Triangle numbers

There are 30 NRICH Mathematical resources connected to Triangle numbers

problem

Favourite

Summing consecutive numbers

Age

11 to 14

Challenge level

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

problem

Favourite

Route to infinity

Age

11 to 14

Challenge level

Can you describe this route to infinity? Where will the arrows take you next?

problem

Favourite

Triangle numbers

Age

11 to 14

Challenge level

Take a look at the multiplication square. The first eleven triangle numbers have been identified. Can you see a pattern? Does the pattern continue?

problem

Favourite

Mystic rose

Age

14 to 16

Challenge level

Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.

problem

Favourite

Handshakes

Age

11 to 14

Challenge level

Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?

problem

Favourite

Light the lights again

Age

7 to 11

Challenge level

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

problem

Favourite

Iff

Age

14 to 18

Challenge level

Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?

problem

Favourite

Picturing triangular numbers

Age

11 to 14

Challenge level

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

problem

Favourite

Take ten sticks

Age

11 to 16

Challenge level

Take ten sticks in heaps any way you like. Make a new heap using one from each of the heaps. By repeating that process could the arrangement 7 - 1 - 1 - 1 ever turn up, except by starting with it?

problem

Favourite

Factors and multiples puzzle

Age

11 to 14

Challenge level

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

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For younger learners

Triangle numbers

Summing consecutive numbers

Route to infinity

Triangle numbers

Mystic rose

Handshakes

Light the lights again

Iff

Picturing triangular numbers

Take ten sticks

Factors and multiples puzzle