3.OA.6 - About the Math, Learning Targets, and Rigor

Grade 3 Multiplication and Division

3.OA.B.6

About the Math

Full Standard

Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

 

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. 

  • Explain the relationship between multiplication and division.

Multiplication and division are inverse operations. They both involve a number of groups, a number in each group, and a total number.

  • Use multiplication to find an unknown in a division equation.

We can use the relationship between multiplication and division to find unknowns. This is helpful in various problem-solving situations. It is also helpful when one cannot recall a related basic fact. We can use multiplication to find an unknown in a division fact. We can do so by connecting the known fact or by building up by groups or rows/columns in an array to find the unknown. Students should have experience with both. The basic fact strategy "Think Multiplication" is grounded in this understanding.

  • Use division to find an unknown in a multiplication equation

Similarly, division can be used to find an unknown in a multiplication equation. Again, the relationship between the two can be leveraged using basic facts. However, this can be more challenging as students are more likely to learn/remember multiplication facts first. Students should understand that they can find a factor by dividing or taking away equal groups. 

 

 

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
  • Explain the relationship between multiplication and division.
  • Use multiplication to find an unknown in a division equation.
  • Use division to find an unknown in a multiplication equation

*Revisit this standard through warm-ups, classroom routines, discussions, and other activities throughout the year.

 

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
Divide multi-digit dividends  (4.NBT.6)

 

 

 

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Instructional Tasks

TASKS

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

  • Display the following multiplication problems on the board: 6 x ___ = 42, 7 x ___ = 35, 9 x ___ = 27, and 3 x ___ = 15. Have students model and solve each problem using centimeter cubes (or ones blocks). Then find the corresponding division problems.
  • Jayden was sharing his candy with his friends. He shared 32 pieces of candy. How many friends could he have shared the candy with?
  • Danielle has 48 lollipops to share with her friends. If she has 6 friends, how many lollipops would each friend get? If she has 8 friends, how many lollipops would each friend get? Why does the number of lollipops change based on the number of her friends?
  • Explain how you can use multiplication to solve a division problem. Use models, drawings and/or examples to support your answer.
  • Rachel says that if you know 4 x 6 = 24, then you know what n equals in 24 ÷ n = 6. Why is she correct?
  • Use the numbers 5, 6, and 30 to write a multiplication story. Write a related division story.

 

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 6 • Multiplication & Division

Division as an Unknown Factor:

 

 

 

Additional Tasks 

These links provide instructional ideas connected to this standard. 

 

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 Thumbnail Book Title Grade Pages

 Teaching Student-Centered Mathematics 

 K-3 84 (The Broken Division Key, Activity 3.7)
  Problem-Driven Math 3 102 - 104, (Sharing Stamps) 
  Math Intervention: Building Number Power 3-5

89-94

113-117
  Roads to Reasoning 3 6, 9, 10, 11, 23, 41, 62, 63, 66, and 69

Math in In Practice

Teaching Third-Grade Math

 3 Module 1

More Ideas

 

 

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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.

 

 

 

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

Full Standard

Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

 

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 2

  • Use multiplication to find an unknown in a division equation.
  • Use division to find an unknown in a multiplication equation.
  • Explain the relationship between multiplication and division.

 

3OA6 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).

Screenshot 2023-06-12 104305.png

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.

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 This course content is offered under a CC Attribution Non-Commercial Share Alike Links to an external site. license. Content in this course can be considered under this license unless otherwise noted.