Understanding math through ‘Number Sense’

(November 15, 2012) School is in full swing and kids are trying their best to keep up in math. What can we as parents do to help them understand their homework without doing it for them? Math is a cumulative skill and many children struggle today because they have missed something in the past.

Successful problem-solving skills are based on having an intuitive sense of the problem.  That is, being able to recognize its different “parts” and how they relate to the “whole.”  In math, this intuition and visualization of how numbers relate and can be manipulated is called “Number Sense.” Like most skills, Number Sense can be developed through mastery of foundational concepts.

Among the most indispensible of these basic skills is counting and grouping (“seeing” numbers in groups). To develop counting skills, parents can utilize exercises to help children learn to count from any number, to any number, by any number. Do these exercises forward and backward:

• Count by 1’s, starting at 0 (0, 1, 2, 3…),
  • then starting at any number (e.g., 28, 29, 30, 31…).
• Count by 2’s, starting at 0 (0, 2, 4, 6…),
  • then starting at 1 (1, 3, 5, 7…),
  • then starting at any number (e.g., 23, 25, 27, 29…).
• Count by 10’s, starting at 0 (0, 10, 20, 30…),
  • then starting at 5 (5, 15, 25, 35…),
  • then starting at any number (e.g., 37, 47, 57, 67…).
• Count by ½’s, starting at 0 (0, ½, 1, 1 ½…),
  • then by ¼’s starting at 0 (0, ¼, ½, ¾…),
  • then by ¾’s starting at 0 (0, ¾, 1 ½, 2 ¼…).
• Count by 15’s, starting at 0 (0, 15, 30, 45…).
• Count by 3’s, 4’s, 6’s, 7’s, 8’s, 9’s, 10’s, 11’s, 12’s, 20’s, 25’s, 50’s, 75’s, 100’s, and 150’s, starting at 0.

The benefits of this type of counting practice are strong addition skills and ultimately, the painless mastery of multiplication facts. As counting skills develop, fractions can be introduced. Long before introducing words like numerator and denominator, teach children that half means “2 equal parts.” Have them use this knowledge to figure out:

• How much is half of 6? 10? 20? 26? 30? 50? 100? 248? 4,628?
• How much is half of 3? 11? 15? 21? 49? 99? 175? 999? 2,001?

As the ability to split numbers in half develops, add questions like:

• How do you know when you have half of something?
• Half of what number is 4? 25? 2 ½?
• How many half sandwiches can you make out of three whole sandwiches?
• How much is 2 plus 2 ½? How much is 3 ½ plus 4?
• How much is 7 take away 2 ½? How much is 7 ½ take away 2?
• How much is 2 ½, four times? Seven times? Two-and-a-half times?
• How much is a half plus a quarter?
• What part of 12 is 6? Is 4? Is 3? Is 1? Is 9? Is 8? Is 12? Is 24? Is 30?

These strategies can be started in kindergarten; however, they are appropriate for any any age. The trick is to do these exercises both orally and visually, with little to no writing.  As your child’s Number Sense develops, the cycle of confusion, frustration and intimidation that has developed in prior years can be broken.

By Bob and Becky Barnes with Mathnasium Learning Center, located at 919 E. Interstate 30, Suite 126 in Rockwall. Email them at rockwall-heath@mathnasium.com or visit mathnasium.com/rockwall-heath.  

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