Multiplication and Division, Part 1

Lesson 15

Objective

Solve two-step word problems involving multiplication and division and assess the reasonableness of answers.

Materials and Resources

Common Core Standards

Core Standards

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  • 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).

Criteria for Success

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  1. Solve two-step word problems involving multiplication and division (MP.4). 
  2. Assess the reasonableness of an answer (MP.1).

Tips for Teachers

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As mentioned in Unit 1 Lesson 14, students are expected to interpret and understand equations with just one operation (3.OA.1, 3.OA.2), but whether students should know how to write an equation for a two-step word problem is less clear. The Progressions state, “more difficult problems may require two steps of representation and solution rather than one” (OA Progression, p. 28). Thus, it is left to the teacher to decide what “more difficult” means for your students, and when to make the transition to representing some two-step word problems with one step of representation/one equation, which you could do here or wait for subsequent lessons and units to do so. As some general guidance, it seems reasonable to expect every student to be able to write an equation for all one-step problems and for two-step problems where the unknown is isolated on one side of the equal sign in the equation without needing to manipulate it by the end of the year. For example, see #42 on Grade 3 Common Core Mathematics Test Released Questions May 2016

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Anchor Tasks

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Problem 1

Version 1: Mrs. Powell buys a few boxes with some binders in each box. She plans to give out the binders to some students. 

Version 2: Mrs. Powell buys a few boxes with some binders in each box. She plans to give out the same number of binders to each student. 

Version 3: Mrs. Powell buys a few boxes with some binders in each box. She plans to give out 3 binders to each student. 

Version 4: Mrs. Powell buys a few boxes with the same number of binders in each box. She plans to give out 3 binders to each student. 

Version 5: Mrs. Powell buys a few boxes with 6 binders in each box. She plans to give out 3 binders to each student. 

Version 6: Mrs. Powell buys 4 boxes with 6 binders in each box. She plans to give out 3 binders to each student.

Guiding Questions

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References

EngageNY Mathematics Grade 3 Mathematics > Module 1 > Topic F > Lesson 21Application Problem

Grade 3 Mathematics > Module 1 > Topic F > Lesson 21 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 The Match Foundation, Inc.

Problem 2

Ten children equally share 40 almonds. How many almonds will 3 of those children get?

Guiding Questions

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References

EngageNY Mathematics Grade 3 Mathematics > Module 1 > Topic F > Lesson 20Concept Development

Grade 3 Mathematics > Module 1 > Topic F > Lesson 20 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 The Match Foundation, Inc.

Discussion of Problem Set

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  • How did your answer in Part (a) of #1 help you solve for Part (b)? 
  • How did you solve #5? Was anyone able to solve it in one step? How? 
  • How did you solve #8? What made this problem more challenging than many of the others? 
  • How did you solve #9? What made this problem more challenging than many of the others? 
  • How did you check the reasonableness of your answers to each problem?

Target Task

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Problem 1

Thirty-two jellybeans are shared by 4 students. 

a. How many jellybeans will each student get? 

b. How many jellybeans will 3 students get?

References

EngageNY Mathematics Grade 3 Mathematics > Module 1 > Topic F > Lesson 20Exit Ticket, Question #1

Grade 3 Mathematics > Module 1 > Topic F > Lesson 20 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 The Match Foundation, Inc.

Problem 2

The teacher has 5 apples that she cuts into 6 slices. She then gives an equal number of apple slices to 3 students. How many apple slices does each child get?

References

EngageNY Mathematics Grade 3 Mathematics > Module 1 > Topic F > Lesson 20Exit Ticket, Question #2

Grade 3 Mathematics > Module 1 > Topic F > Lesson 20 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 The Match Foundation, Inc.

Mastery Response

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