U.S. Traditional Multiplication
U.S. traditional multiplication (standard) is familiar to most adults and
many children. A person using this algorithm multiplies from right to left,
regrouping as necessary.
The traditional method for teaching this algorithm is to begin with models
(such as base-10 blocks) and then gradually move toward the use of
symbols (that is, numerals) only.
Since students will need a sharp eye for place value to succeed with this
algorithm, conduct a basic-facts review—with a place-value twist. Have
students take out their slates and chalk, or paper and pencils. On their slates,
have them copy the chart shown in the margin. Tell them that you will call out
problems and that they should write the answers on their slates with the digits
written correctly in the chart.
Ask a volunteer to read her or his answer and identify the value of each
digit (for example: “72; 7 tens and 2 ones”). After reviewing some of the basic
multiplication facts, expand the review to include multiples of ten. Use such
problems as 30 ∗ 8; 60 ∗ 4; 200 ∗ 7; and 500 ∗ 5. Make sure students expand
their place-value charts to accommodate their 3- and 4-digit answers.
Using page 49, explain that with this method of multiplying, students will
begin with the ones digit in the bottom factor. Use questions such as the
following to guide students through the example (and through other examples
• Will you begin multiplying with the digits on the right or on the left?
(on the right)
• What is the correct method for recording each individual product? (If the
product has one digit, align it in the correct column under the two factors.
If the product has two digits, align the right digit below the two factors, in
the correct column, and regroup the left digit at the top of the next place-
value column to the left. If there are no columns to the left, then record the
Watch for students who skip a digit when they multiply a
3-digit number by a 2-digit number. Have students use their index fingers
to point to each digit in the top factor as they work. This method may help
ensure that students multiply every digit in the bottom factor by every digit in
the top factor.
Divide students into pairs. Have them solve the problem 572 ∗ 43. Tell them to
write neatly, and then have them exchange papers with their partners. Direct
students to check each other’s problems. If they find a mistake, ask them
to identify the mistake. When you are reasonably certain that most of your
students understand the algorithm, assign the “Check Your Understanding ”
exercises at the bottom of page 49. (See answers in margin.)