Grade 3 Multiplication and Division

3.OA.A.1

About the Math

Full Standard

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.

Measurement Topic

This standard is reported on the report card in these quarters as follows:

**3rd Grade Students Learning 3rd Grade Standards**
Quarter 1	Quarter 2	Quarter 3	Quarter 4
Report Card Measurement Topic: Demonstrates understanding of multiplication.	Report Card Measurement Topic: Demonstrates understanding of multiplication.

Learning Target

Represent multiplication with equal groups.
Represent multiplication with arrays.
Relate repeated addition to representations of multiplication.
Represent multiplication as equal jumps on a number line.
Describe how a multiplication chart relates to these representations.
Write an equation for a multiplication situation.
Represent multiplication with an area model (3rd quarter after the concept of area is taught).

About the Math

Multiplication is a major third-grade concept. Students must understand it deeply.

Represent multiplication with equal groups.

An equal group situation might be something like baskets of apples. Here, there are groups of apples. We can find the number in all by multiplying the number of groups by the number of things in each group. Students should use physical models to show equal groups and connect them to drawings and equations. Looking at a problem such as, "How many apples in 4 baskets of 8 apples each?", students need to think multiplicatively about this problem. They need to think there are four sets of eight. Children conceptualize each group of eight as a single item to be counted.

Represent multiplication with arrays.

Arrays are arranged in rows and columns of things. One can find the total number of objects by multiplying the number in each row by the number of rows. The difference between an array and area is clear. An array can be an arrangement of any shape or thing in rows or columns. For example, an array could be rows of flowers in a garden. Area is an array of squares with no gaps or spaces. If color tiles are all connected they are an area model. If they are separated by space they are an array.

Relate repeated addition to representations of multiplication.

A product can be found with repeated addition. Repeated addition can represent the action of adding equal groups or rows/columns. However, it is critical that students do not overly rely on repeated addition.

Represent multiplication as equal jumps on a number line.

Multiplication can be represented on a number line to find a product. Multiplication on a number line should be connected to other representations and equations.

Describe how a multiplication chart relates to these representations.

Students should be able to explain how a multiplication chart works and how it can be used for division (see 3.OA.2). Students should connect representations to equations and the multiplication chart. Students should use the chart consistently so that students find the correct products.

Write an equation for a multiplication situation.

Multiplication can be represented with equations. Students should connect multiplication equations to representations beginning with their first experiences with multiplication. In context, 5 x 7 refers to 5 groups of 7. For example, if asked how many cookies are in 5 bags of 7 cookies, a student's representation/reasoning should show 5 groups of 7 in each. However, in situations without context, overemphasis on the order of factors is not necessary because the commutative property tells us that 5 x 7 = 7 x 5. "Naked numbers" are examples of situations without context. In these cases, students could show either order of factors to represent their understanding.

Represent multiplication with an area model (3rd quarter after the concept of area is taught).

Understanding multiplication as it relates to area is a critical understanding in mathematics. This understanding should be developed after students understand what area is. Students are not to learn the formula for area. Instead, students should understand area as lenghth x length regardless of a rectangle's orientation. Also, students should connect decomposing of area to the distributive property.

Essential vocabulary for this standard includes multiplication, factor, product, array, equal group, groups of, area, and repeated addition.

Progression of Standard within Grade 3

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Progression Throughout Year
Quarter 1	Quarter 2	Quarter 3	Quarter 4
Represent multiplication with equal groups. Represent multiplication with arrays. Relate repeated addition to representations of multiplication. Represent multiplication as equal jumps on a number line. Describe how a multiplication chart relates to these representations. Write an equation for a multiplication situation.		Represent multiplication with equal group with an area model (3rd quarter after the concept of area is taught).

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map. Information is not the complete standard.

Progression Across Grades
Grade 2	Grade 4
Work with equal groups of objects and arrays (2.OA.4) Determine whether a group of objects (up to 20) has an odd or even number of members ( 2.OA.3 )	Multiplicative Comparison (4.OA.1) Multiply a fraction by a whole number (4.NF.4)

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Instructional Tasks

Tasks

These tasks can be used with small group or whole group instruction.

