![Picturing Square Numbers](/sites/default/files/styles/medium/public/thumbnails/content-id-2275-icon.png?itok=k5l23Kai)
problem
Picturing Square Numbers
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
![Elevenses](/sites/default/files/styles/medium/public/thumbnails/content-id-6390-icon.png?itok=1dcdS-Fl)
problem
Elevenses
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
![Shifting Times Tables](/sites/default/files/styles/medium/public/thumbnails/content-id-6713-icon.png?itok=y_Wtw3Cv)
problem
Shifting Times Tables
Can you find a way to identify times tables after they have been shifted up or down?
![Charlie's delightful machine](/sites/default/files/styles/medium/public/thumbnails/content-id-7024-icon.png?itok=TnFInR1F)
problem
Charlie's delightful machine
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
![What numbers can we make?](/sites/default/files/styles/medium/public/thumbnails/content-id-7405-icon.png?itok=AGBx2S5H)
problem
What numbers can we make?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
![Odds, Evens and More Evens](/sites/default/files/styles/medium/public/thumbnails/content-id-7529-icon.png?itok=9Abf3oXj)
problem
Odds, Evens and More Evens
Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...
![Consecutive Sums Poster](/sites/default/files/styles/medium/public/thumbnails/content-id-7999-icon.png?itok=DMo6W3RR)
![Beach Huts](/sites/default/files/styles/medium/public/thumbnails/content-id-11008-icon.png?itok=y7UlgTmV)
![Growing Surprises](/sites/default/files/styles/medium/public/thumbnails/content-id-11212-icon.jpg?itok=bs0Du2U4)
![Days and Dates](/sites/default/files/styles/medium/public/thumbnails/content-00-04-15plus1-icon.png?itok=iJ_VkR9D)
problem
Days and Dates
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
![Summing Consecutive Numbers](/sites/default/files/styles/medium/public/thumbnails/content-97-05-six4-icon.png?itok=qriTyABd)
problem
Summing Consecutive Numbers
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?
![Frogs](/sites/default/files/styles/medium/public/thumbnails/content-00-12-game1-icon.gif?itok=HbJX89ir)
problem
Frogs
How many moves does it take to swap over some red and blue frogs? Do you have a method?
![Picturing Triangular Numbers](/sites/default/files/styles/medium/public/thumbnails/content-id-2274-icon.png?itok=97WlDq_l)
problem
Picturing Triangular Numbers
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
![Seven Squares - Group-worthy Task](/sites/default/files/styles/medium/public/thumbnails/content-id-2290-icon.png?itok=onTztJr5)
problem
Seven Squares - Group-worthy Task
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?
![Coordinate Patterns](/sites/default/files/styles/medium/public/thumbnails/content-id-2292-icon.png?itok=tWsgfytK)
problem
Coordinate Patterns
Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?
![Squares in rectangles](/sites/default/files/styles/medium/public/thumbnails/content-id-4835-icon.png?itok=WIB6uV96)
problem
Squares in rectangles
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?
![Triangle Numbers](/sites/default/files/styles/medium/public/thumbnails/content-id-5525-icon.png?itok=epXj0vjW)
problem
Triangle Numbers
Take a look at the multiplication square. The first eleven triangle
numbers have been identified. Can you see a pattern? Does the
pattern continue?
![Squares In Rectangles Poster](/sites/default/files/styles/medium/public/thumbnails/content-id-5586-icon.gif?itok=FIA46tbp)
![Tower of Hanoi](/sites/default/files/styles/medium/public/thumbnails/content-id-6690-icon.png?itok=VXO_iBIu)
problem
Tower of Hanoi
The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
![Seven Squares](/sites/default/files/styles/medium/public/thumbnails/content-id-8111-icon.png?itok=_4UM0hZd)
problem
Seven Squares
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
![What numbers can we make now?](/sites/default/files/styles/medium/public/thumbnails/content-id-8280-icon.jpg?itok=ba4RvjmQ)
problem
What numbers can we make now?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
![1 Step 2 Step](/sites/default/files/styles/medium/public/thumbnails/content-00-10-penta1-icon.png?itok=wey3aDMe)
problem
1 Step 2 Step
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?
Image
![Patterns and Sequences - Stage 3 STEM footer Patterns and Sequences - Stage 3 STEM footer](/sites/default/files/styles/large/public/thumbnails/content-id-13486-STEMlogo.png?itok=-JmACkHL)
You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.