Lesson 10 | Multi-Digit Multiplication | 4th Grade Mathematics

Objective

Multiply two-, three-, and four-digit numbers by one-digit numbers and assess the reasonableness of the product.

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 two-, three-, or four-digit whole number by a one-digit whole number using the partial products algorithm and/or the standard algorithm.
Assess the reasonableness of answers using mental computation and estimation strategies including rounding (MP.1).
Solve one-step word problems involving multiplication of up to four-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

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 2 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

Here are two algorithms for finding the value of 64 × 2.

Patrice’s method	Jerome’s method

a. How is Patrice’s method similar to and different from Jerome’s method?

b. How do you think Jerome found the product 128?

Guiding Questions

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References

Two Algorithms to Multiply — Grade 4 Unit 6 Lesson 11 Activity 1

Problem 2

Patrice solved the problem 813 × 7 using the partial products algorithm, as shown below:

Jerome solved in a different way from Patrice. Here is what he did:

First, he found the partial product of 3 ones and 7, which is 21 ones, or 2 tens 1 one. He wrote the ones digit, 1, under the equal bar, and the 2 tens on the equal bar above the tens place in smaller handwriting.	Then, he found the partial product of 1 ten and 7, which was 7 tens. Because he had the 2 tens from the first partial product, he added those tens together and wrote 9 in the tens place in the product. Because he had accounted for the 2 tens from his first partial product, he crossed it off.	Finally, he found the partial product of 8 hundreds and 7, which was 56 tens. He wrote 56 in the hundreds and tens place in the product.

a. How is Patrice's method similar to and different from Jerome's method?

b. What are the advantages and disadvantages of Patrice's method? Of Jerome's method?

Guiding Questions

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Problem 3

Try using the standard algorithm to solve. If you get stuck, use an area model and/or the partial products algorithm to help. Then assess the reasonableness of your answer.

a. $$54\times6$$

b. $$9\times673$$

c. $$1,605\times4$$

Guiding Questions

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Problem Set

Problem Set

Answer Keys

Unlock the answer keys for this lesson's problem set and extra practice problems to save time and support student learning.

Discussion of Problem Set

Look at #1. Which problems were particularly difficult to solve? Why?
Look at #2. Were there any answers you could eliminate right away as being unreasonable?
Look at #4. Where did the 3 come from? What value does it have—ones? Tens? Hundreds? Thousands? What is the final product?
Look at #5. What is a possible number that Casey multiplies 178 by? Are there other possibilities? How did you find them? What product do they result in?
Did you use any strategies from Lesson 6 to solve any problems on today’s Problem Set? For example, #1d?

Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Problem 1

Anika begins to solve 562 × 4 below.

Complete the algorithm that Anika has started.

Problem 2

Solve. Assess the reasonableness of your answer.

a. 81 × 5

b. 6 × 2,348

Student Response

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Student Response

An example response to the Target Task at the level of detail expected of the students.

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Additional Practice

The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Extra Practice Problems

Extra Practice Problems

Answer Keys

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Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Lesson 9

Lesson 11

Lesson Map

Topic A: Multiplicative Comparison

Solve multiplicative comparison problems with a larger unknown. Distinguish multiplicative comparison from additive comparison.

4.OA.A.1 4.OA.A.2

Solve multiplicative comparison problems with a smaller unknown.

4.OA.A.1 4.OA.A.2

Solve multiplicative comparison problems with an unknown multiplier. Interpret a multiplication equation as a comparison.

4.OA.A.1 4.OA.A.2

Topic B: Multiplication of up to Four-Digit Whole Numbers by One-Digit Whole Numbers

Multiply 10, 100, and 1,000 by one- and two-digit numbers.

4.NBT.B.5

Multiply multiples of 10, 100, and 1,000 by one-digit numbers. Estimate multi-digit products by rounding numbers to their largest place value.

4.NBT.B.5

Multiply two-, three-, and four-digit numbers by one-digit numbers using a variety of mental strategies.

4.NBT.B.5

Multiply two-digit numbers by one-digit numbers.

4.NBT.B.5

Multiply three-digit numbers by one-digit numbers.

4.NBT.B.5

Multiply four-digit numbers by one-digit numbers.

4.NBT.B.5

Multiply two-, three-, and four-digit numbers by one-digit numbers and assess the reasonableness of the product.

4.NBT.B.5

Topic C: Multiplication of Two-Digit Whole Numbers by Two-Digit Whole Numbers

Multiply two-digit multiples of 10 by two-digit multiples of 10. Estimate multi-digit products by rounding numbers to their largest place value.

4.NBT.B.5

Multiply two-digit multiples of 10 by two-digit numbers.

4.NBT.B.5

Multiply two-digit numbers by two-digit numbers using a variety of mental strategies.

4.NBT.B.5

Multiply two-digit by two-digit numbers using four partial products.

4.NBT.B.5

Multiply two-digit by two-digit numbers using two partial products and assess the reasonableness of the product.

4.NBT.B.5

Topic D: Multi-Step Word Problems

Abstract the formulas for the area and perimeter of a rectangle and apply those formulas in real-world and mathematical problems involving multiplication, addition, and subtraction.

4.MD.A.3 4.OA.A.3

Solve two-step word problems involving multiplication, addition, and subtraction.

4.OA.A.2 4.OA.A.3

Solve multi-step word problems involving multiplication, addition, and subtraction.

4.OA.A.3

Multi-Digit Multiplication

Objective

Common Core Standards

Core Standards

Number and Operations in Base Ten

Foundational Standards

Number and Operations in Base Ten

Number and Operations in Base Ten

Number and Operations in Base Ten

Operations and Algebraic Thinking

Operations and Algebraic Thinking

Criteria for Success

Tips for Teachers

Anchor Tasks

Problem 1

Guiding Questions

References

Problem 2

Guiding Questions

Problem 3

Guiding Questions

Problem Set

Discussion of Problem Set

Target Task

Problem 1

Problem 2

Student Response

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

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