Curriculum  /  Math  /  3rd Grade  /  Unit 3: Multiplication and Division, Part 2  /  Lesson 18

Multiplication and Division, Part 2

Lesson 18

Math

Unit 3

3rd Grade

Lesson 18 of 23

Objective

Multiply one-digit whole numbers by two-digit whole numbers using the associative and distributive properties.

Common Core Standards

Core Standards

  • 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.
  • 3.OA.A.4 — Determine the unknown whole number in a multiplication or division equation relating three whole numbers. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ?
  • 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.)

Criteria for Success

  1. Make use of structure by using the associative property to decompose two-digit numbers in a multiplication problem into smaller factors, then multiply those values in any order (MP.7).
  2. Make use of structure by using the distributive property to decompose the two-digit number in a multiplication problem into a sum or difference of benchmark numbers, multiplying those values separately by the other factor, then adding or subtracting, respectively, those products to give the overall product (MP.7).

Tips for Teachers

Most of the computations in this lesson involve multiplication within 100, an expectation of this grade level, but involve teen numbers, arguably beyond the scope of 3rd grade standards. However, students have all of the skills needed to solve problems of this nature, including multiplication of single-digit number by multiples of ten (3.NBT.3), fluency with multiplication of two one-digit numbers (3.OA.7), and the application of the associative property and distributive property to multiply (3.OA.5). Thus, by extending the work of previous lessons to simple cases of multiplying a one-digit number by a two-digit number, it provides an opportunity to connect two domains in the grade, 3.OA and 3.NBT. It also nicely prepares students for extensive work with multi-digit multiplication in Grade 4.

Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Tasks

25-30 minutes

Problem 1

Latonia and Floyd are trying to solve $$5 \times 12$$. Here are their strategies.

Latonia:

$$ \begin{align} 5\times 12 &= 5\times (10+2) \\ &= (5\times10)+(5\times2) \\ &= 50 + 10 \\ &= 60 \end{align}$$

 Floyd:

$$ \begin{align} 5\times12&= 5\times(2\times6) \\ &= (5\times2) \times 6 \\ &= 10\times 6 \\ &= 60 \end{align}$$

What is similar about these strategies? What is different? 

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Student Response

Upgrade to Fishtank Plus to view Sample Response.

Problem 2

To find the value of $$2\times37$$, Mel started by writing this equation:

$$2\times30=60$$

Describe or show what Mel would do to finish finding the value of $$2\times37$$.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Student Response

Upgrade to Fishtank Plus to view Sample Response.

References

Illustrative Mathematics Multiply Numbers Larger than 20 — Grade 3 Unit 4 Lesson 16 Activity 2

Multiply Numbers Larger than 20, accessed on Aug. 24, 2022, 6:21 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem 3

Solve. Show or explain your work. 

a.   $$18\times 3=$$ _____

b.   _____ $$=4\times16$$

c.   _____ $$=14\times 5$$

d.   $$6\times 15=$$ _____

e.   _____ $$=6\times 21$$

f.   $$19\times 7=$$ _____

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Student Response

Upgrade to Fishtank Plus to view Sample Response.

Problem Set

15-20 minutes

Discussion of Problem Set

  • In #1, how do the computations on the bottom make the computations on the top easier? 
  • In #4, how did Marlys convert this to an easier problem?
  • Which strategy did you tend to rely on in #5? For which problems were certain strategies not possible to use? Why? 
  • In #8, how did Charlotte convert this to an easier problem?

Target Task

5-10 minutes

Problem 1

Decide whether each expression is equal to $$3\times 14$$. Select whether the expression is True or False.

  True False
$$3\times (10+4)$$    
$$6\times 11$$    
$$(3\times10)+4$$    
$$(3\times2)\times7$$    
$$3+(10\times4)$$    

Student Response

Upgrade to Fishtank Plus to view Sample Response.

Problem 2

Solve. Show or explain your work.

$$28\times 5$$

Student Response

Upgrade to Fishtank Plus to view Sample Response.

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

Solve two-step word problems involving all four operations.

Lesson 19
icon/arrow/right/large

Lesson Map

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

Topic A: Introduction to The Properties of Operations

Topic B: Multiplication and Division by 6 and 7

Topic C: Multiplication and Division by 8 and 9

Topic D: Multiplication and Division by Values Greater than 10

Topic E: Two-Step Word Problems and Patterns in Arithmetic

Request a Demo

See all of the features of Fishtank in action and begin the conversation about adoption.

Learn more about Fishtank Learning School Adoption.

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Yes

No

Any other information you would like to provide about your school?

We Handle Materials So You Can Focus on Students

We Handle Materials So You Can Focus on Students

We've got you covered with rigorous, relevant, and adaptable math lesson plans for free