# Creating and Manipulating Linear and Quadratic Expressions - Stage 3

This is part of our Secondary Curriculum collection of favourite rich tasks arranged by topic.

### Number Pyramids

##### Stage: 3 Challenge Level:

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

##### 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?

### 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?

### 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?

##### Stage: 3 Challenge Level:

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

### More Number Pyramids

##### Stage: 3 Challenge Level:

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

### 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!

### Always a Multiple?

##### Stage: 3 Challenge Level:

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

### 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?

### Creating and Manipulating Linear and Quadratic Expressions Stage 3 - Short Problems

##### Stage: 3

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

### The Simple Life

##### Stage: 3 Challenge Level:

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