Triangular numbers

In this festive maths activity, students will learn about triangular numbers and how, when a number sequence is added together, they can be drawn to make triangles as dots. They will also add together triangular numbers using a staircase and a formula to calculate any triangular number.

This activity could be used as a main lesson activity to teach learners how to use addition and multiplication to solve practical problems. It could also be used as one of several activities within a wider scheme of learning, focusing on the use of maths to understand ratios and proportion.

Activity: Triangular numbers

This activity is one of a set of resources developed to support the teaching of the primary national curriculum. They are designed to support the delivery of key topics within maths and science. This resource focuses on the calculation of triangular numbers using the staircase method and the formula to calculate any triangular number n.

We can use our maths knowledge to understand better how to solve problems involving addition and multiplication. As we handle money and make food for big parties of people, we learn how to use addition and multiplication in everyday life.

How long will this activity take?

This activity will take approximately 40-60 minutes to complete.

Resources required

• Grid paper
• Pencils
• Erasers
• Rulers
• Calculators

The engineering context

Engineers need to know how many items are in a sequence. For example, production engineers in ice cream manufacturing need to know the number of double-scoop ice creams possible, given the number of flavours available.

Triangular numbers are also used in a variety of other engineering calculations. For example, they can be used to calculate the number of steps in a staircase, the number of bricks in a wall, and the number of components in a circuit.

Suggested learning outcomes

By the end of this activity, students will know what a triangular number is, they will be able to calculate a triangular number using a staircase, and they will be able to calculate any triangular number (n) using a formula.

Download the free Triangular numbers activity sheet below!

All activity sheets and supporting resources are free to download, and all the documents are fully editable, so you can tailor them to your students’ and your schools’ needs.

The activity sheet includes teacher notes, guidance, useful web links, and links (where appropriate) to the national curriculum in each of the four devolved UK nations; England, Northern Ireland, Scotland and Wales.

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