Lesson 14 | Multi-Digit Multiplication | 4th Grade Mathematics

Objective

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

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

Understand that products can be computed by decomposing numbers into base-ten units, finding partial products of these base-ten units, then adding these partial products together based on the distributive property (e.g., $$36\times54=(30\times50)+(30\times4)+(6\times50)+(6\times4)$$). (Note that students need not know the term “distributive property.”)
Multiply a two-digit whole number by a two-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 two-digit by two-digit numbers (on the Problem Set and Homework) (MP.4).

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Throughout the remainder of the topic, the main visual model used is the area model. If students seem to be struggling with place value understanding or don’t yet seem ready for the area model for some other reason, you might create a lesson to use before this one that focuses on the use of the base ten block array and/or graph paper array to build understanding toward the area model. The applet Partial Product Finder by The Math Learning Center may be helpful if you take that route. (See Unit-Specific Intellectual Prep section of the Unit Overview for examples of those representations.)
Lessons 14 and 15 move through the various methods much more quickly than was done in Topic B, since they are already familiar with these methods and just extending them to two-digit by two-digit multiplication. If students struggled in Topic B, you might choose to use a flex day to solidify the strategies with two-, three-, and four-digit by one-digit multiplication or to extend Topic C over more days, having it more closely resemble Topic B.
“When written methods are abbreviated, some students have trouble seeing how the single-digit factors are related to the two-digit numbers whose product is being computed (MP.2). They may find it helpful initially to write each two-digit number as the sum of its base-ten units (e.g., writing next to the calculation 94 = 90 + 4 and 36 = 30 + 6) so that they see what the single digits are. Some students also initially find it helpful to write what they are multiplying in front of the partial products (e.g., 6 × 4 = 24). These helping steps can be dropped when they are no longer needed” (NBT Progression, p. 15).

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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

Mr. Wynn now wants to cover a part of the gym with butcher paper to work on a large painting. He covers a section of the gym that is 30 feet long and 35 feet wide. Then he realizes he needs a bit more space for the painting and adds a section of butcher paper that is 4 feet long and 35 feet wide.

a. How many square feet of butcher paper did Mr. Wynn use for his painting?

b. What is the total length and width of Mr. Wynn’s painting?

Guiding Questions

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References

EngageNY Mathematics Grade 4 Mathematics > Module 3 > Topic H > Lesson 36 — Concept Development

Grade 4 Mathematics > Module 3 > Topic H > Lesson 36 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

a. Label the area model to represent 31 × 23 and to find that product.

Decompose each number into its base-ten units (tens and ones) and write them in the boxes on each side of the rectangle.

Label regions A, B, C, and D with their areas. Show your reasoning.
Find the product that the area model represents. Show your reasoning.

b. Here is one way to calculate 31 × 23. Each number with a box gives the area of one region in the area model.

In the boxes next to each number, write the letter of the corresponding region.
There is a 1 above the hundreds digit in the sum. What does that 1 represent?

Guiding Questions

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References

Open Up Resources Grade 6 Unit 5 Lesson 7 (Teacher Version) — Activity 4

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 each product. Then use any method to solve.

a. $$26\times37$$

b. $$81\times52$$

c. $$68\times73$$

Guiding Questions

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References

EngageNY Mathematics Grade 4 Mathematics > Module 3 > Topic H > Lesson 36 — Concept Development

Modified by Fishtank Learning, Inc.

Problem Set

Problem Set

Answer Keys

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Discussion of Problem Set

Why is it possible to represent #8 with an area model even though it is not an area problem?
When working with a two-digit by two-digit multiplication problem, how many partial products are there usually? What if one of the two-digit numbers has a 0 in the ones place? What if they both do?
How did our previous work with area models and partial products help us to be ready to solve two-digit by two-digit multiplication problems using four partial products?
How could you explain to someone that ones x tens equals tens but tens x tens equals hundreds?

Target Task

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

Zora solves 12 × 64 using an area model.

Use the same reasoning as Zora to solve 35 × 19. Find each partial product in the area model and then fill in the blanks to complete the equation.

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 13

Lesson 15

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

References

Problem 3

Guiding Questions

References

Problem Set

Discussion of Problem Set

Target Task

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

Lesson Map

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