The problems in this masterclass package are intended to offer students the opportunity to engage in a key mathematical activity: moving from particular instances to general cases. Along the way, students can notice patterns, make conjectures and choose representations to help justify and prove.
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Can you describe this route to infinity? Where will the arrows take you next?
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
How is it possible to predict the card?