# Rich Maths Task 9 - Simultaneous Equations Staircase

Created by
MrBartonMaths

Have a play around with this task, and please share any questions, extensions, simplifications, modifications, or lines of inquiry in the comment box below. The idea is to collect loads of suggestions that can then be used for effective differentiation. The full set of these tasks, along with additional notes, can be found here: http://www.mrbartonmaths.com/richtasks.htm

Free

### Info

Created: May 19, 2015

Report a problem

### 4 Reviews

55
• 5Recommended
10 months agoreport

This rich task from the legendary Mr Barton will really spark students interest. Starting with linear sequences, students form a pair of simultaneous equations and solve them. What happens if they start with 2 different sequences? Try it yourself and see if your curiosity isn't piqued!

• 5
2 years agoreport

Nice rich task, which develops higher order thinking.

• 5
2 years agoreport

• 5Recommended
2 years agoreport

Can you explain what you have discovered?

How would you convince someone it always works?

How would you explain why it works?

The other way around: If a pair of equations has a solution of x = -1, y = 2, does it mean they are in a sequence?

Can you make up pairs of equations that have solutions:
x = 1, y = -2
x = -1, y = -2
x = 1, y = 2

What other questions might a mathematician ask?

Can you explain what you have discovered?

How would you convince someone it always works?

How would you explain why it works?

What happens if you try linear sequences that descend?

Are there any linear sequences that don’t have solutions? Why is this?

What happens if you have subtractions?

What happens if you use negative numbers, decimals or fractions?

What happens if you use another type of sequence?

What happens if one of the equations is linear and the other a quadratic?

What other questions might a mathematician ask?

Ideas for other sequences to try:

Descending linear

Fibonacci

Geometric

Pascal’s Triangle

3D (x, y and z)