# Multiplication and Division, Part 1

## Objective

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

## Common Core Standards

### Core Standards

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• 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.

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• 2.NBT.A.2

• 2.OA.C.3

• 2.OA.C.4

## Criteria for Success

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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

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• 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, thus prescribing the order in which factors should be written in array situations for the time being. In Lesson 7, students will learn the commutative property, after which they’ll be given much freer reign over the order in which they write their factors. But for now, and for the sake of learning their meaning, stick to the convention. 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). But, since students are still only seeing array situations as equal groups without the use of the term column and have not yet explored the commutative property, students are temporarily asked to think of the row as the first factor and the number of objects in each row as the second.
• Students were introduced to arrays and their associated vocabulary in Grade 2 (2.OA.4).
• 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.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

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### 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.

#### 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 The Match Foundation, Inc.

### Problem 2

Can you rearrange the following groups so that they are in an array? Why or why not?

#### 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 The Match Foundation, Inc.

### Problem 3

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

1. Draw an array to represent the desks in Ms. Piatt’s room.
2. Write a multiplication equation to represent the number of desks in Ms. Piatt’s room.

#### 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 The Match Foundation, Inc.

## Discussion of Problem Set

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• 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?

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### Problem 1

There are 4 rows of stars. How many stars are in each row? __________

Write a multiplication equation to describe the array. __________

#### References

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

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..

### Problem 2

Judy collects seashells. She arranges them in 3 rows of 6. Draw Judy’s array to show how many seashells she has altogether. Then, write a multiplication equation to describe the array.

#### References

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

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..

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