Triangle numbers

There are 31 NRICH Mathematical resources connected to Triangle numbers
Speedy summations
problem

Speedy summations

Age
16 to 18
Challenge level
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Watch the video to see how to add together an arithmetic sequence of numbers efficiently.

Summing Consecutive Numbers
problem
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Summing Consecutive Numbers

Age
11 to 14
Challenge level
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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?
Light the Lights Again
problem
Favourite

Light the Lights Again

Age
7 to 11
Challenge level
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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?

Slick Summing
problem
Favourite

Slick Summing

Age
14 to 16
Challenge level
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Watch the video to see how Charlie works out the sum. Can you adapt his method?

Handshakes
problem
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Handshakes

Age
11 to 14
Challenge level
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Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
Mystic Rose
problem
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Mystic Rose

Age
14 to 16
Challenge level
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Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
Triangular Clock
problem

Triangular Clock

Age
11 to 14
Challenge level
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Trinni rearanges numbers on a clock face so each adjacent pair add up to a triangle number... What number did she put where 6 would usually be?
Triangle Numbers
problem
Favourite

Triangle Numbers

Age
11 to 14
Challenge level
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Take a look at the multiplication square. The first eleven triangle numbers have been identified. Can you see a pattern? Does the pattern continue?
Route to infinity
problem
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Route to infinity

Age
11 to 14
Challenge level
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Can you describe this route to infinity? Where will the arrows take you next?
Factors and Multiples Puzzle
problem
Favourite

Factors and Multiples Puzzle

Age
11 to 14
Challenge level
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Using your knowledge of the properties of numbers, can you fill all the squares on the board?