You say pre-school and 3 months ago. School only started in August and that's only 3 months ago.
So I assume you are not actually talking about a pre-school class in a public school but a child care classroom.
So no, they don't actually have to have a curriculum and go by it. In child care the emphasis is on children learn as they play. Google that if you're not familiar with the term.
We actually never sat down and did math or reading words or anything like that in child care and I have worked with the older kids classes for over 13 years.
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What my day was like with the 4 year old (all day in the same class) and 5 year old kids that did half day kindergarten Different group in the morning then they switched out when the other kids went to afternoon classes) was like this.
8am go to work, take my class from the general "come in and sit down until the teachers come to work room"...don't know what else to call it.
8-8:30 get everyone situated, get them headed toward circle time starting at 8:30.
During circle time we'd do the day of the week, the weather, the color of the month, the color of that week, the topic of the week, etc...we'd sing songs, march around with instruments to music, do stretches and exercises, act out things like a plant growing from a seed along with the music, talk about our morning, that sort of stuff.
After circle time, often 9:15-9:30 we'd have a morning snack then go to table time. BUT we might also go paint, do an art project, write in their journals, and all sorts of things like that. Not sit down and do math but more of a hands on to what we talked about during circle time.
After doing some table activities we'd play, either outside or in the play areas. Then it was time to clean up and get ready for lunch then nap time. They'd wake up from naps around 2:30/3pm and have a snack. Then it was play time until parents picked them up. As the classes got smaller they combined and did stuff that didn't have to be cleaned up like watching a movie or reading books or something like that.
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One of my average months might look like this. (I used the Mailbox Curriculum for preschool age kids)
February, the colors of the month would be red, white, pink, silver.
Numbers of the month probably 5, 6, 7, and 8 since those are the weeks of the year.
Then the week topics would be:
1st week U S Mail
2nd week Valentines Day
3rd week Human Heart
4rd week Dental Week
For the mail week I'd have called each family and asked them to let every relative know we wanted the kids to receive a ton of mail at the center. Every kids needed something every day. We often had mail coming in from other countries! The kids could go to the post office for a tour before 9-11 but that stopped then. We could go and tour the P O Box area and the Post Masters office but that wasn't fun. We'd write letters to others and go put it on the mail box for the carrier to pick up. This really helped the kids understand how mail worked AND it brought other family in to their lives because they got cards, letters, and pictures that week. Then they kept coming all year!
For Valentines Week we used all the colors to make Valentines for all sorts of people then we actually would go deliver them in small groups in my van. I'd take a few kids and we'd take a bunch to a nursing home or a hospital ward, lots of getting out of the building.
Of course we had a Valentine's Day party at the end of the week too.
For the human heart we'd lead into this naturally from a Valentine heart to what the human heart does and looks like. We made booklets out of the curriculum and I went and bound them at a local support place with a machine. The kids did activities all week and learned a ton of stuff about the heart.
For dental week we made a box into a smiling mouth with teeth, the kids would use yarn to "floss" the teeth, we cut a huge toothbrush out of a box so they could "brush" it's teeth. We bought the kids each a toothbrush that week and they'd go brush their teeth every day after snacks and lunch.
I did a good job with the kids but we didn't sit down and do math, didn't sit down and work on spelling or reading or a school classroom situation. We played and had fun and the kids soaked it up.
If you're talking about a child care setting for your child then perhaps you'd have been happier with an actual public school pre-school class instead. It might not be too late to enroll her in the one in your neighborhood. I know it's a hassle due to them getting out earlier than the other kids and them not having after school care but still, it might just make you feel better if she's in an actual classroom instead.