Finger-painting with yogurt, pudding, whip cream

Play-doh

Sandboxes and dirt. Make mud pies. Yummy!!

Water tables -- can be filled with water, rice, sand, feathers, hay, anything just be creative. Use various things to play with such as utensils, measuring cups and spoons, funnels, tongs, sifter,... Remember to include some things that won't work to further enhance the experience.

Nature walks -- sit and watch the ants, look for birds in the trees and new plants sprouting up. Look for changes in the colors around you, weather changes, and more.

Hand rhymes and songs

Lacing shapes, string wooden beads, and puzzles

Chores and basic hygiene

Legos, wooden blocks, Lincoln logs,

Cutting paper

Coloring

Magnetic letters with a lap size magnet board (you can use an old cookie sheet for this)

Stickers

Notebooking

Own homeschool stuff, as much as possible. including a  notebook to draw/write, own pencil box with whatever drawing implements she is permitted (if they can be different or new from her usual drawing materials, so much the better), safety scissors (they make some that only cut paper, not hair or clothes, if you think that's an issue.) and glue stick. 

Own "worksheets" at the pre-K level matching, coloring, etc - there's lots of printable stuff on the internet, just do a search for printable worksheets

Special math manipulatives, counters, bears, linking cubes, pattern blocks etc. My younger son's favorite was real coins, used with supervision, of course.

Craft stick games - get a bunch of craft sticks and use markers to color  designs on them in matching pairs, using different shapes, colors or numbers of dots. mix and let her match. Or turn over to blank side and play memory or make a set with ascending numbers of marks, and order them.

Old deck of playing cards - let her do what she wants with them, or suggest ideas like sorting, or use with play dough to build structures

rounded point toothpicks and play dough - if you are really ambitious, you could draw some simple designs on index cards (2D) or make samples (3D) for her to try to copy.

 A 9 x13 baking dish or jelly roll pan with a thin layer of flour or cornmeal in the bottom for drawing with a finger  OR spray shaving cream on a baking sheet and draw, shape, etc.

A coloring book with large, simple line drawings for mosaic fun -  fill in the drawings with small pieces of colored construction paper (cut into squares or tear; paint sample cards free from your local home store is great for this) glued on with glue stick.

Foam letter and/or number puzzles. for usual use, and for relief rubbings (put a sheet of paper over the piece and rub with a crayon)

A large bin (like the Rubbermaid under bed storage kind) filled a couple of inches deep with rice, and a set of measuring cups and spoons. Put a sheet down on the floor first for easy clean-up, or let her clean up with a small dustpan and hand whiskbroom.

Push a stepstool or chair up to the kitchen sink and let her "wash" a selection of plastic ware. OR find a small pitcher and let her pour into small cups (like small sippy cups without lids) and bowls. Fill  the sink with water or use a large bowl full of water in the sink to dip the
pitcher into to be filled. In the other sink put a baking dish or large food storage container with short sides to hold the cups to be filled. If you don't have another sink, put the pan on the counter next to the sink and monitor the spill level in the pan, or you could have quite a mess

Encourage her to pour the filled cups back into the reservoir (sink or bowl). Can use measuring cups and spoons here, too.

Take a sheet of paper and draw some coin sized circles on it. Let her cover the circles with counters or coins. Have some sheets with more circles and some with less. To make it harder, use different sized counters or coins and make the circles different sizes too.

Take several colors of construction paper or card stock, and cut different shapes - circles, squares, triangles. Sort or line up by color or shape. Make it harder by making more than one size of each shape, or adding more  shapes, or more colors. You can use these when she is older (or with older children) by making patterns in the lineup and having her figure out the pattern and choose what comes next. Or making rules to follow in building the lineup - the next piece must have one thing in common with the one before, or two things in common, etc.

Paperclips, regular or large size, to chain or lump together, or whatever.

A set of large stencils - the ones with small designs are just frustrating for little kids.

A hole punch and/or staple remover. My younger son went through a period of fascination with the staple remover at about 4 year old. He used it to "bite" paper. He named it Fang, and he played with it every day for long periods of time. He still loves to hole punch (he's 6 1/2 now).

Shelling salted peanuts- and then when a large enough amount has been shelled ( and not already consumed) you can put them in the  blender with a dash of vegetable oil and make peanut butter. Then the younger one can spread the peanut butter on crackers, and have snack during the next lesson period.

On a similar vein- using cookie cutters ( stars, hearts, etc. ) to cut out pieces of bread. Then spreading cream cheese on with a butter  knife and decorating the surface with raisins, nuts, olives etc. ( if  you use a circle as a cutter-they can make faces- and use sprouts or  cut up vegetables too.)

Spice paintings- using white glue on construction paper and then using  any old spices out of your cupboard as "glitter".
 
Good old ooblek ( cornstarch/water/food color)- try making two or three colors and filling "honey bears" plastic squeeze bottles with  them. Then give her a rectangular cake pan to squeeze them into. ( A 
plastic table cloth laid down first is a really good idea.)

Sorting buttons and beads. Stringing beads in simple patterns.  Attaching buttons and beads to Styrofoam blocks with old fashion hair pins (like bobby pins but with thinner wire)
 
Speaking of wire- playing with twisteez (plastic coated wires --twisteez are for all ages!) and playing with pipe cleaners- the more the better.

Using eye droppers to mix colored water. Fill an assortment of small plastic cups with colored water (I use liquid watercolor from discount school supply- but food color will also work) Make sure the colors are fairly diluted- then give one small cup of clear water and let the color mixing begin.

Taking the kernels off Indian corn. And in case you happen to have a hand crank wheat mill around- grinding wheat berries into flour. (I  know - most people don't have a wheat grinder- but if you do, it should keep your little one entertained for a while. Especially if  the goal is enough flour to then make pretzels or pizza for lunch)
 
Using the Handwriting Without Tears laminated letter cards and play dough or pretzel dough to form the letters.
 
Using mini cupcake tins, and cookie cutters with play dough along with  an assortment of plastic gems for decorating with.
 
Using measuring spoons to move colored pebbles ( the type for aquariums) from one container to another. Add colored sand to the  pebbles, pour the mix into a tub and a use sandbox sifter to separate  them. (again Discount School Supply has the colored sand)
 
And finally Dover Publications has a bunch of reusable sticker sets - some with imaginary scenes and some with scenes from different  environments and different times in history. I'm going to try to get  some that correspond with some of the subjects my older child is working on and see if they keep my littlest one engaged.

As a different approach- sometimes we move the "schoolroom"  into the back yard. Then my littlest can play while my older one has lessons. Granted this works best for either me reading to him- or his  reading to me. But we have also managed to do math lessons out there. I have also taken to giving my older one a break between subjects by reading aloud a book that both he and my 2 year old will  enjoy. This seems to help too.

The main thing to remember is to keep whatever activities you choose special for school time only, not other times. Anything that looks like or is what big people use is fun and special.