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.