Paperclay is a combination of paper fibers and regular pottery clay, which can be store bought, mix from regular pottery clay or from wild clay, dug up from your garden. In the video I used egg carton. I find it breaks down easily.  
It can be mixed in ratios of 1: 3 or 1: 2 or 1:1, depending what the purpose of the clay may be. For children's projects I prefer a 1:1 ratio since it makes it easier to bond clay without making too much mistakes. For wheel throwing less paper is desired. 
It is much easier to fix broken objects made by children. It is also a perfect opportunity for them to learn some problem-solving skills when they get to fix their own mistakes. 
Below are images of children working in various settings with paper clay. 
It is the perfect activity for arts integration in the classroom. 

1. Refining small and large motor skills by playing
2. Children learn problem solving skills without knowing they are fixing issues. By doing so it become second nature for them without the pressure of failure. 
3. Their decision making skills develop. 
3. Flexibility is a virtue any person needs in their life. By making small decision on where and how to to attach an arm on a doll or a snout on an animal sculpture, children learn not only to be flexible but also to analyze. 
4. Children that can express themselves in any way are happier children. 
5. By playing their way through personal issues they build confidence, get rid of stress and feel in control of something. 

There are much more to say about the value of letting children do art, especially working with clay. The most important fact is that children get a chance to see 3-dimentionally, something that is becoming more important in a world where flat computer and TV screens rule the day.  

Child Development and Learning Strategies Through Clay​
How to mix and preserve paper porcelain clay​

​In the same way that clay is pinched to stretch it out and to make it thinner, it can also be manipulated to change its form and  become thicker. It takes an understanding of what happens to the clay particles.

How to use your pinching skills to create a pinched teapot.