Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
Place Value: Understanding the value of digits in 3-digit numbers (Hundreds, Tens, Ones).
Partitioning: Breaking numbers into smaller parts (e.g., ) to make mental calculation easier.
Regrouping (Carrying): In column addition, when the sum of a column is 10 or more, the 'ten' is moved to the next column to the left.
Regrouping (Borrowing): In column subtraction, if the top digit is smaller than the bottom digit, you must 'take' one from the next column to the left.
Compensation: A mental strategy where you adjust a number to a 'friendly' number (e.g., to add 99, add 100 then subtract 1).
Inverse Operations: Understanding that addition is the opposite of subtraction, used for checking answers.
📐Formulae
(Commutative Property: Order does not matter in addition)
(Inverse Property: Subtraction can be checked with addition)
💡Examples
Problem 1:
Solve using the column method.
Solution:
731
Explanation:
- Add the ones: . Write 1 in the ones place and carry 1 to the tens. 2. Add the tens: . Write 3 in the tens place and carry 1 to the hundreds. 3. Add the hundreds: . Result: 731.
Problem 2:
Solve using regrouping.
Solution:
376
Explanation:
- Ones: , borrow from tens. . 2. Tens: (left over) , borrow from hundreds. . 3. Hundreds: (left over) . Result: 376.
Problem 3:
Use a mental strategy to calculate .
Solution:
763
Explanation:
Use the compensation strategy. Add 200 instead of 199: . Since we added 1 too many, subtract 1: .
Problem 4:
Find the missing number: .
Solution:
370
Explanation:
Use the inverse operation. To find the starting number in a subtraction problem, add the difference to the subtrahend: .