Sets of small play balls or baby sensory balls are easy to pick up, and here are some fun 1 year old activities using them.
This is one of the most popular toddler play ideas. Simply collect various sturdy, medium-sized containers such as a bucket/pail, large plastic food containers, baskets (check for sharp parts), small storage boxes/bins, high-sided trays that food comes in, along with small play balls.
For a DIY ball pool you could use a laundry basket (watch out for tipping), sturdy under-bed type boxes, or a small dry wading/paddling pool. I found that 1 year olds tend to throw the balls out when they’re in a ball pit, and I tend to throw them back in. It's very simple, yet it can engage a little one for a long time!
If your toddler is lucky enough to have a slide at home, set a box of balls next to it or place the slide over the edge of a ball pool.
Toy box lids and large books placed on cushions can create slopes for any balls or rolling toys you have.
Cardboard balanced on a box can also create a slope for the rolling game too.
I recommend looking in the direction the balls will roll in ahead of the game, to avoid annoying fetches from under furniture.
You can collect cardboard inner tubes from toilet rolls or kitchen rolls. Stand the tubes upright and place a box or basket of play balls or baby sensory balls next to them. Encourage your 1 year old to balance the balls on top of each of the tubes. This helps to develop hand-eye coordination and motor skills.
This is my photo, but not my activity, so I'm sorry I can't help with the details. If you or a loved one is handy with PVC pipes and has tools, then you might be in luck. I would suggest mounting one plain PVC pipe vertically or at an angle to a wall because that would be enough for your 1 year old. Be mindful of where the balls will end up, especially if the ball pool or the basket/box underneath is moved.
Click the link for more fun Activities for 1 Year Olds.