Lesson 5 Multiplication of Multi-digit Numbers

    • Let’s multiply multi-digit numbers.

Warm-up Estimation Exploration: A Silly Riddle

silhouette of child with a wagon containing 7 fish bowls
  • Seven teachers are going to the park.

  • Each teacher is taking 7 students.

  • Each student is bringing 7 fishbowls.

  • Each fishbowl has 7 fish.

How many are going to the park?

Record an estimate that is:

too low

about right

too high

Activity 1 Two Methods Revisited

Problem 1

Earlier in the course, we used these two ways to multiply numbers:

multiplication algorithm showing 416x2 and solution 832
  1. In method A, where do the 12, 20, and 800 come from?

  2. In method B, where does the 1 above 416 come from?

Problem 2

Diego used both methods to find the value of  but ended up with very different results.

multiplication algorithm showing all steps to find 215x2. final solution as 645.
multiplication algorithm showing 215x2=6,315
  1. Without calculating anything, can you tell which method shows the correct product? How do you know the other one is not correct?

  2. For the incorrect result, explain what was correct and what was incorrect in his steps. Then, show the correct calculation using method B.

Problem 3

Use either way to find the value of each product. Show your reasoning.

Activity 2 Two by Two

Here are two ways to find the value of .

multiplication algorithm
Multiplication algorithm

Problem 1

In method A, where do the 4, 30, 80, and 600 come from?

Problem 2

In method B, which two numbers are multiplied to get:

  1. 34?

  2. 680?

Problem 3

Use the two methods to show that each equation is true.

  1. two multiplication algorithms 44x12 with final solution 528 with blank spaces for work in each.
  2. two multiplication algorithms 63x21 with final solution 1,323 with blank spaces for work in each.