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, underdanding this relationship between numbers is called “Number Sense.” Like most skills, Number Sense can be developed through a few 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 the following exercises to help children learn to count from any number, to any number, by any number. These exercises should be done both 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, students should learn that half means “2 equal parts,” and can use this knowledge to figure out things like:
- 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, students should be challenged with 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 used as early as kindergarten; however, they are appropriate for any person of any age! The trick is to do these exercises both orally and visually, with little to no writing. As Number Sense develops, the cycle of confusion, frustration, and intimidation can be broken!
