Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
The picture illustrates the sum 1 + 2 + 3 + 4 = (4 x 5)/2. Prove the general formula for the sum of the first n natural numbers and the formula for the sum of the cubes of the first n natural numbers.
Show that if three prime numbers, all greater than 3, form an
arithmetic progression then the common difference is divisible by
6. What if one of the terms is 3?
Many standard questions give exactly the information required to solve them. In this problem, students need to go in search of the information and work in a systematic way in order to make sense of the results they gather.
This task will require students to have access to computers. If this is not possible, Four Coloured Lights provides students the opportunity to make sense of numerical rules without the need for computers.
Which numbers will you try first?
A Little Light Thinking invites students to explore turning on multiple lights simultaneously.
Learners could use a 100 square (Word, pdf) to record which lights turn on for each number they try.
In the Hint there is a version of the interactivity with just two lights which students might find more accessible.