Make 3D objects out of Play Doh. Recipes for imitation Play Doh can be found online.
Understanding Common Core Math (Standard K.G.B.5) by Understanding Common Core Math
Conclude by giving your students this challenge: 8 identical squares have been stacked in the figure below. All but the first square are partially covered. Label the squares 1-8, from top to bottom.

Here's the solution.
With Play Doh we can create any solid, whereas sticks and clay balls limit us to polyhedron.
I should add an Amazon affiliate link for Play Doh. In the future I would like to sell various manipulatives, such as Play Doh.
K.G.B.5: Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.