problem

Favourite

### 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...

problem

Favourite

### 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?

problem

Favourite

### Tilted Squares

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

problem

Favourite

### 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?

problem

Favourite

### 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.

problem

Favourite

### Translating Lines

Investigate what happens to the equation of different lines when
you translate them. Try to predict what will happen. Explain your
findings.

problem

Favourite

### Cyclic Quadrilaterals

Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

problem

Favourite

### Diminishing Returns

How much of the square is coloured blue? How will the pattern continue?

problem

Favourite

### Growing Surprises

Can you find the connections between linear and quadratic patterns?

problem

Favourite

### Counting Factors

Is there an efficient way to work out how many factors a large number has?

problem

Favourite

### 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?

problem

Favourite

### 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?

problem

Favourite

### 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.

problem

Favourite

### Opposite vertices

Can you recreate squares and rhombuses if you are only given a side or a diagonal?

problem

Favourite

### What numbers can we make now?

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

problem

Favourite

### Wipeout

Can you do a little mathematical detective work to figure out which number has been wiped out?

problem

Favourite

### Terminating or not

Is there a quick way to work out whether a fraction terminates or recurs when you write it as a decimal?

problem

Favourite

### 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?

problem

Favourite

### 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?