Multiplication and Division Concepts 165Successful Strategies
One of the reasons students struggle with the traditional
algorithm is the inaccurate descriptions of the procedures
they have heard. Unfortunately, many people use digit
names rather than number values, creating potential
misconceptions. When solving 21 x 6, they may say 6 x 1
and 6 x 2. The accurate description is 6 x 1 and 6 x 20. The
partial products concept is embedded in place value and
conceptual understanding, which help remedy algorithmic
misconceptions. Even if students successfully use the
traditional algorithm, learning the partial products concept
strengthens conceptual understanding, increases mental math
capacity, and improves fl exibility and fl uency.
partial, part, product,
multiplication, multiply, equation,
equal, distributive propertyMath Words to Use
Questions at Different Levels of Cognitive Demand
Recall: What is 27 x 8?
Comprehension: How did you solve the problem?
Application: What picture could you draw to show the
partial products?
Analysis: How would you compare the partial products?
Evaluation: Which products are easier to work
with? Why?
Synthesis: How would you design a template for
recording partial products?EASYCOMPLEX