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Renaming and Grouping

Which is Less/More
The ability to quickly determine which of two sums is less/more than the other is both a more complex exercise than Arranging Numbers based on size and a key building block for more advanced mathematical concepts, such as multiplication and percentages. A real world example might be comparing the price of two different sets of ingredients for two meals to find the cheapest.
 
Renaming
Knowledge of the various combinations of numbers that can make up a larger number allows a student to quickly subtract numbers from each other in their head, no matter the size.