Hands-On Activity

Triangular Numbers

Need a fun way to teach your students about Triangular Numbers? The group activity below is pretty effective for engaging kids and gets them thinking about and understanding this concept of a Triangular Number. 

The Basics of Triangular Numbers...

A Triangular Number is a number that can make an equilateral triangular dot pattern. For example, 3 and 6 are Triangular numbers because equilateral triangles can be formed with 3 dots and 6 dots as seen below.

triangular numbers

Triangular Number Activity

  • This is a good activity to have students work together in small groups.
  • Give each group of students 30 - 50 pennies, bingo chips, or any other similar type objects and separates them into work groups. 
  • Have the students create triangles made by stacking the pennies in rows so they touch. Each row having one less penny as the row below it as seen in picture below. 

This penny triangle

represents the  

 Triangular Number - 3

This penny triangle

represents the  

 Triangular Number - 6
  • Students in each group should work to build triangles of different sizes.
  • After building a triangle the group writes down the number of pennies that make up each triangle. Each of these numbers is a Triangular Number.
  • As each group builds triangles they should fill in the missing blanks on their worksheet with the correct number of dots for the given triangle. 
  • Have the groups fill out the worksheet as they build triangles.

More About Triangular Numbers

  • The first Triangular Number is 1 and can be referred to as T1. The second Triangular Number is 3 and can be referred to as T2.  And so on.....

Above, the first 4 triangular numbers are listed in order from smallest to largest. Notice that the number of circles that make up each triangle is the sum of the consecutive numbers beginning with the number 1.

For example,

  • 2nd Triangular Number, T2: 1 + 2 = 3
  • 3rd Triangular Number, T3: 1 + 2 + 3 = 6 
  • 4th Triangular Number, T4: 1 + 2 + 3 + 4 = 10
  • 5th Triangular Number, T5: 1 + 2 + 3 + 4 + 5 = 15
  • And so on.....

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