Lesson 10 Using Algorithms with Partial Products: 2 Two-digit Numbers

- Let’s try to multiply two-digit numbers with an algorithm that uses partial products.

Warm-up Number Talk: Products

Find the value of each expression mentally.

$30 \times 7$
$15 \times 14$
$50 \times 8$
$25 \times 16$

Activity 1 Partial Products, Recorded

Tyler used an algorithm to find the value of $64 \times 87$ .

multiply. sixty 4 times eighty 7.

How do you think he arrived at the last five numbers? Record your thinking. Be prepared to share it with a partner.
Use Tyler’s method to find the value of $31 \times 15$ . Then, draw a diagram to check your answer.

Activity 2 Han’s Multiplication Mishap

Problem 1

Decide with your partner who will find each product. Show your reasoning.

Problem 2

Here is Han’s computation of $51 \times 47$ .

multiply. fifty 1 times 47. 7 rows.

What error or errors did Han make?
Show the correct computation for finding the value of $51 \times 47$ .

Practice Problem

Problem 1

Here is an incomplete calculation that uses partial products of $65 \times 43$ .

Write multiplication expressions that the numbers 15, 180, 200, and 2,400 each represent. Then, find the value of $65 \times 43$ .
Find the value of the product $45 \times 38$ .