# Creating and Manipulating Linear and Quadratic Expressions - Stage 4

### 2-digit Square

##### Stage: 4 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?

### Plus Minus

##### Stage: 4 Challenge Level:

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

### What's Possible?

##### Stage: 4 Challenge 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?

##### Stage: 4 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.

### Always Perfect

##### Stage: 4 Challenge Level:

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:

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:

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

### Multiplication Square

##### Stage: 4 Challenge Level:

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

### Finding Factors

##### Stage: 4 Challenge Level:

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

##### Stage: 4 Challenge Level:

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

### Pythagoras Perimeters

##### Stage: 4 Challenge Level:

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:

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

### Hollow Squares

##### Stage: 4 Challenge Level:

Which armies can be arranged in hollow square fighting formations?

### Harmonic Triangle

##### Stage: 4 Challenge Level:

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

### Puzzling Place Value

##### Stage: 4 Challenge Level:

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

### Brian's Number

##### Stage: 4 Short Challenge Level:

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

### Choir Boys

##### Stage: 4 Short Challenge Level:

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

### Thousands of X

##### Stage: 4 Short Challenge Level:

Solve the equation $(x-2013)(x-2012)-(x-2012)(x-2011)=0.$