Investigative approach to number
 Consecutive numbers
Take any 5 consecutive numbers, add them together, divide the
answer by 5 and subtract 2 from the answer.
What happens?
Investigate.
Does the rule hold for 6 consecutive numbers? …
 Digit sum
Take a 3-digit number and write down all the possible 2 digit
arrangements from them.
Sum them.
Can you predict this total from the original 3-digit number
chosen?
Extend. Generalise. Prove.
 Can you work out the sum of the first 100 counting numbers
1 + 2 + 3 + 4 + … + 99 + 100 = ?
in less than 1 minute?
 Consecutive sums
Some numbers can be written as the sum of two or more
consecutive numbers.
Investigate.
Extensions: what happens if you include negative numbers?
What about consecutive odd numbers? What happens if you
sum the squares of consecutive numbers?
 Form a chain of numbers as follows:
multiply the units digit by 9
add to it the tens digit
and repeat
eg
37  66  60  6  54
Investigate chains of this type.
 Consecutive numbers again!
Take any three consecutive numbers, square the middle one and
multiply the other two.
Investigate.
 Products
The product of any two consecutive numbers is a multiple of 2.
The product of any three consecutive numbers is a multiple of 3.
The product of any four consecutive numbers is a multiple of ?
Investigate.