That adorable puppy photo on Facebook instantly melts hearts: awkward fuzziness capped by satellite-dish ears she’s still growing into. Best of all, her twinkling eyes radiate the mischief, curiosity and vibrancy unique to a lanky, goofy puppy. The caption beneath the photo confirms the mischief part. “Hello. My name is NO!”

Puppyhood is a special phase, but even in later years dogs occupy our homes and lives like 70-pound toddlers with sharp teeth. Cats climb curtains and scale furniture like spider monkeys with Velcro paws. It’s only natural for a weary parent to resort to “No!” and “Stop that!” But how about providing parent-approved mischief to keep your rascals occupied.

Every kid needs to work out the wiggles, and activities need to be mentally engaging to really capture their attention. It’s their braininess that gets them into trouble! Keeping clever craniums occupied can be full-time job, but there are plenty of options for giving your little Einstein a mental workout. Enrichment activities can be as simple as taking the $120 work shoes from your dog and offering an appealing chew toy (along with glowing praise for relinquishing the prized footwear), to endless possibilities ranging from high-end electronic gadgets to empty toilet paper tubes.

In the critter game and puzzle world, technophiles have amazing options, including an interactive device that lets you see, talk to, and treat your furkids while you’re away. In the mid-budget range are gads of gadgets at your local pet supply, including puzzles with compartments for hiding treats. There are several varieties with different levels of difficulty, and most promise to appeal to both dogs and cats. If you go this route, browse the options with your Einstein’s temperament in mind. There are the rough-and-tumble toys that dispense goodies when smacked or rolled or dropped, and less-physical brain teasers with compartments that slide or swivel. Is your kid more likely to join the chess club or the rugby team? Keep in mind that your rugby player will smack and roll the more sedentary brain teasers too, but they’re durable enough to take the punishment.

Countless parents have seen new cat toy lie untouched while kitty spends hours tossing and pouncing on the package . . . or perhaps a stray household cotton ball. Rest assured your critters couldn’t care less how much their games cost. The do-it-yourself realm is limited only by your imagination, and it’s all free.

Empty TP and paper towel tubes are great hiding places for little treats, as are small boxes and kitchen containers.

For rainy-day activities or to distract a kid while you leave the house, hide their breakfast or dinner kibble all around — either scattered openly on the floor or tucked cleverly behind doors, under tables, and in corners. Make it easy at first and gradually increase the hide-and-seek challenge for a longer-lasting game.

Hide yourself! This works best with dogs. Put Fido in a sit-stay, then get behind a tree, couch, or door, and call to him. Some dogs get deliriously happy with this one.

Turn scary fireworks or thunder into a popcorn party. Use an air popper, which both masks scary sounds and dispenses treats. You can place the popper at the edge of a counter so popped kernels scatter on the floor, or pop them into a bowl and scatter them yourself. This game is always a hit with food hounds.

Old socks make easy catnip pouches, and can be tossed in the trash after happy felines have slobbered on and mopped the floors with them.

If you have dogs who destroy soft toys to capture the squeakers, repurpose the squeaker and old stuffing by tying them into an old sock or stitching them into a fabric pouch. Just watch these intense toy-shredders (see Hall Pass for hilariously instructive squeaker tales) and keep a close eye — swallowed squeakers can mean an expensive vet bill.

With a little imagination and anywhere from a few bucks to several hundred, you can expand your kiddo’s mental horizons and keep them out of trouble at the same time. As tuition goes, it’s a bargain. As peace of mind goes, it’s priceless.

Michelle Blake is a Salem, OR-based massage therapist and freelance writer whose work has appeared in national publications. Her husband warns you to know she's a REALLY crazy dog lady too.

Recess: Brain Games for the Furry Set