Lesson 6 Multiply Two-digit Numbers and One-digit Numbers

- Let’s multiply two-digit and one-digit numbers.

Warm-up Notice and Wonder: With and Without a Grid

What do you notice? What do you wonder?

diagram, rectangle. Partitioned into 4 rows of 13 of the same size squares.

diagram, rectangle. Partitioned into 4 rows of 13 of the same size squares, 40 squares shaded.

Rectangle. Horizontal side, 13. Vertical side, 4.

Diagram, rectangle partitioned vertically into 2 rectangles. Left rectangle, vertical side, 4, horizontal side, 10. Right rectangle, horizontal side, 3.

Activity 1 Tyler’s Diagrams

Problem 1

To find the value of $4 \times 36$ , Tyler uses a base-ten diagram, as shown here.

base ten diagram. 4 rows of 3 tens and 6 ones.

Where is the 36 in Tyler’s diagram?
Where is the 4 in Tyler’s diagram?
What is the value of $4 \times 36$ ?

Problem 2

Here is a diagram Tyler made to find the value of $9 \times 18$ .

Explain or show how his diagram helps him find the value of $9 \times 18$ .

base ten diagrams. 9 tens. 9 rows of 8 ones.

Activity 2 Two Kinds of Diagrams

Problem 1

Priya drew a base-ten diagram to multiply $6 \times 53$ . She said it shows that the product can be found by adding 300 and 18.

Base ten diagram. 6 rows. each row with 5 tens and 3 ones.

Where do you see 6 and 53 in her diagram?
Where do you see 300 and 18 in Priya’s diagram? What do they represent?

Problem 2

Han drew this diagram to multiply $6 \times 53$ :

Diagram, rectangle partitioned vertically into 2 rectangles.

Where do you see 300 and 18 in his diagram? What do they represent?
Which diagram do you prefer for multiplying $6 \times 53$ : Han’s way or Priya’s way? Explain your reasoning.
Find the value of $6 \times 53$ .

Problem 3

Draw a diagram to represent each multiplication expression. Then, find the value of each product.

$6 \times 48$
$9 \times 67$

Practice Problem

Problem 1

Find the value of $7 \times 64$ . Use a diagram if it is helpful.

diagram, rectangle