Creating and Manipulating Linear and Quadratic Expressions - Stage 4
2-digit Square
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
Can you explain the surprising results Jo found when she calculated the difference between square numbers?
What's Possible?
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
Why 24?
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
Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.
Pair Products
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Perfectly Square
The sums of the squares of three related numbers is also a perfect square - can you explain why?
Multiplication Square
Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?
Finding Factors
Can you find the hidden factors which multiply together to produce each quadratic expression?
Factorising with Multilink
Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?
Pythagoras Perimeters
If you know the perimeter of a right angled triangle, what can you say about the area?
Difference of Two Squares
What is special about the difference between squares of numbers adjacent to multiples of three?
Hollow Squares
Which armies can be arranged in hollow square fighting formations?
Harmonic Triangle
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
A collection of short problems on creating algebraic expressions.
Square Number Surprises
There are unexpected discoveries to be made about square numbers...
Puzzling Place Value
Can you explain what is going on in these puzzling number tricks?
Brian's Number
Brian chooses an integer and operates on it. Work out the largest integer that he could have chosen.
Choir Boys
Can you work out how many members this choir has from these percentages?
Cuboid Perimeters
Can you find the volume of a cuboid, given its perimeters?
Third Side
What are the possible lengths for the third side of this right-angled triangle?
Stolen Pension
How much money did the pensioner have before being robbed?
Clever Calculation
Find the shortcut to do this calculation quickly!
Length, Width and Area
The area of a rectangle is 225 square units. Find its width.