Lesson 8 | Multi-Digit Multiplication | 4th Grade Mathematics

Objective

Multiply three-digit numbers by one-digit numbers.

Common Core Standards

Core Standards

The core standards covered in this lesson

4.NBT.B.5 — Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Number and Operations in Base Ten

4.NBT.B.5 — Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Foundational Standards

The foundational standards covered in this lesson

3.NBT.A.3

Number and Operations in Base Ten

3.NBT.A.3 — Multiply one-digit whole numbers by multiples of 10 in the range 10—90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.
4.NBT.A.1

Number and Operations in Base Ten

4.NBT.A.1 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
4.NBT.B.4

Number and Operations in Base Ten

4.NBT.B.4 — Fluently add and subtract multi-digit whole numbers using the standard algorithm.
3.OA.B.5

Operations and Algebraic Thinking

3.OA.B.5 — Apply properties of operations as strategies to multiply and divide. Students need not use formal terms for these properties. Example: Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) Example: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.)
3.OA.C.7

Operations and Algebraic Thinking

3.OA.C.7 — Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Multiply a three-digit whole number by a one-digit whole number using area models and the partial products algorithm.
Estimate products by rounding factors to the largest place value.
Solve one-step word problems involving multiplication of three-digit by one-digit numbers (on the Problem Set and Homework) (MP.4).

Tips for Teachers

Suggestions for teachers to help them teach this lesson

In this lesson, the partial products are listed in decreasing order. This is the way students are likely to write them given the way the area model tends to be set up. Also, “at any point before or after their acquisition of fluency, some students may prefer to multiply from the left because they find it easier to align subsequent products under the biggest product” (NBT Progression, p. 15). Thus, it is included here. But, students will see in Lesson 9 that the partial products can also be written in increasing order. If a student chooses to do so in this lesson, allow them to do so but wait to discuss this with the whole class until Lesson 9.
Note that the last Criteria for Success is not addressed in the Anchor Tasks below, since each problem type involving multiplication has been explored in previous lessons. However, if it seems students need additional practice with any type (particularly multiplicative compare with larger unknown), then you can use the values in Anchor Task 3 in the context of a word problem.

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Anchor Tasks

Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding

Problem 1

The area model below can be used to find 7 × 851.

To find 7 × 851,

a. Decompose each number into its base-ten units and write them in the corresponding boxes of the model.

b. Write the area of each region in the model. Then find the area of the entire model. Show your reasoning.

Guiding Questions

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References

Open Up Resources Grade 6 Unit 5 Lesson 8 (Teacher Version) — Activity 2, "Calculating Products of Decimals"

Grade 6 Unit 5 Lesson 8 (Teacher Version) is made available by Open Up Resources under the CC BY 4.0 license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed Dec. 14, 2018, 4:02 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

Ayana used an area model to solve 746 $$\times$$ 8.

a. Use the area model to find 746 $$\times$$ 8.

b. Ayana recorded her work in a different way, as shown below.

In Ayana’s calculation, how are each of the partial products obtained? For instance, where does the 5,600 come from?
How are the partial products in Ayana’s calculation related to the numbers in the area model?

Guiding Questions

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References

Open Up Resources Grade 6 Unit 5 Lesson 7 (Teacher Version) — Activity 2, "Connecting Area Diagrams to Calculations with Whole Numbers"

Grade 6 Unit 5 Lesson 7 (Teacher Version) is made available by Open Up Resources under the CC BY 4.0 license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed Dec. 14, 2018, 4:05 p.m..

Modified by Fishtank Learning, Inc.

Problem 3

Estimate the product. Then use any method to solve.

a. $$940\times5$$

b. $$7\times589$$

Guiding Questions

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Problem Set

Problem Set

Answer Keys

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Discussion of Problem Set

Did you draw an area model for #2b? How may sections did it have? Why?
Look at #2d. What did you estimate the product to be? Do you still think your product is reasonable despite it being hundreds away from the actual product? Why was the estimate hundreds away from the actual product?
How did you determine what the values of A, B, C, and D were in #4?
Did you use any strategies from Lesson 6 to solve any problems on today’s Problem Set? For example, #5d?