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Multiply Two-digit Numbers and

One-digit Numbers

Grade 4: Unit 6: Lesson 6

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Lesson Purpose

The purpose of this lesson is for students to multiply a two-digit number and a one-digit number

using place value understanding.

Lesson Narrative

In the previous lesson, students solved two-digit multiplication problems in a way that made sense

to them. They discussed decomposing factors and considered different representations of their

strategy. In this lesson, students extend these ideas to find the value of products beyond 100,

focusing on representations and strategies based on place value and the properties of operations,

which are familiar from grade 3.

Students analyze base-ten diagrams and diagrams that involve rectangles, some of which are

partitioned by place value. They explain how the diagrams represent multiplication and make

connections between them, deepening their understanding of place value and properties of

operations. At the end of the lesson, students consider a rectangular diagram that will be used

through the rest of the section.

Learning Goals

• Multiply two-digit and one-digit whole numbers using place value understanding and

properties of operations.

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

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Notice and Wonder: With and Without a Grid

Warm-Up

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What do you notice? What do you wonder?

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Let’s Talk About It!

What do you know about the 13 and 4 in the first ungridded rectangle?
What about the 10, 3, and 4 in the second ungridded rectangle?
How are the four diagrams related? Name as many connections as you see.

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Tyler’s Diagrams

Activity 1

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

a. Where is the 36 in Tyler’s diagram?

b. Where is the 4 in Tyler’s diagram?

c. What is the value of 4 x 36 ?

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Here is a diagram Tyler made to find the value

of 9 x 18 .

Explain or show how his diagram helps him find the value of 9 x 18 .

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Let’s Talk About It!

• How are these methods the same? How are they different?

• How are these methods like what Tyler did to find the value of ? How are they different?

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Two Kinds of Diagrams

Activity 2

MLR1: Stronger and Clearer Each Time

This activity continues to encourage place value reasoning for finding the product of a two-digit

factor and a one-digit factor.

Students make sense of two representations that show the two-digit factor decomposed by place

value: a base-ten diagram and a rectangle. The latter looks like an area diagram that students have

used in grade 3, where the side lengths of a rectangle represents two factors. As the factors become

larger, however, it becomes necessary to draw rectangles whose side lengths are not proportional.

When rectangles no longer accurately represent area, the term “area diagrams” is not used. Instead,

“rectangular diagrams” is used in teacher materials and “diagrams” in student materials.

Students then choose a representation to use to find products and write corresponding

expressions. In the synthesis, they learn that the results of multiplying a part of one factor by the

other factor can be called “partial products.” In future lessons, students will use rectangular

diagrams to represent multiplication of larger numbers.

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Priya drew a base-ten diagram to multiply 6x53. She said it shows that the product can be found by adding 300 and 18.

a. Where do you see 6 and 53 in her diagram?

b. Where do you see 300 and 18 in Priya’s diagram? What do they represent?

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Han drew this diagram to multiply 6 x 53 :

a. Where do you see 300 and 18 in his diagram? What do they represent?

b. Which diagram do you prefer for multiplying 6 x 53 : Han’s way or Priya’s way? Explain your reasoning.

c. Find the value of 6 x 53.

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

6 x 48
9 x 67

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Let’s Talk About It!

• How are they different?�

• What expressions can you write to show how to multiply ? What is the product?

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Lesson Synthesis

8 x 79 =

How could we use this rectangle to represent ?

How does this diagram help us find the value of 8 x 79 ?

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Represent the Product

Cool-Down

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Find the value of 6 x 83 . Use a diagram if it is helpful.

Cool-Down: Represent the Product

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Image Citations

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