Multiplication and Division, Part 1

Lesson 2

Math

Unit 2

3rd Grade

Lesson 2 of 21

Objective


Identify and create situations involving arrays and describe these situations using the language and notation of multiplication.

Common Core Standards


Core Standards

  • 3.OA.A.1 — Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.

Foundational Standards

  • 2.NBT.A.2
  • 2.OA.C.3
  • 2.OA.C.4

Criteria for Success


  1. Understand that an array is an arrangement of objects into rows and columns. (Note that the term "column" will be introduced in Lesson 7.)
  2. Relate arrays to equal groups, relating rows to the number of groups and the number of objects in each row to the size of groups (MP.7). 
  3. Write multiplication equations to represent arrays and to find the total number of objects in an array (MP.2). 
  4. Translate a written description of an array into a picture of one.

Tips for Teachers


  • Similar to Lesson 1, students will understand a row as an equal group and the number of objects in a row as the size of the group, thinking of 4 rows of 3 objects as 4 $$\times$$ 3. Use the conventional way of writing factors when addressing the whole class, but allow individual students to write them in whatever order they like so long as they are able to explain the meaning of each factor. Then in Lesson 7, students will learn the commutative property using arrays, seeing that "in the array situations, the roles of the factors do not differ. One factor tells the number of rows in the array, and the other factor tells the number of columns in the situation. But rows and columns depend on the orientation of the array" (OA Progression, p. 24). After that lesson, students will have even more flexibility in the order in which they write their factors.
  • Students were introduced to arrays and their associated vocabulary in Grade 2 (2.OA.4), but is included here as new vocabulary given its importance to student understanding.
  • As a supplement to the Problem Set, we recommend 2 additional games you can play with students:
    • A modified version of the game "Circles and Stars" from YouCubed.org. Instead of having students draw circles and stars, they can create rows of a certain group size. (Similar to yesterday, modify the options for numbers rolled so that students only work with factors 2-5 and 10.)
    • "Tic-Tac-Toe Array" from Building Conceptual Understanding and Fluency Through Games by the North Carolina Department of Public Instruction.

Lesson Materials

  • Optional: Counters (15 per student or small group) — Students might not need these depending on their reliance on concrete materials.
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Anchor Tasks


Problem 1

Jordan's mom is making cookies. Here's what they look like when they come out of the oven:

Jordan said that he could write a multiplication equation to represent the number of cookies. Do you agree or disagree? Explain.

Guiding Questions

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References

EngageNY Mathematics Grade 3 Mathematics > Module 1 > Topic A > Lesson 2Concept Development

Grade 3 Mathematics > Module 1 > Topic A > Lesson 2 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

Arrange the following groups into an array. Then write a multiplication equation that represents that array. 

Guiding Questions

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References

EngageNY Mathematics Grade 3 Mathematics > Module 1 > Topic A > Lesson 2Concept Development

Grade 3 Mathematics > Module 1 > Topic A > Lesson 2 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 3

Ms. Piatt puts her students’ desks into an array. There are 6 rows of desks with 2 desks in each row. 

a.   Draw an array to represent the desks in Ms. Piatt’s room. 

b.   Write a multiplication equation to represent the number of desks in Ms. Piatt’s room.

Guiding Questions

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References

EngageNY Mathematics Grade 3 Mathematics > Module 1 > Topic A > Lesson 2Concept Development

Grade 3 Mathematics > Module 1 > Topic A > Lesson 2 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

  • Were there certain options in #1 that you could rule out right away? Why? How did you narrow down the possibilities from there? 
  • Compare #7 and #8. What’s similar about these arrays? What’s different? 
  • Compare equal groups in scattered configurations and arrays. 
  • How many possibilities did you come up with for #9? How did you find the total number of objects in the array?

Target Task


Problem 1

Use the following array to answer the questions below.

a.   There are 3 rows of buttons. How many buttons are in each row? 

b.   Write a multiplication equation to describe the array. 

Student Response

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Problem 2

Nita collects baseball cards. She puts her baseball cards in 2 rows of 5.

a.   Draw an array to show how she arranged her baseball cards.

b.   Write a multiplication equation to describe the array you drew in Part (a).

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.

Extra Practice Problems

Answer Keys

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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.

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Lesson 1

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Lesson 3

Lesson Map

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

Topic A: The Meaning of Multiplication and Division

Topic B: Multiplication and Division by 2, 5, and 10

Topic C: Multiplication and Division by 3 and 4

Topic D: More Complex Multiplication and Division Problems

Topic E: Scaled Picture and Bar Graphs

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