Using Compensation for Addition
Using compensation for addition is a Grade 5 math skill in enVision Mathematics, Chapter 2: Use Models and Strategies to Add and Subtract Decimals. Students adjust one addend to a nearby round number by adding c, compute the sum, then subtract c to compensate: a + b = a + (b + c) - c. This mental math strategy makes decimal addition easier by temporarily working with rounder numbers.
Key Concepts
To mentally calculate the sum $a + b$, you can change one addend by an amount $c$ to make it an easier number to work with, and then adjust the sum by subtracting $c$. $$a + b = a + (b + c) c$$.
Common Questions
What is compensation in addition?
Compensation means adjusting one addend to a nearby round number, adding the rounded version, then subtracting the adjustment. For example, 4.7 + 2.9 becomes 4.7 + 3.0 - 0.1 = 7.6.
Why use compensation for addition?
Round numbers are easier to add mentally. Compensation lets you work with simple numbers first, then make a small correction to get the exact answer.
What is 3.6 + 4.8 using compensation?
Round 4.8 to 5.0: 3.6 + 5.0 = 8.6. Adjust: subtract 0.2. Answer: 8.4.
Where is compensation for addition taught in enVision Grade 5?
Chapter 2: Use Models and Strategies to Add and Subtract Decimals in enVision Mathematics, Grade 5.
Is compensation only useful for decimals?
No, compensation works with whole numbers and fractions too. It is a flexible mental math strategy for any addition or subtraction problem.