The journey to understanding number is one of wonder and exploration, and I continue to be amazed by how children’s brains build these concepts from the ground up. The fact that all brains tend to follow a similar path is equally astounding. This common journey provides a road map for how we can best support children as they develop these big ideas. By knowing where your child is now and where they’re headed, you can determine where to focus your attention.
Below, you will find a progression of number concepts that children develop from ages 3-6 (the end of kindergarten). I use age markers for the sake of simplicity, but note that every child’s journey is different. While children’s brains tend to follow the same path, they do so at different paces. I encourage you to view the progression as a learning tool rather than one of judgement. Instead of Oh no, my child is behind in counting!, use the progression to identify where your child is now in their counting skills and determine what skill your child is building towards.
I also encourage you to take a moment to view the progression with awe. Isn’t it amazing how these concepts grow over time?
Number Concepts Progression
Find a pdf of the chart here!
Key Concepts Glossary
- Verbal counting refers to reciting the number-word sequence (“One, two, three…”). Children begin with rote memorization of the words and order, but as their understanding of number grows, they assign meaning to the memorized words. A key understanding here is for children to find the pattern in the number-word sequence. Children love to find out that they can just keep counting as long as they know the name of each ten.
- A child counts with one-to-one correspondence when they count one number-word for each object. Many times children will physically touch each object or move objects to one side to remember which objects have been counted and which haven’t. Children who count the same item multiple times or skip over items have not yet mastered one-to-one correspondence.
- Cardinality refers to the understanding that the last number counted represents the total number of items in the set.
- Numerals are the written number symbols. Understanding numerals means making connections between the number word, the quantity, and the numeral: three = 3 = a group of 3 objects.
- Subitizing is recognizing how many are in a group without counting each individual item. Our subitizing powers are limited to about 4 objects. For larger groups, our brains tend to chunk objects into groups to figure out how many.
- Comparing numbers is all about understanding relationships in equal and unequal groups. Children first look at equality through the lens of one-to-one correspondence. You can determine if two sets are equal by pairing them off, one object from Set A with one object from Set B. If there are no objects left over, Set A and Set B have equal amounts. Any number of leftover objects means that the sets are unequal.
- Download a pdf of the chart here for future reference!
- Identify where your child is in each of these categories. Embrace how much they are learning!
- Identify where that understanding goes next. Check out the “Experiences that Build Understanding” section of the posts below to find concrete strategies you can use to help your child build progress in their understanding.
Feikes, David., Schwingendorf, Keith. and Gregg, Jeff. (2018) Children’s Mathematical Learning. Retrieved from this website.
Reed, K. and Young, J. (2017). Play Games, Learn Math! Number Path Games. Teaching Young Children 11(1). Retrieved from https://www.naeyc.org/resources/pubs/tyc/apr2019/number-path-games.
Wagner, Julie. (2014) Learning Pathways in Numeracy: Addressing Early Numeracy Skills. Retrieved from https://www.k12.wa.us/sites/default/files/public/mathematics/pubdocs/learningpathwaysinnumeracy.pdf.