In the previous blogpost on how to Change math task so that they become more challenging, we wrote about guidelines on how to change existing tasks. In this blogpost we discuss how to design new math tasks. Challenging maths tasks give students the opportunity to learn, think, explore, discuss, be creative and learn (about) different strategies and respresentations or visualisations in the process.
The guidelines below are particularly useful when you design new, challenging tasks.

Can you make it into an activity?

Can you make it handson: use materials, equipment and tools?

Can you make it into an experiment?

Can you use problems from the real world?

Can you integrate it with other subjects?
H) Fold an airplane from and A4 piece of paper and measure whose airplane gets farthest. Pupils work in groups. (They decide how many tries they are allowed, how they can measure in a fair way, how they can improve their paper plane etc.)
I) Use polydron squares. See the blogpost Cube 3D2D and Make a cube and fold it out into a nett. How many different netts can you find?
J) Let the students measure the schools playground using ‘steps’ (or a rope). What is the shortest way to cross the playground? Ask them to draw the playground and their shortest route on cm2 grid paper.
K) Plan a trip from your home town to Oslo. Work out and compare different options.
When is the trip fastest? Which means of transport is cheapest? Depending of how much time you want to spend on the project, you can decide how much information you give: timetables, maps, pricelists.
L) The task in the blogpost on Balancing Act is both physics and maths. It offers students the opportunity to investigation, experiment, and to find the rule. The last step is generalisation and (early) algebra. Instead of using a computerprogram you can also use a real balance/scales or have the students construct their own.