3.OA.7 - About the Math, Learning Targets, and Rigor

Grade 3 Multiplication and Division

3.OA.C.7

About the Math

Full Standard

Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

 

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.

 

Report Card Measurement Topic: Demonstrates understanding of division.

Report Card Measurement Topic: Demonstrates understanding of multiplication.

 

Report Card Measurement Topic: Demonstrates understanding of division.

Report Card Measurement Topic: Demonstrates understanding of multiplication.

 

Report Card Measurement Topic: Demonstrates understanding of division.

 

Learning Targets

  • Recall basic facts quickly.
  • Use strategies to recall facts when needed.

 

About the Math

Learning math facts provides a foundation for success in mathematics. It takes time for students to develop quick recall of facts. Organizing facts can be extremely helpful for developing fluency. Multiplication and division of related facts should be taught simultaneously so that students can make use of the relationship. The strategies outlined in this standard support student development. These algebraic strategies also help students develop mental math skills that can be applied to larger numbers. 

  • Recall basic facts quickly.

Quickly is not measured with a specific amount of time. It should also be noted that students' speed of recall can fluctuate for a myriad of reasons.

This is the order of fact strategies taught in third grade. Multiplication and division are taught together to leverage relationships. 

  • x2 because students have an innate ability to double and this helps develop the concept of multiplication/division.
  • x10 is connected to skip counting skills. x10 also follows a pattern that can be applied to any factor.
  • x5 is a similar skip counting example. x5 can be applied to other numbers when considering 5 is half of 10. Therefore, products of 5 are half of the product of the factor and 10 (i.e. 4 x 5 is half of 4 x 10).
  • x1 and x0 are introduced after these first 3 sets of facts. Although these facts are easy to learn or recall, the idea of 1 group of something or 0 groups of something can be quite abstract for students.
  • x3 facts can be thought of as one more group than double a number. (i.e. 7 x 3 is equivalent to 7 x 2 + 7)
  • x6 facts are equivalent to x5 + x1 or double x3 (i.e. 4 x 6 = 4 x 5 + 4 x 1 -or- 4 x 3 x 2).
  • x9 facts are equivalent to 1 group less than x10 (i.e. 7 x 9 is equivalent to 7 x 10 - 7).
  • x4 facts are equivalent to double double facts (i.e. 3 x 4 can be thought of as 3 x 2 x 2)
  • x8 facts are equivalent to double-double-double facts or 2 groups less than x10
  • x7 facts can employ an array of strategies. However, if the above sequence is followed, 7 x 7 is the only "unknown" fact left.

 

Student ability to recall facts should be assessed in various ways. Students should not take timed fact tests frequently. Fact recall can be assessed through interviews, observations, and other alternatives. 

 

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
  • Recall basic facts quickly.
  • Use strategies to recall facts when needed.

 

x2
  • Recall basic facts quickly.
  • Use strategies to recall facts when needed.

 

÷2, x10, ÷10,  x5, ÷5, x1, ÷1, x0, 0÷ 
  • Recall basic facts quickly.
  • Use strategies to recall facts when needed.

 

 x9, x4, x3, ÷9, ÷4, ÷3
  • Recall basic facts quickly.
  • Use strategies to recall facts when needed.

 

x6, ÷6, x8, ÷8 

 

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
  • Multiplication with multi-digit factors (4.NBT.5)
  • Division with multi-digit dividends (4.NBT.6)
  • Find factor pairs/prime and composite (4.OA.4)
  • Relative size of units and equivalents (4.MD.1 )

 

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Instructional Tasks

Tasks

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

  • Sean is have difficulty when multiplying by 9. Kevin tells him if he knows x10 facts, you can quickly solve x9 facts. Do you agree with Kevin? Why or why not? Use models, equations and/or drawings to support your answer.
  • Explain how x2 facts relate to x4 facts. How do x4 facts help you solve x8 facts?
  • Tara knows strategies for x2, x3, x4, x5, x6, x8, x9, and x10. She asked when she would learn strategies for x7 facts and was told she knew her x7 facts already. Explain how that is.
  • Heather’s teacher told her that if she knows her x10 facts then she also knows her x5 facts. Heather doesn’t understand how. Explain the relationship between the 10’s and 5’s facts.
  • Explain a strategy for multiplying by 3.
  • How does knowing your x5 and x2 facts help you to learn your x7 facts?
  • If you don't know 8 x 6, how can knowing 8 x 5 help?  Use what you know about multiplication to explain how to figure out the product of 8 x 6,
  • Use arrays or drawings to explain why 3 x 8 and 4 x 6 can both have the same product.

 

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.

x/÷ 2

x/÷ 5

x/÷ 10

x/÷ 0

x/÷ 1

x/÷ 3

x/÷ 6

x/÷ 9

x/÷ 4

x/÷ 8

Mixed Facts (All Strategies Taught)

 

 

 

 

Additional Tasks 

These links provide instructional ideas connected to this standard. [NOTE: NCTM membership required for access to Illuminations lessons.]

365 Math

 

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  

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)
 

Mastering the Basic Facts in Multiplication and Division

(All Print resources from Mastering the Basic Facts

Multiplication and Division: x÷facts Links to an external site.)

 

Quarter 1: 1-3

Quarter 2: 4-5

Quarter 3: 6-7

Quarter 4: 7-8
  Hands On Standards 3-4

28 (Multiply by 5)

32 (Multiply by 10)

34 (Factor Pairs)

36 (Exploring Division)
  Math Intervention: Building Number Power 3-5

99 -104 (Multiplying & Dividing by Ten)

105 - 109 (Perfect Squares & Near Squares)

Math In Practice

Teaching Third-Grade Math

 3

Module 3

 

 

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Independent Work

Centers/games

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

New Games and Resources!

 

Current Centers and Games

 

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


  • Recall basic facts quickly.
  • Use strategies to recall facts when needed.

 

Learning targets identify what students should be able to do. The resources below can be used to measure student understanding of the standard. This rubric can be applied to tasks and observations for assessment and/or grading. 

 

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.  

 

Assessment Tasks

These tasks align with the learning targets for the standard. They can be combined with other tasks for extended assessment opportunities. Teachers/students are not expected to complete all these tasks.

 

Basic Fact Interview Recording Sheet (with directions) Links to an external site.

For interviews:
Use the interview recording sheet Links to an external site.with a set of facts that students are working with in the classroom.

For observations:
Use the Download observation recording sheet

with games and activities used in the classroom during independent practice or center time.

 

Basic Fact Assessments:

Note: These assessments do have a recommended timing element. This is not required and the assessments can be used in a variety of ways. Avoid an overemphasis on speed as it can create anxiety and damage student math identity.  

 

 

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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.