Have several lines printed on a piece of paper. Make other sheets of paper, consecutively adding more lines to the page and making the cuts closer and closer together. This teaches the child through progressive cutting, how to cut paper in a straight line and use scissors. If she is advancing quickly, give her the option to skip a couple sheets ahead. Children can use the cuttings to make a collage.
Give each child a piece of paper and ask him to cut straight lines in it without using any guides. Though initially they used guides to cut lines, some in the Montessori community would argue that this stifles creativity, for children have to keep within the lines. Have children practice on several sheets of paper, making closer cuts each time, in order to practice their dexterity and steadiness of hand.
Allow the children to make designs that they desire by freehand cutting. Do not place any lines on the paper, or have the child draw any lines on the paper. See what she can create themselves by what comes to mind or what she feels like creating. Even have her cut out a variety of shapes, provide glue, and have her use the freehand shapes like puzzle pieces in a collage to create a picture.
Have a child come up with his own shape or object and draw it on the paper. Although this is using lines when cutting, the idea is the child's and no creativity is stifled because it is the child who created the lines. Have him slowly cut along the lines he has drawn to create the shape. He can refine the shape by cutting excess paper off the sides if he desires.