Expanding and Factorising Quadratics

2-digit Square

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

Odd Differences

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.

Plus Minus

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

What's Possible?

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

Why 24?

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

Pair Products

Stage: 4 Challenge Level: Challenge Level:1

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

Perfectly Square

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

Multiplication Square

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

Finding Factors

Stage: 4 Challenge Level: Challenge Level:1

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

Factorising with Multilink

Stage: 4 Challenge Level: Challenge Level:1

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

Quadratic Patterns

Stage: 4 Challenge Level: Challenge Level:1

Surprising numerical patterns can be explained using algebra and diagrams...

Pythagoras Perimeters

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

Difference of Two Squares

Stage: 4 Challenge Level: Challenge Level:1

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

Hollow Squares

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Which armies can be arranged in hollow square fighting formations?

Expanding and Factorising Quadratics - Short Problems

Stage: 4 Challenge Level: Challenge Level:1

A collection of short Stage 4 problems on expanding and factorising quadratics.