Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Creating and Manipulating Linear and Quadratic Expressions - Stage 4

### 2-digit Square

### Plus Minus

### What's Possible?

### Why 24?

### Always Perfect

### Pair Products

### Perfectly Square

### Multiplication Square

### Finding Factors

### Factorising with Multilink

### Pythagoras Perimeters

### Difference of Two Squares

### Hollow Squares

### Harmonic Triangle

### Creating and Manipulating Linear and Quadratic Expressions - Short Problems

### Square Number Surprises

### Puzzling Place Value

### Brian's Number

### Choir Boys

### Cuboid Perimeters

### Third Side

### Stolen Pension

### Clever Calculation

### Length, Width and Area

Links to the University of Cambridge website
Links to the NRICH website Home page

Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

Or search by topic

Age 14 to 16

Challenge Level

A 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?

Age 14 to 16

Challenge Level

Can you explain the surprising results Jo found when she calculated the difference between square numbers?

Age 14 to 16

Challenge Level

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

Age 14 to 16

Challenge Level

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.

Age 14 to 18

Challenge Level

Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.

Age 14 to 16

Challenge Level

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

Age 14 to 16

Challenge Level

The sums of the squares of three related numbers is also a perfect square - can you explain why?

Age 14 to 16

Challenge Level

Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?

Age 14 to 16

Challenge Level

Can you find the hidden factors which multiply together to produce each quadratic expression?

Age 14 to 16

Challenge Level

Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?

Age 14 to 16

Challenge Level

If you know the perimeter of a right angled triangle, what can you say about the area?

Age 14 to 16

Challenge Level

What is special about the difference between squares of numbers adjacent to multiples of three?

Age 14 to 16

Challenge Level

Which armies can be arranged in hollow square fighting formations?

Age 14 to 16

Challenge Level

Can you see how to build a harmonic triangle? Can you work out the next two rows?

Age 11 to 16

A collection of short problems on creating algebraic expressions.

Age 14 to 16

Challenge Level

There are unexpected discoveries to be made about square numbers...

Age 14 to 16

Challenge Level

Can you explain what is going on in these puzzling number tricks?

Age 14 to 16

ShortChallenge Level

Brian chooses an integer and operates on it. Work out the largest integer that he could have chosen.

Age 14 to 16

ShortChallenge Level

Can you work out how many members this choir has from these percentages?

Age 14 to 16

ShortChallenge Level

Can you find the volume of a cuboid, given its perimeters?

Age 14 to 16

ShortChallenge Level

What are the possible lengths for the third side of this right-angled triangle?

Age 14 to 16

ShortChallenge Level

How much money did the pensioner have before being robbed?

Age 14 to 16

ShortChallenge Level

Find the shortcut to do this calculation quickly!

Age 14 to 16

ShortChallenge Level

The area of a rectangle is 225 square units. Find its width.