I wrote a blog a while ago about why a bored toddler is actually not a bad thing. My mum's wisdom really did resonate when she said that they do need to learn to be by themselves sometimes and engage with their own imagination.
Over the months, this has become a little easier as our two and a half year old has learned that she can't always be entertained and that, in fact, sometimes mummy isn't such a great play mate when she's doing a million things.
Independent play is a great way to encourage It is important to build up to independent play over time rather than just expect them to get on with it as they need to learn this skill and gain the confidence to utilise their imagination. A realistic approach helps: even just 5-10 minutes solo play is a win, and there will also be days this just doesn't work if they are feeling cuddly or a bit anxious, so take it slow and have fun. Here are some ideas to get your toddler trying new things independently:
A challenge: You will need to start this one with them. Build a castle or whatever takes your fancy and give them a challenge to make it better, bigger, higher, stronger...Not only does this give you five minutes, it also encourages their problems solving skills to develop as they work out which shapes and structures are effective. Anything from wooden blocks to stacking tubs work. Whatever you have available.
Staged areas: Set a small corner of a room up as a staged area. It could be a classroom, kitchen, farm etc. By giving them a new area to explore, they will (hopefully) start to investigate the ways that everyday objects are placed and used. For some reason, toilet rolls are a huge hit in our house and our daughter will spend ages stacking them and making her own wall.
Open ended toys: While a talking teddy might help them sing a song, once that's mastered it's a bit redundant. So try using open ended toys and objects that can do anything. Duplo: building blocks or the longest caterpillar in the world? Spoons: for feeding dolly or making amazing sounds on the tin cans? You get the idea. We need to find things that allow a range of ideas to develop, not just a start to finish toy.
Sorting activities: My sister gave me this idea and it can be used again and again. Cut up some old colour straws, pieces of old colour fabric, magazine pages with colour...anything. Pop them in a tub for safe keeping. Get your child to empty all the pieces out and put them into colour areas (or shapes if you've managed to cut things out carefully). Even if they end up making random piles, they will still have been exploring textures, colours and shapes.
Dens: Dens are a great way to inspire play if you encourage your toddler to set up an area. For example, can they make a den for everyone to sleep in? This will require them to think about where everyone can sleep, what materials are needed, which books etc and will they include the family pets, in which case they will need to think about food and water bowls ;-)
These are just a few ideas and http://www.toddlerapproved.com/2013/05/simple-independent-play-activities-for.html has many more ideas to explore.