Map the route he walks every single day
An elderly dog does not need the whole house carpeted; he needs the paths he actually uses to stop being skating rinks. Watch him for a day and note the chain: bed to water bowl, water bowl to back door, back door to food bowl, and the hallway he crosses to greet you. Lay runners or long non-slip mats along those exact lines, with rubber backing or rug tape at the corners so the mat itself cannot surf away when he pushes off. Remove small loose rugs entirely, because a rug that bunches is worse than bare floor. Leave a firm island of mat beside his bed and his bowls, wide enough for all four paws, since standing to eat and drink is when a stiff, tired dog is most likely to splay and panic.
Help his paws grip and his joints cope
Flooring is only half the grip problem. Keep the long hair that grows between an older dog's paw pads trimmed level with the pads, keep nails short so his weight sits on the pad rather than tipping back onto the nail, and wipe wet paws dry at the door before he steps onto hard floors. For dogs who still slip on a mat, well-fitted non-slip socks or boots for indoor use can help, introduced for a few minutes at a time with treats so he learns to walk in them rather than high-stepping and freezing. Place food and water bowls on a mat, raise them only if your vet has suggested it for his neck or back, and light his night route to the garden, because an old dog who needs the toilet at night should not have to cross a dark, slick kitchen to get there.
Change the house, not just the floor
Think about the moments that force a sudden move: the doorbell, a dropped pan, another pet charging past, or you calling him quickly from another room. Give him a calm waiting spot away from the front-door rush, block stairs he no longer manages safely with a gate, and consider a ramp over the one or two steps he uses daily, with a grippy surface and a gentle slope he can walk rather than leap. Help him into the car with a ramp or a supported lift instead of letting him jump down onto a driveway. Keep his bed on the ground floor if stairs have become a strain, near warmth but away from draughty doorways, and keep walkways free of shoes, bags and charging cables that turn a steady route into an obstacle course.
Know when slipping is a health signal, not a flooring problem
New or worsening slipping deserves a vet visit rather than another mat. Book promptly if one back leg starts crossing over the other, if his paws knuckle and drag, if he cries getting up, stops wanting walks he used to enjoy, or begins falling even on carpet and grass. Those changes can point to pain, weakness or a nerve problem that flooring alone cannot fix, and earlier assessment gives you more options for keeping him comfortable and mobile. Between visits, note which surfaces and times of day are hardest for him and share that pattern at the appointment. Recording the runner checks, nail trims and any new falls as dated duties in KinsLe Care Teams means everyone helping with his care sees the same picture of how his mobility is changing.