This item is excellent when trying to add numbers quickly. Some students don't like using their fingers in fear of others watching. However, they can touch the numbers with their pencils on the dots as they count. The goal is that they remember where the dots are and can use the technique without them. The dots with overlapping circles like on 6-8 mean those circles are repeated. On 9, the 3 circles mean that you count each dot three times. I hope this helps. I post these in my ESE classrooms for my students.