Title: Sqaure & Triangle Numbers
Learning Objectives
To investigate the relationship between square numbers, triangle number and the real world.
What is the quickest way of finding the 1000th triangle number?
Resources
Starter
We will come back to this topic later.
Level 4
Now we will take a look at the maths behind handshakes.
Now think about what would happen if you increased the number of people in the room.
We could solve this problem by experiment however the problem quickly gets much more difficult as the number of people increases. We need a method.
Below is one method, this involves drawing all of the people around a circle and joining up the points.
You can see an animated version of this method on the NRich website.
By using the website or drawing the circle work out how many handshakes are needed in each case. Can you see a pattern?
Level 5
We are now going to look at two different types of numbers. We will record these numbers along with the Square Numbers on a table so that we can compare them.
Rectangle Number
Triangle Numbers
Now using our table we can compare the square, rectangle and triangle numbers.
Are there any patterns?
What is the connection to the handshake problem?
Is there a quick way of finding the number of handshakes?
