Multiplication and Division, Part 2

Lesson 3

Math

Unit 3

3rd Grade

Lesson 3 of 23

Objective


Understand the role of parentheses and apply to solving problems.

Common Core Standards


Core Standards

  • 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.D.8 — Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

Foundational Standards

  • 3.NBT.A.2
  • 3.OA.A.1
  • 3.OA.A.2

Criteria for Success


  1. Understand the following conventions for precisely reading an expression that has more than one operation (MP.6):
    1. "Do the operation inside the parentheses before an operation outside the parentheses (the parentheses can be thought of as hands curved around the symbols and grouping them).
    2. If a multiplication or division is written next to an addition or subtraction, imagine parentheses around the multiplication or division (it is done before these operations)" (OA Progression, p. 27), and 
    3. In the absence of parentheses or precedence, operations are performed from left to right.
  2. Evaluate an expression using the conventions above.

Tips for Teachers


  • The use of the acronym PEMDAS or GEMDAS can mislead students to always perform multiplication before division and addition before subtraction. Thus, the use of PEMDAS or GEMDAS (or other acronyms) should be avoided in favor of helping students understand the three general conventions mentioned in Criteria for Success #1 above.
  • As the OA Progression states, "at Grades 3 through 5, parentheses can usually be used for cases [in which a multiplication or division is written next to an addition or subtraction] so that fluency with this rule can wait until Grade 6." Thus, students are introduced to the convention that without parentheses, multiplication and division take precedence over addition and subtraction but will not encounter cases where no parentheses are used and must exercise this convention to solve correctly.
  • "The symbols of arithmetic, $$\times$$ for multiplication and $$\div$$ for division, continue to be used in Grades 3, 4, and 5" (OA Progression, p. 27). Thus, students are not expected to understand that a number written before an opening parenthesis implies multiplication, for example, but rather will always see the traditional symbols for each operation. 
  • The first question on the Problem Set is actually a question from the Massachusetts Comprehensive Assessment System (MCAS) that is aligned to Grade 5. However, I think it’s within the scope of expectations of Grade 3, so it is included here. Students might be very excited and encouraged to hear that they are able to solve a Grade 5 problem!
Fishtank Plus

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

Anchor Tasks


Problem 1

Richard and Geline are both trying to find the value of $$14 - 6\times2$$. Richard thinks its value is $$16$$. Geline thinks its value is $$2$$.

a.   How did Richard get his answer?

b.   How did Geline get her answer?

Guiding Questions

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

Problem 2

Solve.

a.   $$(4+2)\times5=$$ ______

$$4+(2\times5)=$$ ______

b.   $$15-(12\div3)=$$ ______

$$(15-12)\div3=$$ ______

Guiding Questions

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

References

EngageNY Mathematics Grade 3 Mathematics > Module 3 > Topic C > Lesson 8Concept Development

Grade 3 Mathematics > Module 3 > Topic C > Lesson 8 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


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

  • How did you discover where the parentheses belonged in #3 and #6?
  • Can you think of an equation besides the one in #8 where moving the parentheses won’t change the answer? What do those equations have in common? 

Target Task


Problem 1

Use parentheses to make the equations true.

a.   $$4+5\times 3=19$$

b.   $$4+5\times 3 =27$$

c.   $$10=16-9+3$$

d.   $$4=16-9+3$$

Student Response

Create a free account or sign in to view Student Response

Problem 2

Katya and Billy are trying to solve the following equation. 

15 ÷ 5 – 2 = ________

Katya says it equals 1. Billy says it equals 5. Show how the placement of parentheses in the equation can make both answers true.

Student Response

Create a free account or sign in to view Student 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.

Extra Practice Problems

Answer Keys

Answer keys for Problem Sets and Extra Practice Problems are available with a Fishtank Plus subscription.

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.

icon/arrow/right/large copy

Lesson 2

icon/arrow/right/large

Lesson 4

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?

Effective Instruction Made Easy

Effective Instruction Made Easy

Access rigorous, relevant, and adaptable math lesson plans for free