Addition and Subtraction Concepts 91Successful Strategies
Using number lines that include negative numbers helps
students understand how to fi nd the partial differences when
the ones digit value of the minuend is greater than the ones digit
value of the subtrahend. It also helps us focus on mathematical
truths. It really is a lie when we tell students you cannot take
6 from 4. You can take 6 from 4. The result is –2. When the partial
differences are combined, you just subtract without the need to
memorize rules about adding positive and negative numbers.
As with partial sums, even if students successfully use the
traditional algorithm, learning the partial differences concept
strengthens their conceptual understanding, increases mental
math capacity, and improves fl exibility and fl uency.
partial, part, difference, subtract,
subtraction, strategy, equation,
equal, subtrahend, minuendMath Words to Use
Questions at Different Levels of Cognitive Demand
Recall: What is 46 – 21?
Comprehension: How did you solve the problem?
Application: What picture could you draw to show
partial differences?
Analysis: How would you compare the partial
differences?
Evaluation: What is helpful about the partial
differences concept?
Synthesis: What if the partial differences were half as
many?EASYCOMPLEX