Pose a scenario to students about rows of chairs (perhaps you the teacher want to arrange the chairs in your classroom), and ask students to use color tiles to show and tell how many chairs if arranged in 8 rows of 4 chairs. Highlight the concept of an array and what rows and columns are. Make a connection between repeated addition and the multiplication expression. Repeat with other examples (i.e. 3 rows of 5, 6 rows of 4, etc.)
Pose a scenario involving equal groups (art teacher puts 5 paintbrushes in each of 4 different cups, 7 apples in each of the 3 baskets) and ask students to represent the scenario with counters (lima beans, cubes, etc.). Highlight equal groups and make connections between repeated addition expression and the multiplication expression. It is very important that when given a context, that the representation match the context. For example, 3 students in each of the 8 work groups should be shown with 8 groups with 3 in each group, not 3 groups with 8 in each group. Although the product will be the same, the commutative property does not apply when representing a multiplication situation that has a context. The representation needs to match the context when a context is provided.
Provide students with counters and a multiplication expression such as 6x2 and asks students to represent the expression with equal groups and/or an array. Make connections to repeated addition expressions. Repeat with other multiplication expressions. Without a context, students can use the commutative property to represent the expression either way. For example, students might show 6 rows of 2 or 2 rows of 6 OR 6 groups of 2 or 2 groups of 6. Either is correct because there is no context with a "naked" expression.
Teacher shows an array. Have students list all equations that it represents. (Ex. 4 rows, 5 columns: 4 x 5, 5 x 4, 20/4, 20/5, 4 + 4 + 4 + 4 + 4, 5 + 5 + 5 + 5
Create 3 different multiplications arrays that represent 24.
Kim has 4 boxes with 7 flowers in each box. Kathleen has 3 boxes with 8 flowers in each box. Kathleen says she has more flowers because there are more in each box. Is she correct? Use an array, equal groups or repeated addition to show your understanding.
Use a number line to show how 3 x 4 and 6 x 2 both equal 12.
The product is 48. What could the factors be?
Explain the relationship between a factor and product. What happens to the product when one of the factors increases? (Ex. when 3 x 7 becomes 3 x 8)

slide-based Tasks

These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.

Module 4 • Multiplication (Meaning and Representations) and Basic Facts (Multiply by 2)

Use Equal Groups, Arrays, and Repeated Addition to Represent Multiplication:

Additional Tasks

These links provide instructional ideas connected to this standard.

One Hundred Hungry Ants (Georgia Department of Education, pages 20-22)
Arrays in Real Life (ppt lesson seed)
Multiplication and the Meaning of Factors (Achieve the Core Lesson Plan)
Arrays on the Farm (Georgia Department of Education, pages 23-38)

tasks from Print Resources

These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them.

Print Resources
Book Title	Grade	Pages
Teaching Student-Centered Mathematics	K-3	83 (Finding Factors, Activity 3.4) 84 (The Broken Multiplication Key, Activity 3.6)
Fundamentals	3	36 (Multiplication Mania) 40 (Climb the Ladder)
Hands-On Standards	3-4	24 (Multiplying Arrays) 28 (Multiplying by 5) 34 (Finding Factor Pairs) 98 (Square Numbers)
Problem-Driven Math	3	124-126 (Mosquito Munch) 29-30 (Big Rigs) 90-92 (Keeping the Beat)
Developing Number Concepts	Book 3	169-175
Math In Practice Teaching Third-Grade Math	3	Module 1

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Independent Work

Centers

These print resources can be used during independent or center time. These resources could also be used as lesson seeds.

Array Cards (HCPSS-adapted resource)
Creating Rectangles (HCPSS-adapted resource)
Equal Towers (HCPSS-adapted resource)
How Many Arrays Can You Make? (HCPSS-adapted resource)
Making Arrays With Counters (HCPSS-adapted resource)
Rectangle Arrays (HCPSS-adapted resource)
Squares and Circles (HCPSS-adapted resource)
Spin An Array (HCPSS-adapted resource)
What's The Equation? (HCPSS-adapted resource)
Various Rectangles (HCPSS-adapted resource)

INDEPENDENT PRACTICE/HOMEWORK/ASSESSMENT

These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.

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Assessment

Learning Targets

Represent multiplication with equal groups.
Represent multiplication with arrays.
Relate repeated addition to representations of multiplication.
Represent multiplication as equal jumps on a number line.
Describe how a multiplication chart relates to these representations.
Write an equation for a multiplication situation.
Represent multiplication with an area model (3rd quarter after the concept of area is taught).

Learning targets identify what students should be able to do. This rubric can be applied to tasks and observations for assessment and/or grading.

Rubric for Tasks

Visit the SBIR (Standards Based Instruction and Reporting) tab in Course Essentials for more information and clarification. There you will find the measurement topic crosswalk, report card comments, links to professional learning/resources and guidance.

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