I have a loose goal when working with my children when they are five to get them to add numbers that add up to greater than 10. No, I don’t do this to force it or align with state standards. Rather, I do child development work, and I found five-year-old children were naturally interested in this. As such, I want to have some activities on hand to help them, when they show interest. And when they show an interest, there are a number of handy tools you can have up your sleeve, and number lines are one of them.

Very young children can rather easily add up numbers that add up to something less than 10. Their own fingers provide the perfect calculator. I actually found in the late threes children totally marvel at this. They hold up one hand with 3 fingers and another with 2 fingers and they marvel, “THIS MAKES 5!!!” There are plenty of activities to do with young children to encourage counting and adding. Simply counting things works. Playing games where you roll a dice and go that many squares is a good one. Hopping games, like hopscotch work.

At 5, children rather rapidly enter the world of theory. They can bounce ideas around in their head. And I noticed they themselves take an interest in adding numbers that go beyond their own fingers, such as that 8 + 3 equals 11. When my daughter, who is very language-oriented, spontaneously thought about a problem such as this, I simply said she might think of it as 8 + 2 + 1. Spinning off of 5 and 10 is an easy way for humans to do math. I still do this, as an adult. When I think of 8 + 5, sometimes I think, “Two more gets me to 10. Three more gets me to 13.” My oldest child thinks of it as, “Well 6 + 6 is 12, so 6 + 7 is 13.” We probably all do it a bit differently. But there are certain numbers that are easy to add. If we use those as a “base,” we can figure out trickier problems.

I noticed my youngest wanted to solve such problems recently. And he is a very “in the moment” child. He is outstanding at counting. He won’t miss a single item and he won’t count things twice. He is very concrete, and I love that about him. He was showing off that he could count 4 + 4 to make 8. I asked about 5 + 5, which he easily has memorized: it’s 10! I started writing these equations down for him, because he seems to like to look at things. I asked about 5+6 and he got it! It’s 11! He even wrote it down! He was sitting there pondering the math problems, literally putting his writing utensil to his lips as he sat deep in thought.

I was asking him some more questions and I realized a number line would help. This is a nice conceptual aid to have at the ready. With a number line, you literally just draw a line with numbers on it, in consecutive order. You start at, say, 8, and hop over 1 and get 9. You can go left and right all you want, verifying your answer. I think it’s perfect for just about any kid, but it definitely helped my very, very hands-on kid who likes concrete activities that he can touch.

I believe this can safely replace “carrying the 1.” I encourage you to read this study, “The Harmful Effects of “Carrying” and “Borrowing” in Grades 1-4.” Asking students to learn to add numbers with the “carry the 1” method actually made them worse at mental math. Children were better off not having learned it at all. The way I like to explain it is that asking them to carry the 1 asks them to think small and then go big. But children, when left on their own, naturally think big and then go small. If you ask them to add, say, 321 + 110, they would say, “Well 300 + 100 is 400. Plus 20 and 10, we get 430. The answer is 431.” Carry the one asks them to start at the ones column and move over. They get lost in the details. I do think “grocery store math” is relevant here. I graduated at the top of my class and was held up with honors for the math classes I took. But ask me to figure out which box of cereal was more affordable, and I quickly got lost in the numbers. I could barely calculate things related to speed limits unless I had a pen and paper to think of the units. It shouldn’t be like this. We shouldn’t lose our intuition or mental speed after being taught (for years on end) how to do things properly. If you want more about the theories behind teaching math to students, I encourage you to read the word of Denise Gaskins, who explains both the theory and gives many math activities and games you can do with your children.

A child’s true education largely comes down to his or her family. Who is there to foster their growth when they show interest is, based on my observations, more important than their traditional schooling. In truth, I’m not sure what I remember from school. Maybe some stuff. But I do remember playing many games with my mother and aunts, including number related ones, and my father giving me addition problems and explaining things simply to me. And I exceeded at math. I was able to curl up on the couch with my littlest as we went over these problems and he sat in happy deep thought.

In my Misbehavior is Growth books, I have activity ideas at each milestone, in alignment with where children are at developmentally. No, not activity will be for every child. But I can tell you that each activity was a hit. Meaning, I saw, live, that children enjoyed them.

If we surf their wave, instead of asking them to mold to our usually erroneous ideas of what they should be doing, we can see educational success that is both effective and a joy.