# Creating and Manipulating Linear and Quadratic Expressions - Stage 3

### Special Numbers

##### Stage: 3 Challenge Level:

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

### Number Pyramids

##### Stage: 3 Challenge Level:

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

### More Number Pyramids

##### Stage: 3 Challenge Level:

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

##### Stage: 3 Challenge Level:

Think of a number... follow the machine's instructions. I know what your number is! Can you explain how I know?

### Crossed Ends

##### Stage: 3 Challenge Level:

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

### Always a Multiple?

##### Stage: 3 Challenge Level:

Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

### Perimeter Expressions

##### Stage: 3 Challenge Level:

Create some shapes by combining two or more rectangles. What can you say about the areas and perimeters of the shapes you can make?

### Reversals

##### Stage: 3 Challenge Level:

Where should you start, if you want to finish back where you started?

### Fibonacci Surprises

##### Stage: 3 Challenge Level:

Play around with the Fibonacci sequence and discover some surprising results!

### Think of Two Numbers

##### Stage: 3 Challenge Level:

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

##### Stage: 3 Challenge Level:

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

### Grow up Fast

##### Stage: 3 Short Challenge Level:

How old will Julie be when her age is equal to the sum of her daughters' ages?

### 8 in a Row

##### Stage: 3 Short Challenge Level:

The sum of five consecutive integers is equal to the sum of the next three consecutive integers. Can you find the largest of these eight integers?

### Brothers and Sisters

##### Stage: 3 Short Challenge Level:

Can you work out how many brothers and sisters are in the family?

### Cuboid Perimeters

##### Stage: 3 Short Challenge Level:

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

### Black and Gold Storeys

##### Stage: 3 Short Challenge Level:

25 of the storeys of a 50 storey building are painted gold, and the rest are painted black...

### The Simple Lifelive

##### Stage: 3 Challenge Level:

The answer is $5x+8y$... What was the question?