Understanding Compensation
Understanding Compensation is a Grade 4 math skill in enVision Mathematics, Chapter 2: Fluently Add and Subtract Multi-Digit Whole Numbers. Students learn to adjust one or both numbers in a calculation to create friendlier numbers, then compensate the result to maintain accuracy.
Key Concepts
Compensation changes the numbers in a problem to make it simpler without changing the final answer. Addition (Give and Take): The sum is unchanged if you add a value to one addend and subtract the same value from the other.
$$a + b = (a + c) + (b c)$$ Subtraction (Constant Difference): The difference is unchanged if you add the same value to both numbers.
Common Questions
What is compensation in math?
Compensation is a mental math strategy where you change one or both numbers to make a calculation easier, then adjust the answer to account for the change.
How do you use compensation to add numbers?
Round one number up to a friendly number, add, then subtract what you added. For example, 47 plus 98 becomes 47 plus 100 minus 2 equals 145.
How do you use compensation to subtract numbers?
Adjust both numbers by the same amount so subtraction is easier. For example, 73 minus 29 becomes 74 minus 30 equals 44, because adding 1 to both preserves the difference.
Why does compensation work mathematically?
Addition compensation works because adding and subtracting the same value preserves the sum. Subtraction compensation works because adding the same value to both numbers keeps the difference unchanged.
What chapter covers compensation in enVision Mathematics Grade 4?
Understanding compensation is covered in Chapter 2: Fluently Add and Subtract Multi-Digit Whole Numbers in enVision Mathematics Grade 4.