Curriculum  /  Math  /  4th Grade  /  Unit 2: Multi-Digit Multiplication  /  Lesson 14

Multi-Digit Multiplication

Lesson 14

Math

Unit 2

4th Grade

Lesson 14 of 18

Objective

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

Common Core Standards

Core Standards

  • 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

  • 3.NBT.A.3
  • 4.NBT.A.1
  • 4.NBT.B.4
  • 3.OA.B.5
  • 3.OA.C.7

Criteria for Success

  1. 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.”)
  2. Multiply a two-digit whole number by a two-digit whole number using area models and the partial products algorithm. 
  3. Estimate products by rounding factors to the largest place value. 
  4. Solve one-step word problems involving multiplication of two-digit by two-digit numbers (on the Problem Set and Extra Practice Problems) (MP.4).

Tips for Teachers

  • 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

25-30 minutes

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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Student Response

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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. 

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

  1. Label regions A, B, C, and D with their areas. Show your reasoning. 
  2. 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. 

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

Guiding Questions

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Student Response

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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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Student Response

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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 Set

15-20 minutes

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

5-10 minutes

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

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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.

Word Problems and Fluency Activities

Word Problems and Fluency Activities

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

Next

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

Lesson 15
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Multiplicative Comparison

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

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

Topic D: Multi-Step Word Problems

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