Divisible by Three - Simple Math Manipulatives

We made units, tens and hundreds and discovered if the sum of the digits in a number are  divisible by three, then the number is divisible by three.

More than five years ago I constructed these units, tens and hundreds from card stock paper by simply measuring centimeters and cutting. They are one of the most useful visual math manipulatives we have.

They have been extremely helpful in learning addition with carrying numbers, subtraction with borrowing, and place value. Most recently they were used to discover a trick in determining whether a number is divisible by 3.

First, several two and three digit numbers known to be divisible by 3 were displayed using the units. In the picture above moving from right to left, bottom to top the numbers 12, 15, 18, 21, 24, 27, 30, 33, 36, 120 and 141 are represented.

Since no pattern was initially obvious, I asked my son to count the number of pieces of paper in each pile ignoring the fact they represented ones, tens or hundreds. Moving from right to left, bottom to top the numbers of pieces of paper shown are 3, 6, 9, 3, 6, 9, 3, 6, 9, 3, and 6.

Using this process my son noticed a theme and upon further thinking was able to deduce that if the sum of the digits in the number were divisible by three, then the number was divisible by 3. 

My son is a child who learns best by figuring things out for himself. Little information is retained when I explain something, especially in regards to mathematics. Although I lead him in this activity, he discovered the rule making this activity very effective for his learning style.

See our math page for more hands-on math ideas and activities.


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