problem
Picturing Square Numbers
Age
11 to 14
Challenge level
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
problem
Elevenses
Age
11 to 14
Challenge level
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
problem
Shifting Times Tables
Age
11 to 14
Challenge level
Can you find a way to identify times tables after they have been shifted up or down?
problem
Charlie's delightful machine
Age
11 to 16
Challenge level
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
problem
What numbers can we make?
Age
11 to 14
Challenge level
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
problem
Odds, Evens and More Evens
Age
11 to 14
Challenge level
Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...
problem
Beach Huts
Age
11 to 14
Challenge level
Can you figure out how sequences of beach huts are generated?
problem
Growing Surprises
Age
11 to 14
Challenge level
Can you find the connections between linear and quadratic patterns?
problem
Days and Dates
Age
11 to 14
Challenge level
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
problem
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
Frogs
Age
11 to 14
Challenge level
How many moves does it take to swap over some red and blue frogs? Do you have a method?
problem
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
Seven Squares - Group-worthy Task
Age
11 to 14
Challenge level
Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?
problem
Coordinate Patterns
Age
11 to 14
Challenge level
Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?
problem
Squares in rectangles
Age
11 to 14
Challenge level
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle
contains 20 squares. What size rectangle(s) contain(s) exactly 100
squares? Can you find them all?
problem
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
Tower of Hanoi
Age
11 to 14
Challenge level
The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
problem
Seven Squares
Age
11 to 14
Challenge level
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
problem
What numbers can we make now?
Age
11 to 14
Challenge level
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
problem
1 Step 2 Step
Age
11 to 14
Challenge level
Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?
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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.