We also hope they master what's called "hierarchical inclusion," meaning that they know that numbers build by one at a time. For example, if I said "5," I hope they can see and understand that 5 is one more than 4, and one less than 6, and picture those numbers in order. We do lots of games and activities with number lines and counting to help them develop these understandings.
We also work a lot with what is called a "ten frame." Ten is the most important number in our Base 10 number system, so we spend a lot of time becoming familiar with it in kindergarten (and every grade after that...). One way for kids to be comfortable with ten is to use a ten frame when we work with numbers. Here is a picture of a ten frame, which is essentially two rows of five boxes.
To represent a number, we fill in the boxes with the corresponding number of dots. Here is a ten frame for the number 6.
We do many games using ten frames at school, but I wanted to pass one along that can be done at home using a regular deck of cards! This game is called Garbage, and it's a great exercise for kids to become familiar with both ten frames and number order.
The game is somewhat complicated to explain in this short blog post, so instructions for how to play can be found here. But most likely, if you put a deck of cards in front of your kindergartener and ask them to teach you how to play Garbage, they'll be able to tell you with ease! We have been playing often, and the kids love it. (One thing to note: You may need to teach them that jacks, queens, and kings can be used as "10s." The decks of cards we play with at school are math cards, so they have numbers written on them instead of a regular card face.)
Here are some pictures of kindergarteners eagerly playing Garbage with their math partners!