How Do I Keep My 16 Month Old Entertained and Meet Her Curiosity Needs?

The park, lots of books, coloring, singing, blocks, walks. There are also classes etc, Gymboree, Music Together

One thing to remember is their attention span is quite short, so they will want to go from one activity to the next quickly... usually in about 30 seconds! I'm sure you have things you are trying to accomplish on those days when she is home too, so what you have to do is prioritize your work, then figure out how to do it in small spurts, or when she's napping, so you can check in on her frequently. You might also figure out how she can be involved in some of what you are doing. It usually makes our work harder at the time, but is a good learning experience for the child. One of the first things a child is able to 'help' with is usually folding clean clothing. Give her a few items that you don't mind if she messes up in the process, then let her watch as you fold the rest. Talk to her as you are working. This gives her more experience with language development.
She's old enough for you to involve her in some "cooking" projects too. Even if all she does is sit on a chair and watch while you work, as long as you are carrying on a conversation with her and letting her feel like she's a part of what you are doing, she'll enjoy it and be learning at the same time.
As far as just the play aspect goes.... have a time several times a day when you read books with her. Go for a walk or to a park... or just outside in your backyard. Spend a little time with her as she plays with her toys. This can either be involved.. showing her how to stack blocks in a new way, or helping her dress a doll, etc. or it can be just you sitting nearby, watching her and maybe talking with her about what she's doing. You'll learn a lot by doing this too. You'll see her personality and abilities developing and understand who she is a little better.
I agree with the person who said the best toys are the free ones, but look around at the toys she has and see if you have a balanced variety of things... some building toys, some musical or talking toys, some just for the imagination some climbing toys (that one is so important or they want to climb on all your furniture!). If you have an abundance of toys, be sure you put out only a few at a time, and have a place to put the rest away to rotate.
Just a little advice if you are looking to purchase more toys... try thrift shops and yard sales first. Be aware of toys that have been recalled so you don't end up with some of the dangerous ones, but you'll find lots of good used toys at prices far below what you'd pay in the stores, and your child doesn't care if they are a little bit used and worn. Simply clean them with a good disinfectant solution before letting her play with them.
We have an abundance of great toys in our daycare and most of them were used donations or purchased at thrift shops and yard sales. Some of the favorites that we'd never have felt we could purchase at a store are the Leapfrog Alphabug and Counting Pal. The children love those and are learning their alphabet and numbers at early ages just by playing with them. Sometimes they get stuck on one letter or number to the point of distraction for the adults, but they are wonderful toys for the kids and can occupy a little mind for minutes on end.
I mentioned climbing toys. That's one thing we didn't have until this week, and I can tell you from experience that it's much better to have one good climbing toy inside than to keep on having to get kids off of furniture, because most kids are going to climb and will be quite inventive in finding a way if you don't provide one.

Something else you might want to do is just observe for a while in your daughter's daycare. That way you'll see what sort of things she is enjoying there, and you may get some good ideas. Of course one of the things she has there to play with that you don't have at home is the other children, but you can see what she's doing whenever she plays independently there too and get some ideas. Talk with her teachers and find out what sort of things they are introducing. She isn't too young for you to do art activities with her from time to time. Kids this age usually can handle homemade playdough quite well. You will need to be with her and remind her not to eat it, but I found making the one with alum in it helps prevent that, as they immediately don't like the taste. It isn't toxic, though if they ingest too much it might make them upchuck just because those ingredients overload the stomach. But that's why you watch and remind.. to keep them from eating that much of it. You can also use paint as long as you are right there. Get some non-toxic liquid tempera and mix it with dish soap to help prevent stained clothing. Put on a good plastic smock to cover as much as possible, but know that a child this age will figure a way to get the paint under the smock anyway! Another way I like to use paint is to mix it with shaving cream and white glue. This makes a paint that is more like the puff paints you can purchase but less expensive. Again you can see that being right there with her is essential, because you don't want her to eat the paint mixture. One of the favorite art activities of a lot of teachers is simply shave cream art. Just squirt a little blob of shave cream on the tabletop and let her use it like fingerpaint. It's a good sensory experience and depending on the child, can occupy them for a good five minutes or more. Once she's finished with it, wipe the shave cream off with a dry paper towel, then wash the table. If you use water on it first, the shave cream is much harder to remove. I've found a shave cream at the dollar store that is gentle and has a lighter odor than some of them that I use. It's called Pure Silk.

