To get started you need ...
You could buy a school set or have students bring their own as part of their school supplies. A kit like the one featured in the picture costs around $10 and they can sometimes be had at a Dollarstore for less.
A quick internet search will give you loads of ideas.
In this unit students will work through Clothing, Textiles, and Fashion Outcome 2: Hand Sewing. Students will learn how to identify hand sewing tools and how to use them safely.
These could be turned into bean bags, but really all they are for is to give students a chance to cut out something, stuff it and sew it together to practice their stitching.
In this lesson students learn about making their own designs and patterns and then create their own unique stuffed monster using whip stitches, back stitches, and running stitches. Each monster will have two buttons included as well to showcase this skill.
This mitt project can be purchased from a company called "Classy Threads" who has many other projects for sale that may be a fit in your classroom. Ordering kits for all your students costs a bit of money per child, but the elastics, fleece material, and patterns will all be delivered to you. If you order one and reuse the patterns you could upcycle fleece sweatshirts the students may bring in and just have the cost of supplying the elastic.
https://classythreads.com/store/ca/#!/Mitts-Kit/p/86599284
Once you get the hang of this skill there are loads of ideas you can try out like christmas decorations, baby toys, bookmarks, tic tac toe boards, fidgets, etc. In this file you will find some of these ideas collected from outside sources that you may use or may inspire you to try something of your own.
If you have a healthy budget or want to give kids more choice in their projects (if they pay for the materials), 'Classy Threads' sells ready to make hand and machine sewing projects that work well in schools. Kits include the patterns, instructions and materials for kids to practice their skills with.