Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
Partitioning: Breaking numbers into hundreds, tens, and ones to add or subtract separately (e.g., ).
Compensation: Adjusting one number to the nearest 10 or 100 to make the calculation easier, then correcting the difference (e.g., to add 19, add 20 and subtract 1).
Bridging: Moving to the next multiple of 10 or 100 first (e.g., for , do , then ).
Doubling and Halving: Using known doubles to solve multiplication or halving to solve division (e.g., to multiply by 4, double and double again).
Inverse Operations: Using the relationship between addition/subtraction and multiplication/division to check or solve problems.
Near Doubles: Using known doubles to solve close additions (e.g., is double 15 plus 1).
📐Formulae
(Commutative Property)
(Compensation Rule)
(Double-Double Rule)
(Multiply by 10 and Halve)
💡Examples
Problem 1:
Calculate mentally.
Solution:
96
Explanation:
Use the compensation strategy. Round 39 up to 40. . Since we added 1 too many, subtract 1 from the total: .
Problem 2:
Find the result of using bridging.
Solution:
87
Explanation:
Bridge to the nearest hundred. . We still need to subtract 13 more (because ). , and .
Problem 3:
Calculate mentally.
Solution:
80
Explanation:
Use the 'Multiply by 10 and Halve' strategy. . Half of 160 is 80. Alternatively, halve the 16 to get 8 and double the 5 to get 10: .
Problem 4:
Solve using near doubles.
Solution:
93
Explanation:
Recognize that 47 is . Double 46 is 92 (). Then add the extra 1: .