dogs become socially mature between 1 and 3 years. “Think of that as age 13 to maybe 21, 22, 23 — the age when parents say that their kids are normal again,” says Radosta. “Then from 3 to about 10, you’re cruising.”

At the other end of the life span, we see why the seven-year rule seemed to make sense. “People think, my dad lived to 70. Seventy is a decent life span for a human, 10 is decent for a lot of dogs,” says Becker.

But dogs of different sizes tend to have different life spans and age at different rates; it’s important to know when to start looking out for the problems of old age.

“With giant-breed dogs, we have to consider them senior citizens after the age of 5,” says Becker. “With a Lab it might be 7; with a small-breed dog it might be age 9.”

Older dogs’ issues will sound familiar: Joint problems are common, as is putting on weight as the metabolism slows down. Becker says many other problems are associated with obesity — heart, respiratory, even skin problems, and an increased risk of cancer — so keeping weight down is important in your dog’s golden years.

“If you keep your pets leaner — close to what they weighed at a year of age — they’re going to live longer and be healthier,” says Becker.

Dogs can also suffer from dementia, which veterinarians call cognitive dysfunction syndrome. There’s no specific medical test, but you could see behavioral symptoms like house-training accidents, disrupted sleep patterns and changes in social interactions, or they might seem lost and disoriented. Your vet will need to do a thorough exam to rule out physical causes for the symptoms. Radosta says that once dogs reach 11 or 12, about one-quarter have at least one sign of dementia. She provides a screening checklist on her website (flvetbehavior.com/cds-checklist.html).

When you see changes in your older dog, don’t assume that “it’s just old age” and nothing can be done. Even for dementia, vets can prescribe treatments. Or there might be a medical problem that isn’t age-related.

Finally, McConnell says that even when older dogs are relatively healthy, they might see life a little differently. Situations that they used to enjoy or tolerate might not be appropriate anymore.

“They can get tired more easily, be a little grumpier and a little less patient,” she says. “Don’t hold on to the past — look at your dog now.”