Lesson 11 Partial Products and the Standard Algorithm

- Let’s compare multiplication algorithms.

Warm-up Number Talk: The Value of the Digits

Find the value of each expression mentally.

$5 \times 101$
$5 \times 102$
$5 \times 203$
$5 \times 404$

Activity 1 Two Algorithms to Multiply

Problem 1

Here are two algorithms for finding the value of $3 \times 713$ .

multiply. 7 hundred 13 times 3 equals 2 thousand 1 hundred 39. — Kiran

multiply. 7 hundred 13 times 3. 6 rows. — Diego

Discuss with your partner:

How are Kiran’s algorithm and Diego’s algorithm alike? How are they different?
How do you think Kiran found the product 2,139?

Problem 2

Find the value of each product.

$212 \times 4$
$3 \times 4, 132$

Activity 2 Algorithm Comparison

Analyze the two algorithms used to find the value of $4 \times 223$ .

multiply. 3 rows. First row, 2 hundred 23. Second row, multiplication symbol, 4. Horizontal line. 8 hundred ninety 2. — Kiran

multiply. 2 hundred 23 times 4. 6 rows. — Diego

How are Kiran and Diego’s algorithms alike? How are they different?
Where is the 12 in Kiran’s algorithm?
Try using Kiran’s algorithm to find the value of $512 \times 3$ .
Check your work using a different method.

Practice Problem

Problem 1

Here is how Elena calculated the value of $723 \times 3$ .

multiply. 7 hundred 23 times 3, equals 2 thousand 1 hundred sixty 9.

Where does the 9 in Elena’s calculation come from? What about the 6?
Where do the 2 and the 1 in calculation come from?
Use Elena’s method to find the value of $534 \times 2$ .