Comparing and ordering numbers

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

Each child in Class 3 took four numbers out of the bag. Who had made the highest even number?

If p is a positive integer and q is a negative integer, which of these expressions is the greatest?

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?

Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?

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

Is it true that $99^n$ has 2n digits and $999^n$ has 3n digits? Investigate!

Suppose you had to begin the never ending task of writing out the natural numbers: 1, 2, 3, 4, 5.... and so on. What would be the 1000th digit you would write down.

Can you form this 2010-digit number...