This is part of our Secondary Curriculum collection of favourite rich tasks arranged by topic.
Scroll down to see the complete collection, or explore our subcollections on Perimeter and Area in two dimensions, and Surface Area and Volume in three dimensions.
problem
Favourite
Your number is...
Age
7 to 14
Challenge level
Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?
problem
Favourite
The Number Jumbler
Age
7 to 14
Challenge level
The Number Jumbler can always work out your chosen symbol. Can you work out how?
problem
Favourite
Special Numbers
Age
11 to 14
Challenge level
My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?
problem
Favourite
Number Pyramids
Age
11 to 14
Challenge level
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
problem
Favourite
Crossed Ends
Age
11 to 14
Challenge level
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
problem
Favourite
Perimeter Expressions
Age
11 to 14
Challenge level
Create some shapes by combining two or more rectangles. What can you say about the areas and perimeters of the shapes you can make?
problem
Favourite
Think of Two Numbers
Age
11 to 14
Challenge level
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
problem
Favourite
More Number Pyramids
Age
11 to 14
Challenge level
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
problem
Favourite
Always a multiple?
Age
11 to 14
Challenge level
Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...
problem
Favourite
Reversals
Age
11 to 14
Challenge level
Where should you start, if you want to finish back where you started?
problem
Favourite
Fibonacci Surprises
Age
11 to 14
Challenge level
Play around with the Fibonacci sequence and discover some surprising results!
problem
The Simple Life
Age
11 to 14
Challenge level
The answer is $5x+8y$... What was the question?
problem
Favourite
Quadratic Patterns
Age
14 to 16
Challenge level
Surprising numerical patterns can be explained using algebra and diagrams...
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You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.