# Lesson 9 Recording Partial Products: One-digit and Three- or Four-digit Factors

Let’s analyze and try an algorithm that uses partial products.

## Warm-up Which One Doesn’t Belong: Expressions Galore

Which one doesn’t belong?

## Activity 1 An Algorithm for Noah

Noah drew a diagram and wrote expressions to show his thinking as he multiplied two numbers.

How does each expression represent Noah’s diagram? Be prepared to share your thinking with a partner.

Later, Noah learned another way to record the multiplication, as shown here.

Make sense of each step of the calculations and record your thoughts. Be prepared to explain Noah’s steps to a partner.

Complete the diagram to find the value of

. Use Noah’s recording method to check your work.

## Activity 2 Try an Algorithm with Partial Products

## Problem 1

Noah and Mai want to find the value of

How are Mai’s and Noah’s notation alike? How are they different?

Use a diagram to show what each of the partial products 72, 80, 3,200 and 24,000 represent. Then, find the value of

.

## Problem 2

Find the value of each expression. For at least one expression, use the algorithm that Noah used. Show your reasoning.

## Practice Problem

## Problem 1

The diagram and calculations show two ways for finding the value of

How does each part of the vertical calculation relate to the diagram?

Find the value of

using a method of your choice.