By the end of second grade, children have developed the foundation for their future math learning. They know that numbers tell how many, they have explored our base ten number system, and they understand that numbers can be put together and taken apart to create new numbers. In fact, with a handful of exceptions, children have learned all of the essential math concepts they will encounter throughout their mathematical career.
Take a moment to let that sink in. Children’s brains form all of the pathways and connections needed to understand essential math concepts before they turn 9 years old. Amazing, right? From third grade to college, children will draw upon their understanding of these concepts and extend them to include new skills.
The chart below outlines the key understandings and skills that children learn from kindergarten to second grade, according to the Common Core State Standards (see the progression for ages 3-5 here). I encourage you to view this progression not as a list of skills your child has to master, but as a series of understandings your child gets to explore. Your child is going to apply their understanding of these concepts to understand more complex ideas later on, so it’s important that they build a deep and meaningful foundation now.
To support your child in their math journey, use this chart to identify where your child is now, and look forward to what skills lie ahead. Most of all, don’t panic if your child isn’t where you anticipate them to be! If you’re concerned about a specific skill or concept, check out the links in the Take Action section at the bottom of this post.
Number Concepts Progression
Find a pdf of the chart here!
Key Concepts Glossary
- Understanding 10 is essential to a child’s learning because our entire number system is centered around the number 10. It’s important that children understand ten as both ten ones as well as a one unit. Students will go through stages before developing a full understanding.
- Being able to decompose numbers is an essential part of number fluency. You’ll also hear this as part-whole relationships, and the concept is simple: you can break a whole into parts, and you can combine parts to make a whole. Once children understand that numbers can be flexible and manipulated, they can decompose numbers as a strategy for addition and subtraction.
- Counting on is a counting strategy that children use as they bridge the gap between counting and addition/subtraction. When children are first learning to add, they will use the count all counting strategy. Reaching the count on phase enables children to use this strategy to add larger numbers and perform mental math more easily.
- Place value means that in a written number, each position, or place, has a specific value. We use a base ten system, which means that the value of each place is centered around ten: as you move to the left, the value of each position is ten times greater. Zero acts as a placeholder to show that a specific place has no value. Understanding place value is essential for adding and subtracting multi-digit numbers
- 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.
Common Core standards
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.