This was the activity that first attracted me to Montessori- Cylinder blocks.
It consist of 4 blocks and in each block there are 10 (mine only has 5) drilled holes to fit the cylinders in.
Each cylinder differs either in diameter or depth or both. For instance, in one block, all the cylinders have the same diameter. However, they vary increasingly/decreasingly in depth. In another block, all the cylinders have the same depth but vary increasingly/decreasingly in diameter etc (sorry, to lazy to give lengthy explanation but read here if you want to know more)
The direct objective of this activity is to sharpen the child's visual discrimination of varying dimensions. The indirect goals are for pincer grasp exercise (as the child use her index finger and thumb to manoeuvre the knobs on the cylinders) and if I may add, eye-hand coordination skills as well as Mathematical concepts.
During the initial work, present only one block at a time. Once the child is seasoned in working with each block; present all 4 blocks at a go to her & mix the cylinder blocks for more challenging work.
The best part of it is I don't need to give her lengthy lecture. As she worked, she instinctively learn that each cylinders have differing dimensions. I thought it was very interesting how she always pick up the largest pieces first- I guess these were the easiest to identify & match. She naturally discovered that the bigger cylinders don't fit into the smaller ones and some smaller ones don't fit into the smaller holes because they may differ in depth.
According to David Gettman, when the child matures, we can use this to explain the terms 'shallow' vs 'deep', 'thick' vs 'thicker etc.
Admittedly, this is something you can't DIY easily unless you are an expert in sawing and drilling wood- even if you are, you must be well equipped! However, if you like you can pick this book up. It comes with a template, though 2-dimension (but better than nothing & much cheaper than purchasing) which emulate this activity.