See Games page also.
Questions such as this can make a great starter for a lesson and provide the chance to discuss number operations and the relationships between them. Manipulating numbers like this can also help with algebraic manipulation.
Looking for some more examples of this type, I came across a really useful resource on TES, “If I know this then I also know …” by Piers Butler. This would make an ideal lesson starter. As it is an Excel spreadsheet, I thought it would be simple to add another worksheet with the answers and created the Excel file CY If_I_know_this_then_I_also_know_ which is a copy of the original, but just adds another worksheet with the answers.
Manipulate numeric expressions with this TES resource from Piers Butler.
Make 24, see 4 Numbers Game. For further information see this page on the problem and a link to an online program which optionally shows solutions as well as presenting random problems. The program will also show solutions for any given set of four numbers. If you just want to make a note of a few problems and solutions then you could use this page from ResearchManiacs.com.
Clever tricks such as Multiplication by 11 or Squares Ending in 5 can make good starters, with older students algebra can be used to establish why these tricks work. Mudd Math Fun Facts has a wealth of material which works well in the classroom. More Amazing Number Facts are available from the Madras College Mathematics Department site.
YouTube has various videos which could make good starter activities – see Multiplication With Your Fingers for example, Vedic Multiplication or Russian Multiplication see Activity 6.3 in this CIMT Activities booklet for an explanation of Russian Multiplication.
and see this fuller explanation from Chris Lusto