3.OA.4 - About the Math, Learning Targets, and Rigor

Grade 3 Multiplication and Division

3.OA.A.4

About the Math

Full Standard

Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = ? ÷ 3, 6 × 6 = ?

Measurement Topic

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

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

About the Math

Skills and concepts below are learning goals for this standard.

Determine the unknown number in multiplication and division problems such as in the following examples: 8 x 9 = ?, 8 x ? = 48, ? x 3 = 27, 28 ÷ 7 = ?, ? ÷ 6 = 3, and 35 ÷ ? = 7.

It is critical that students can connect an equation to a problem or situation. They should connect equations with unknowns to problems as well. Students need to apply their understanding of multiplication and division to identify an unknown in an equation. Students need to see the relationship between multiplication and division. Students must see the solution to an equation on both sides of the equal sign so 7 =63 ÷ ? Students should be comfortable with the unknown number in an equation being in any position. 8 x n = 24, 4 = 32 ÷ n, 4 x 3 = n.

Essential vocabulary for this standard includes unknown, product, quotient, unknown, multiplication, product, factor, and quotient .

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
.	Determine the unknown number in multiplication and division problems such as in the following examples: 8 x 9 = ?, 8 x ? = 48, ? x 3 = 27, 28 ÷ 7 = ?, ? ÷ 6 = 3, and 35 ÷ ? = 7.	Determine the unknown number in multiplication and division problems related to area such as in the following examples: 8 x 9 = ?, 8 x ? = 48, ? x 3 = 27, 28 ÷ 7 = ?, ? ÷ 6 = 3, and 35 ÷ ? = 7.	Reinforce through work with problem solving.

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.

Progression Across Grades
Grade 2	Grade 4
This concept is not taught prior to grade 3.	Area and perimeter of rectangles in real world and mathematical problems (4.MD.3)

Instructional Tasks

TASKS

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

Write four equations with n, where n would solve all of them. (ie. 4 x n= 8, 10 = 5 x n, n x 6 = 12, 16 = n x 8.
Alesia has 32 cupcakes to sell at the bake sale. What are possible package arrangements that she could make? Write an equation for each arrangement.
The classroom has 30 desks. How many different ways could you arrange the desks?
Explain to a friend how you found n in the equation 4 x n = 40.
There are 50 ants on the ant hill. If there are 5 groups of 4 red ants, how many possible equal groups of black ants are there?

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 12 • Perimeter and Understanding Area and Basic Facts (3s)

Determine the Unknown in a Multiplication or Division Equation:

Additional Tasks

These links provide instructional ideas connected to this standard.

Finding the Unknown in a Division Equation Links to an external site. (Illustrative Math)
What Comes First, the Chicken or the Egg? Links to an external site. (Georgia Department of Education, pages 94-97)
Field Day Blunder Links to an external site. (Georgia Department of Education, pages 158-161)

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	84 (The Broken Multiplication Key, Activity 3.6) 84 (The Broken Division Key, Activity 3.7) 112 (Calculator 2 x Facts, Activity 4.17) 113 (Clock Facts, Activity 4.18) 114 (Pattens in the Nines Facts, Activity 4.19) 118 (Sort Them as You Do Them, Activity 4.22)
Nimble with Numbers	3-4	115-127
Fundamentals	3	36 (Multiplication Mania)
Groundworks: Reasoning with Numbers	3	56 - 63 88-104
Hands on Standards	3-4	26-27 (Lesson 6) 28-29 (Lesson 7) 34-35 (Lesson 10)
Problem-Driven Math	3	73-75
Brain-Compatible Activities for Mathematics	2-3	51-53
Connections	3	16-19 (Pattern Blocks Times Tables) 20-23 (Rainbow 100)
SuperSource (Pattern Blocks)	K-2	34-37
Math In Practice Teaching Third-Grade Math	3	Module 1

More Ideas Inspired by Teaching Student-Centered Mathematics

Independent Work

Centers

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

Missing Numbers with Multiplication Download Missing Numbers with Multiplication
(HCPSS-adapted resource)
Division Missing Numbers Equations Download Division Missing Numbers Equations
(HCPSS-adapted resource)
The Factor Game Links to an external site. (HCPSS-adapted resource)
Homes For Facts Download Homes For Facts
(HCPSS-adapted resource)
What's Your Number? Download What's Your Number?
(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.

Determine the Unknown in a Multiplication or Division Equation:

Relate Multiplication and Division Links to an external site.

Determine the Unknown in an Equation Related to Area:

Assessment

Full Standard

Measurement Topic

The standard is reported on the report card through these measurement topics. Expand the measurement topic for a description of what students who meet expectation are able to do.

2nd Grade Students Learning 3rd Grade Standards by Measurement Topic

Demonstrates understanding of multiplication and division

Quarter 3

Determine the unknown number in a multiplication and division equation relating the three whole numbers involved.

3OA4 Anecdotal Data Collection Tool Links to an external site.

Visit the SBIR (Standards Based Instruction and Reporting) page in Course Essentials for more information and clarification.

Rubric (for thinking and reasoning evidence)

Use this rubric for observation and constructed responses (tasks that require explanation, justification, and/or representation).

Rubric for Tasks (pdf) Links to an external site.

Exemplars for this standard (if available)

These samples are examples of what it might look like for a student who MEETS EXPECTATIONS, is MAKING PROGRESS, and/or is MAKING LIMITED/NO PROGRESS.