This searchable collection, Mudd Math Fun Facts from Harvey Mudd College Math Department has resources that can make great starter activities, perhaps try Squares Ending in 5 and Multiplication by 11 both made excellent starters. I have looked at proofs for these with students as well as enjoying the mental Maths tricks!

It is possible to search by topic, difficulty level and keywords.

Examples to try:

• Multiplication by 11
• Difference of Squares
• Magic 1089
• Squares Ending in 5 
• Multiplying Complementary Pairs
• Kaprekar’s Constant

You will find more lightning arithmetic suggestions on the site.