Comparing and ordering numbers

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?

Use the fraction wall to compare the size of these fractions - you'll be amazed how it helps!

How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?

Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?

Pick two rods of different colours. Given an unlimited supply of rods of each of the two colours, how can we work out what fraction the shorter rod is of the longer one?

From a group of any 4 students in a class of 30, each has exchanged Christmas cards with the other three. Show that some students have exchanged cards with all the other students in the class. How many such students are there?

How many ways can you write the word EUROMATHS by starting at the top left hand corner and taking the next letter by stepping one step down or one step to the right in a 5×5 array?

What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.