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Cardinality of a Set
Cardinality of a Set
Before we begin to add or multiply we learn to count. We learn to count numbers as a list. 1, 2, 3, 4, 5, and so on. No number appears twice but only once. This way of counting is usually mastered first before moving onto the second way we learn to count. Cardinality of a set refers to how many things are in a set. Learning the concept is easy if there are 2 or 3 in a set as it's easy to recognize. You don;t need to count the numbers individually.
One-to-One Correspondence
One-to-One Correspondence
When children count objects one by one they are making a one-to-one correspondence. For example if they count five apples beginning with 1, 2, 3, 4, 5 they are correlating each apple with one number and vice versa. This is connecting listing numbers and cardinality. The most important take away here: "The last number we say when we count a set of objects tells us the total number of objects in the set" (Beckman, 2022).
Base Ten
Origins of the Base 10-
Tallies were used to work with larger numbers.
Creation of V-
To increase functionality of the system, the introduction of 'V' came about. 'V' = 5.
The Roman devised new symbols of X for 10, L for 50, C for 100, D for 500, and M for 1000.
The base-ten system and decimal system is what we use today without having to create more symbols.
Click above for examples you can do with your students in the classroom in regards to counting. Counting real objects with students can help them learn and master the art of counting. Engaging with students during this process can help you understand where a child is in the process of learning how to count as well as how to better improve their methods. I as a teacher plan to observe as much as possible, especially considering every student learns with different methods and at a different pace.
“450 Base Ten Blocks Royalty-Free Images, Stock Photos & Pictures | Shutterstock.” Base Ten Blocks, www.shutterstock.com/search/base-ten-blocks. Accessed 5 May 2025.
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