Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
Partitioning: Breaking numbers into hundreds, tens, and ones to add or subtract them separately (e.g., 45 + 32 = (40+30) + (5+2)).
Compensation: Rounding one number to the nearest 10 or 100, performing the operation, and then adjusting the result (e.g., adding 19 is like adding 20 and subtracting 1).
Bridging: Moving to the nearest multiple of 10 or 100 as an intermediate step (e.g., 8 + 7 as 8 + 2 + 5).
Counting On: For subtraction, finding the difference by counting up from the smaller number to the larger number.
Doubles and Near Doubles: Using known doubles (like 25 + 25 = 50) to solve nearby problems (like 25 + 26 = 51).
Commutative and Associative Properties: Reordering numbers to make calculations easier (e.g., 17 + 5 + 3 = 17 + 3 + 5).
📐Formulae
(Commutative Property)
(Associative Property)
(Constant Difference Rule for Subtraction)
(Compensation for Addition)
💡Examples
Problem 1:
Calculate mentally.
Solution:
196
Explanation:
Use the compensation strategy. Round 39 up to 40. . Since you added 1 too many, subtract 1 from the result: .
Problem 2:
Calculate using partitioning.
Solution:
48
Explanation:
First, subtract the tens: . Then, subtract the remaining units: . To do easily, bridge through 50: , and .
Problem 3:
Find the difference between 1003 and 997 mentally.
Solution:
6
Explanation:
Use the 'Counting On' strategy. Start at 997. Add 3 to get to 1000. Add another 3 to get to 1003. Total added is .
Problem 4:
Solve .
Solution:
475
Explanation:
Use the associative property to reorder the numbers. Add first to get 300 (a friendly number). Then add .