Goals
Learn the technique for checking addition, subtraction, multiplication or division problems using the 'casting out nines' technique.
Get some understanding of why this method works.
What To Do
Create 5 addition and 5 multiplication sums. Make one of each type incorrect. Find the incorrect ones.
Teach method of 'casting out nines' for addition problems
Test it out on the 5 problems above and other problems
Ask students to guess how to use the same technique for checking multiplication problems - test out any proposed methods
Teach method of adding nines for multiplication problems
Discuss how to do this for subtraction and division too - for division, convert the problem to a multiplication one.
Look at cases where the 'casting out nines' technique does not find a wrong answer. What cases does this happen with - start with simple example
Look at clock arithmetic of size nine. Look at adding the clock digits only.
Inspiration
Numberphile again: Casting Out Nines