I apologize for such a lengthy response, but hope some of this will be helpful.

Sing songs and play music for her. Dance with her. You will feel very silly, but it is lovely fun. It often ends in laughter. Get some washable markers and color with her. My little one's jaw dropped when he realized that Mommy could draw animals (he was very impressed until he saw Daddy draw a truck). Any item that allows her to imitate you will also be a big hit (cellphone, keys, shoes).

I also put baskets of toys in every room and encourage self-entertainment. In addition to regular toys, I put all sorts of things: bags (coin purses, wallets) with zippers and snaps packed with random small things, wooden spoons, shiny fabric, small boxes filled with noisy things.... At 16 mos, he loved opening and closing cabinets, climbing inside. Also encourage her to look at books on her own by leaving board books accessible.

Self-entertainment only works when they are well-rested, so pay attention to naps and early bedtimes.

I'm not too proud to admit that when all else fails, I will turn on the TV. I am selective about what he watches--I dvr Yo Gabba Gabba, Jack's Big Music Show, and Sesame Street. No commercials and very stimulating. And limited to 30 mins (usually longer than his attention span anyway).

Dear R.,
Give her some plastic bowls, measuring cups and spatulas.
Try to find a box you can open on both ends big enough for her to crawl through. My kids used to LOVE to play in boxes and make forts and take toys in there.
Get her a purse and a set of plastic keys, a little hairbrush or comb, they sell pretend lipstick. The dollar store is great for that kind of thing. Just find some things she can put in her purse to play with. My daughter loved having her purse on her shoulder, carrying her keys and her baby around the house and pretending she was going to the store...which was our pantry. I got her one of those little shopping carts she could push around and had things down that were safe enough for her to reach so she could shop. I gave her one of my old wallets and put some playing cards in it. She pretended it was money.
Also, they have wonderful paint books. All it requires is plain water and the paper changes color instead of putting actual paint on it. I can't remember where I got it, but my kids had a plastic thing that they put down on the floor. It had all kinds of pictures on it that they colored with crayons on. Then the crayon wiped off with a little eraser that came with it. They loved to lay on it and color.
I'm sure you'll get some other great ideas too.
Have fun!

Teaching a baby to be self entertaining starts with putting them on the floor to play when they are a month old. I did this daily with both of my kids and never had to keep them entertained. Now you will have to try to train her to self entertain by doing it now just letting her play on the floor with the things she likes or colorful blocks. It will be harder now because I assume she is mobile now.

help you with laundry.
give her a cabinet in the kitchen with bowls and utensils that are safe to play with.
Get a tub of water and put it on the kitchen floor with soap and a sponge and let her try to wash some plastic bowls, etc.
color
finger paint
work with her to practice climbing up and down stairs (if you have them)
have her help you prepare her snack at a low kids table

In my experiene, they toys they like best are free. Over the years I've bought my kids all kinds of fancy educational toys, and they always like the stuff I have laying around the house better. For instance, they love to play with the cardboard rolls that are inside paper towel rolls or toilet paper rolls (looking through them, talking through them, etc). Rocks, playdoh, tupperware bowls, metal bowls (with wooden spoons to play drums with!), happy music combined with a place to dance, some of mommy's old clothes to play dress-up with, and whatever other doo-dads you have laying around. At that age, they will play with just about anything. My kids liked to stack things (like nesting bowls or boxes), or put things inside larger containers (such as any small items inside a box or purse... taking them in and out, over and over again). I hope that helps! They are so fun at that age, enjoy every minute!!

There are a couple of good books that discuss in detail different activities that are good for this age group and what skills they develop (I have Toddler Play, but there are many and they are pretty similar). Also, just going out and about--to the grocery store, playgroups, and labelling everything, teaches so much.

If you're in the East Bay I would recommend an Oakland Zoo/Lindsay Wildlife Museum membership. It's $65 a year and good at both places, and gets you discounts at other museums too. My son loves it, and every time we go he gets excited about a different animal or activity. So nice to always have somewhere to go on a rainy day!

I don't like encouraging the "boob tube" but Signing Time videos are great - learn them along with her and you can communicate with her even when she can't verbally tell you what she wants. (Check them out from the library. Signing Time has a whole series and they are the best.)

