In this article for teachers, Bernard Bagnall describes how to find digital roots and suggests that they can be worth exploring when confronted by a sequence of numbers.

A game that tests your understanding of remainders.

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?

Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?

Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?