# Creating and Manipulating Linear and Quadratic Expressions - Stage 4 ### 2-digit Square

##### Age 14 to 16Challenge 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? ### Plus Minus

##### Age 14 to 16Challenge Level

Can you explain the surprising results Jo found when she calculated the difference between square numbers? ### What's Possible?

##### Age 14 to 16Challenge Level

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make? ### Why 24?

##### Age 14 to 16Challenge 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. ### Always Perfect

##### Age 14 to 18Challenge Level

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

##### Age 14 to 16Challenge Level

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

##### Age 14 to 16Challenge Level

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

##### Age 14 to 16Challenge Level

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

##### Age 14 to 16Challenge Level

Can you find the hidden factors which multiply together to produce each quadratic expression? ##### Age 14 to 16Challenge Level

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

##### Age 14 to 16Challenge Level

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

##### Age 14 to 16Challenge Level

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

##### Age 14 to 16Challenge Level

Which armies can be arranged in hollow square fighting formations? ### Harmonic Triangle

##### Age 14 to 16Challenge Level

Can you see how to build a harmonic triangle? Can you work out the next two rows? ### Creating and Manipulating Linear and Quadratic Expressions - Short Problems

##### Age 11 to 16

A collection of short problems on creating algebraic expressions. ### Square Number Surprises

##### Age 14 to 16Challenge Level ### Puzzling Place Value

##### Age 14 to 16Challenge Level

Can you explain what is going on in these puzzling number tricks? ### Brian's Number

##### Age 14 to 16 ShortChallenge Level

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

##### Age 14 to 16 ShortChallenge Level

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

##### Age 14 to 16 ShortChallenge Level

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

##### Age 14 to 16 ShortChallenge Level

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

##### Age 14 to 16 ShortChallenge Level

How much money did the pensioner have before being robbed? ### Clever Calculation

##### Age 14 to 16 ShortChallenge Level

Find the shortcut to do this calculation quickly! ### Order the Products

##### Age 14 to 16 ShortChallenge Level

Can you put these products in order of size? ### Length, Width and Area

##### Age 14 to 16 ShortChallenge Level

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

##### Age 14 to 16 ShortChallenge Level

Find a factor of $2^{48}-1$.