# Creating and Manipulating Algebraic Expressions

### 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 and 4 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?

### Harmonic Triangle

##### Stage: 3 Challenge Level:

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

### 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?

### Puzzling Place Value

##### Stage: 4 Challenge Level:

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

### Fibonacci Surprises

##### Stage: 3 Challenge Level:

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

### Creating and Manipulating Algebraic Expressions - Short Problems

##### Stage: 3 and 4

A collection of short Stage 3 and 4 problems on creating algebraic expressions.

### 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...