# Levels For Single-Digit Addition: Where Is Your Child?

‘Tis the season in Kindergarten for learning addition and subtraction. You may wonder where your child is with respect to these foundational operations. Most educators will think about their students’ learning of single digit addition/subtraction as a 3-level progression. I will focus on addition for sake of space.

#### Level 1: Counting All

This is where most kinders should be. They can even end the year in this level and be awesome! At Counting All, students typically use concrete objects to count one-by-one in order to find the sum. Below is an example, using 2 + 3.

#### Level 2: Counting On

This is the “trap and keep” idea. The first addend is “trapped” in your mind, and you count on from that value. This is a more sophisticated idea, because you have to understand that the first addend is a quantity of its own, and you are moving forwards from that value (versus starting at 1 every time). Often your child will “trap and keep” the first addend by taking their hand to their head to “trap” it in their mind, then use their fingers to count on. So for 5 + 3, they would “trap the 5” and count on, “siiix….sevennnnn…eighhhht”. This is a level many children live in for quite some time.

#### Level 3: “Messing with Math!”

That is actually NOT what it’s called, but I like this title much more! This is when children start realizing that there are certain “cheats” that they can use to do more of the math in their head. (Mathematically, they are called properties, but that is for another blog!) I will actually devote an entire set of blogs for this Level, as it is that important. But for now, here is an example using ten-frames with the expression, 9 + 5.

Students can see that, if they take one of the five (reds) and move it up with the nine (blues), they can make a 10. 9+5 can be renamed as 10+4=14. This is HUGE for students in terms of flexibility with numbers and algebraic thinking!

Children will ebb and flow between these three levels. The important thing is to play, explore, and play some more! The next few blogs will encourage this through games that I am trying out with my son’s Kinder class!!!