![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...
![Largest product](/sites/default/files/styles/medium/public/thumbnails/content-96-11-six6-icon.png?itok=visW6w7i)
![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?
![Tilted Squares](/sites/default/files/styles/medium/public/thumbnails/content-id-2293-icon.png?itok=q-hpU9S_)
problem
Tilted Squares
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
![Parallel lines](/sites/default/files/styles/medium/public/thumbnails/content-id-5609-icon.jpg?itok=WNXYu0AW)
problem
Parallel lines
How does the position of the line affect the equation of the line?
What can you say about the equations of parallel lines?
![Reflecting Lines](/sites/default/files/styles/medium/public/thumbnails/content-id-6471-icon.jpg?itok=_vqW58fF)
problem
Reflecting Lines
Investigate what happens to the equations of different lines when you reflect them in one of the axes. Try to predict what will happen. Explain your findings.
![Translating Lines](/sites/default/files/styles/medium/public/thumbnails/translating-lines.jpg?itok=_v1DZ7lJ)
problem
Translating Lines
Investigate what happens to the equation of different lines when
you translate them. Try to predict what will happen. Explain your
findings.
![Diminishing Returns](/sites/default/files/styles/medium/public/thumbnails/content-id-6700-icon.jpg?itok=z1TjlH_Y)
![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?
![Wipeout](/sites/default/files/styles/medium/public/thumbnails/content-id-10996-icon.png?itok=j3fpxJ14)
problem
Wipeout
Can you do a little mathematical detective work to figure out which number has been wiped out?
![Terminating or not](/sites/default/files/styles/medium/public/thumbnails/content-id-14531-icon.jpg?itok=eRQghi_3)
problem
Terminating or not
Is there a quick way to work out whether a fraction terminates or recurs when you write it as a decimal?
![Counting Factors](/sites/default/files/styles/medium/public/thumbnails/content-97-01-six1-icon.jpg?itok=k7J5c7_5)
![Legs Eleven](/sites/default/files/styles/medium/public/thumbnails/content-98-04-six1-icon.png?itok=H0rg-1Tk)
problem
Legs Eleven
Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?
![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?
![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.
![How Many Miles To Go?](/sites/default/files/styles/medium/public/thumbnails/how-many-miles-to-go-.gif?itok=s4ss-dDK)
problem
How Many Miles To Go?
How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?
![Generating Triples](/sites/default/files/styles/medium/public/thumbnails/content-id-7282-icon.png?itok=rxebyRVc)
problem
Generating Triples
Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?
![Mixing More Paints](/sites/default/files/styles/medium/public/thumbnails/content-id-4794-icon.png?itok=lFUr_0w-)