Fractional Numbers

The National Mathematics Advisory Panel, a federal task force created under formal President George W. Bush, concluded that one of the most important foundational skill not being sufficiently developed today is proficiency with fractions. 

Fractions play a central role in mathematics learning.  Fractions require a deeper understanding of numbers and numerical operations than the understanding that comes from working solely with whole numbers.  Competency with fractions is absolutely crucial for success in more advanced mathematics.

Pi Q Math has developed a curriculum following the advice of Dr. Thomas Carpenter, emeritus Professor at the University of Wisconsin-Madison and a researcher at the Wisconsin Center for Education Research.  We encourage children to use their intuitive understanding of sharing to explore fractional numbers.  These problems allow children to develop their own deep and connected understanding of division, multiplication, naming fractional numbers and the magnitude of fractional numbers. 

Pi Q Math believes developing an understanding of fractional numbers is critical before teaching a child paper and pencil procedures.  Research has shown that once a child has learned standard procedures, they will then apply minimal effort to develop an understanding.  As an example, a child who forgets the procedure when adding 3/4 + 1/2 to get 4/6 should be able to explain why their answer is non-sensical and ideally can then solve the problem based on their understanding versus blindly applying a procedure.

The curriculum at Pi Q Math successfully helps children learn to solve challenging problems involving fractional numbers with understanding and confidence.  Children who successfully complete the fraction curriculum will continue on to a short introduction to percents, rates and ratios.


This 1st grade girl is creating her own understanding of fractional numbers and division by sharing 5 cookies between 4 children.

“So, I didn’t even need to solicit feedback from my son.  The very first thing he said when he opened the car door after school on Thursday was “Mom, I really liked Pi Q Math!”  He said the problems he was working on were hard, but at his level.  He definitely likes to use his brain and be challenged!”  - Corey, mother of a 2nd grader at Logan.