Have a cabinet in the kitchen that is OK for her to get into. Bowls, some wooden spoons, cups, etc. Let her get those out (yes, you will tire of this long before she will but, it's GOOD for her) and "cook" with them.

If you have a good floor, some water play (or do this in the bathtub). Just enough water and plenty of cups and sieves and bowls for her to pour and play in. Sand or rice also works well, but you'd want to have a "sand table" I saw rice used in one of those at a preschool and it was GREAT! (However you do NOT want to get it wet! It molds and stinks, hoo boy! but as long as it doesn't do that, it is great and much cleaner than sand to play with.)

If you are blessed with a patch of bare dirt, let her out to play and dig in it!! (empty clean tin cans make great diggers/scoopers!)

Is she ready to color? Get a big roll of newsprint and cover your table/floor with it, then give her regular sized papers to color on. (newsprint to be a protective tablecloth and regular sized paper to practice the concept that you color only on papers, not everything is a mural!)

Read books. Go to the library weekly. (There are also toddler story times as well!)

Give her a few toys at a time, rotate them. (Fisher Price Little People are great - well I like the old style WITHOUT all the lights and noise and talking. Children need to create their own dialogue script not let toys do the imagining and playing for them.) Toys that she can play and pretend with.

A few things, like a long t-shirt can be a dress for her, beads, make a tiara crown. And of course shoes! the clunkier & louder the heels are, the better! (yes I know... slippers would be so much better on your ears, but that's not nearly as fun!)

Play phones (or an old cell phone that's no longer activated) are always a favorite at this age.

Parents Choice has this Animal Hospital that is a GREAT toy for toddlers up to 5+ years old. For now your daughter will enjoy the keys & animals part of it (the rest of it you could probably put away for a year or two, then add it to the hospital to breathe new life and play into it later).

Paper bag puppets. Cardboard/toilet paper tubes. Empty egg cartons, with various things - chunky beads, different colored toys, even as a tray with an assortment of foods for lunch - diced ham in one, frozen peas in another, cheese cubes, cooked rice, fruit, etc! (feeding is a whole nuther topic, but I'm sure that idea will help you out too!)

Empty cardboard boxes are the best!!! Blanket draped over a chair or two for a "tent". (Children like little houses & spaces to play in.)

Go to the park! Take advantage of the great weather before it gets too hot, go play at the park. Find a grassy slope to roll down. Go for walks, see how many different things you can find. (Great way to learn/practice colors, numbers, etc)

Some of these might be "too old" for a 16 month old, so really, just take it at her level and let her explore and play with and then grow into activities (like paper bag puppets - it may frustrate you to make them then have her crumple it up because at this point, she's all about exploring textures and physical properties of brown paper bags rather than playacting with the puppet character the paper bag is supposed to be - if that made sense to you?)

Have fun! Let her "parallel play" with you. When you're in the kitchen, she's going to want to be in there too - so have a cabinet (as close but not underfoot as you/your kitchen can manage) for her "cooking supplies". When you're at the table/desk writing or reading, let her do the same.

Do not feel you have to be with/entertain her all day long! She's gotta learn to play sometimes on her own, and play sometimes with you.

It's not too early to start playing with letters & numbers. Either magnetic on the fridge or drawn out when you're also playing with her, or foam letters, whatever you have.

Something small and simple but has been well worth the purchase price ten times over - in Walmart they have a box of "Counting Bears" You get 5 colored cups and 10 of each color little plastic bears (if your daughter is still putting things in her mouth, might want to wait a little while, as they're only about an inch in size). My son is 6.5 and STILL plays with those bears!! Your daughter may not play with them as long as I am sure she'll have plenty of little girly dolls/people to play with but my son loves those bears and still incorporates them into his lego/block/train play. You/she can line them up, sort them, count them, mix them, make patterns with them, copy each other's patterns, do the same pattern but with different colors, ETC. Only $5 I think! WELL worth it!

Well, I've written a book now. Hope some of those ideas are helpful to you. :-) Whatever you do, be sure to read to her a little bit everyday. It does wonders for them.

I find that if you leave your kid alone for a long enough time, they will entertain themselves just fine. Not always with things that you may want them to play with ;), but they find ways. My daughter usually gets into everything she shouldn't but I like that she is curious and wants to know what things do and feel like.