Build the Largest or Smallest Value from Digit Cards
To maximize (or minimize) a number, product, quotient, or mixed number, place the biggest available digits in the places that carry the most weight. The reasoning starts with whole numbers, then governs products and quotients (where a small divisor enlarges the result), decimals, and mixed numbers. It is place-value comparison turned into an optimization strategy.
grade 2–6 Base-ten numbersFractionsOperations Make a Systematic ListGuess and Check
Progression (12)
g4 1. Count numbers built from digit cards Base-ten numbers
g3 2. Big digits in high places Base-ten numbers
g3 3. Place digit cards for largest or smallest product Base-ten numbersOperations
g4 4. Place big digits high to maximize a decimal Fractions
g3 5. Place big digits high for largest product OperationsBase-ten numbers
g4 6. Smaller divisor makes a bigger quotient Base-ten numbers
g4 7. Build largest and smallest mixed numbers from cards Fractions
g5 8. Make result largest or smallest Operations
g5 9. Build the largest proper fraction Fractions
g5 10. Place big digits in high places to maximize product Base-ten numbers
g6 11. Dividing a smaller number by a bigger one shrinks the quotient Number systemExpressions
g6 12. Dividing a bigger number by a smaller one grows the quotient Number systemExpressions
Bridges to competition (8)
Reasoning problems that extend this idea toward competition:
Arrange cards for the smallest valid result Number arrangement
Largest and smallest from flipped cards Number arrangement
Largest and smallest product Number arrangement
Build division to extremize quotient or remainder Number arrangement
Build fractions from digit cards Number arrangement
Make the largest and smallest number Number arrangement
Place digit cards to maximize or minimize a result Optimization
Make numbers from digit cards Number arrangement