Number Sense Assessment

I’ve been working on a few books to give teachers (and parents) activities to help build number sense and develop flexibility with their addition facts.  It is one of my goals for the summer to complete them, but in the meantime I will be posting an activity each week.  This isn’t just to get you interested in the books…I am doing it because a friend of mine asked me to give her some ideas and activities to help her 2nd grade child who is struggling with math.  My belief is that most kids who struggle with math do so because they don’t have a solid foundation to build all of mathematics off of, and that foundation starts early.  Everything you find out there about what number sense is, gives a general idea…like “fluidity and flexibility with numbers” (Gersten & Chard, 2001).  That is nice but it doesn’t give teachers any idea on how to help kids develop it.  I think Van de Walle (2014) found the Holy Grail of Number Sense.  In Teaching Student-Centered Mathematics Grades Pre K-2 (aka my Math Bible), Van de Walle mentions four Number Relationships that kids need to build around the numbers up to 20 (in previous editions of the book it was numbers up to 12, but the recent edition says up to 20), but the more I work with these four ideas I’ve come to see that they need to be developed for all numbers (details on that in a future post).  I firmly believe that if we help build these four ideas around all numbers that kids will be able to work fluidly, flexibly, and fluently within all areas of mathematics:

Spatial Relationship – recognizing how many without counting by seeing a visual pattern.

One and Two More/Less – this is not the ability to count on two or count back two, but instead knowing which numbers are one and two less or more than any given number.

Benchmarks of 5 & 10 – ten plays such an important role in our number system (and two fives make up 10), student must know how numbers relate to 5 and 10.

Part-Part-Whole – seeing a number as being made up of two or more parts.

So, my first weekly activity to give you are my ideas on how to assess whether or not kids have these four relationships built around numbers.  That way you know which of these relationships kids need to work with more.  This Number Sense Assessment and the forthcoming weekly activities will be focusing on numbers 0-20…they would need to be modified for larger numbers but the general ideas still remain.  As you give this assessment to children, feel free to report back on what you learned about the child and post any questions you have in the comments.