Lesson 5 Standard Algorithm: Multi-digit Numbers without Composing

- Let’s use the standard algorithm to multiply two-digit numbers and three-digit numbers.

Warm-up Number Talk: Partial Products

Find the value of each product mentally.

$20 \times 3$
$24 \times 3$
$120 \times 3$
$140 \times 3$

Activity 1 Compare Two Algorithms

Two algorithms for finding the value of $413 \times 21$ are shown.

multiply. four hundred thirteen times 21.

multiply. four hundred thirteen times 21. 3 rows. First row: four hundred thirteen. Second row: multiplication symbol, 21. Horizontal line. Third row: 3 — Step 1

multiply. four hundred thirteen times 21. 3 rows. First row: four hundred thirteen. Second row: multiplication symbol, 21. Horizontal line. Third row: 13 — Step 2

multiply. four hundred thirteen times 21. 3 rows. First row: four hundred thirteen. Second row: multiplication symbol, 21. Horizontal line. Third row: four hundred thirteen — Step 3

multiply. four hundred thirteen times 21. 4 rows. First row: four hundred thirteen. Second row: multiplication symbol, 21. Horizontal line. Third row: four hundred thirteen. Fourth row: two hundred sixty — Step 5

multiply. four hundred thirteen times 21. 4 rows. First row: four hundred thirteen. Second row: multiplication symbol, 21. Horizontal line. Third row: four hundred thirteen. Fourth row: eight thousand two hundred sixty — Step 6

multiply. four hundred thirteen times 21. — Step 7

How are the two algorithms the same? How are they different?
Explain or show where you see each step from the first algorithm in the second algorithm.
How do the final steps in the two algorithms compare?

Activity 2 Use the Standard Algorithm

Problem 1

Use the standard algorithm to find the value of each expression.

$202 \times 12$
$122 \times 33$
$321 \times 24$

Problem 2

Diego found the value of $301 \times 24$ . Here is his work. Why doesn’t Diego’s answer make sense?

multiply. three hundred one times 24.

Practice Problem

Problem 1

Find the value of $322 \times 41$ using the standard algorithm.