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

Grade 3 Multiplication and Division

3.OA.A.3

About the Math

Full Standard

Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

 

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: Solves one and two-step word problems with any operation.

 

 

Learning Targets

  • Represent a multiplication or division word problem with models, drawings, and equations.
  • Solve word problems with multiplication or division.
  • Use estimation or related facts to determine if answers are reasonable.

 

About the Math

To solve problems, we must understand the problem, select a strategy, and assess if our solution is reasonable. It is critical for students to develop these skills through practice and conversation. As teachers, we must be careful not to highlight or modify a singular approach to solving any one problem.
  • Represent a multiplication or division word problem with models, drawings, and equations.

Students should consistently represent problems. At first, physical models are necessary. In time, students should shift to drawings as appropriate. In all cases, students should connect an equation to their models or drawings. Note that representations should match the problem type. For example, baskets of apples should not be represented with an array or area model. 

Working with Representations:

There are many ways that students can represent problems to solve them. We should be sure to encourage diverse representations. We also should be sure to connect representations. For example, it is important to connect drawingsand equations or physical models and equations. Bar diagrams are highly useful representations that help students develop an understanding of the relationships within a problem. Thinking Blocks Links to an external site. (pictured to the right) is an online resource that helps students develop an understanding of different problem solving situations by modeling them with bar diagrams.

Key Words:

Key words are not a viable strategy for solving word problems. Instead, we want students to make sense of problems and make use of their understanding to solve the problems. Moreover, research tells us that the use of key words as a strategy for solving problems adds to our students inability to solve problems. 

  • Solve word problems with multiplication or division.

The chart to the right shows the different problem types for multiplication and division. It is important to note that students do not learn about multiplicative comparison until 4th grade. 

  • Use estimation or related facts to determine if answers are reasonable.

We can help students develop a sense of reasonableness of their answers. One way to do this it to estimate the approximate solution of the problem before finding the exact solution. 

 

Essential vocabulary for this standard includes: arrays, unknown, multiplication, division, array, product, factor, quotient, repeated addition, and repeated subtraction. 

 

 

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 a multiplication or division word problem with models, drawings, and equations.
  • Solve word problems with multiplication or division.
  • Use estimation or related facts to determine if answers are reasonable.
  • Represent a multiplication or division word problem with models, drawings, and equations.
  • Solve word problems with multiplication or division.
  • Use estimation or related facts to determine if answers are reasonable.
  • Reinforce through work with problem solving with all operations.
  • Reinforce through work with problem solving with all operations.

 

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  Grade 4

This concept is not taught prior to grade 3.

 Multiply/divide to solve multiplicative comparison word problems (4.OA.2)

 

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Instructional Tasks

Tasks

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

  • Provide students with counters (cubes, two-sided counters, lima beans, etc.). Pose word problems involving multiplication or division (within 100). Just as with 3OA1 and 3OA2, ask students to represent the problem with the materials as well as with equations. Some examples include: There are 8 students in the dance club at school. Juan brought a bowl of 48 cherries to share among the members. How many cherries will each student get? In gym class, there are 5 teams with 5 players on each team. How many students are in the gym?
  • We need 52 juice boxes for our class party. Juice boxes come in packs of 6 or 8. How many packs of each do you need to have enough for each student?
  • Jim purchased 5 packages of muffins. Each package contained 3 muffins. Describe another situation where there would be 5 groups of 3 or 5 x 3.
  • The monkey keeper at the zoo needs 7 apples a day to help feed the monkeys. She has 50 apples at the start of the week. Will she have enough apples for the entire 7 day week ? Explain your reasoning.
  • Chris has 36 pencils and 4 jars to place them in.  How can you represent this situation to show how many pencils can be in each jar, if there are an equal number of pencils in each jar.
  • Lisa has 30 shoes and says that she owns 12 pairs. Explain why she is correct or incorrect.
  • Grace has 54 cookies and wants to put them on plates for a party.  She wants the same number of cookies on each plate.  How many cookies will be on each plate?  Can you solve this problem?  If not, what information do you need?
  • Multiply or Divide to solve?  Jimmy ran 6 miles each day for 5 days.  How many miles did he run after 5 days?  Jimmy ran 6 miles each day and when he was done, he had run a total of 30 miles.  How many days did he run?
  • Phil is planting flowers and has a garden with 7 rows and room for 8 flowers in each row.  He has 50 flowers to plant.  Will he fill the entire garden?  
  • Write a word problem that the number sentence 72 ÷ 9 could be used to solve. Note: This is a way to increase rigor but is not required for demonstrating proficiency with this standard.
  • Write a word problem with the product of 35. Note: This is a way to increase rigor but is not required for demonstrating proficiency with this standard.

 

 

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

Solve Multiplication and Division Word Problems:

 

 

Additional Tasks 

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

 

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
  Hands On Standards

1-2

 

3-4

 56-57 (Repeated Subtraction)
58-59 (Equal Sharing)


24 (Multiplying with Arrays)
28 (Multiplying by 5)
34 (Finding Factor Pairs)
98 (Square Numbers) 
 

Fundamentals

 		  3  

36 (Multiplication Mania)
40 (Climb the Ladder)
   Problem Driven Math  3 124 - 126 (Mosquito Munch) 

29 - 30 (Big Rigs)

90 - 92 (Keeping the Beat)
   

Brain-Compatible Activities for Mathematics

 2-3

40-43
44-47
   Developing Mathematics with Base Ten  

44-46

67-70
  Math Intervention: Building Number Power  3-5 82-84
 

Developing Number Concepts

 		  Book 3

169-175
182-210
  SuperSource: Pattern Blocks K-2 34-37 
  NumberSense 3-4 59-61
  Roads to Reasoning

2

3

 66 (Pencil Put Away )

20, 25, 51

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.

 

 

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.

 

Solve Multiplication Word Problems:

Solve Division Word Problems:

Solve Multiplication and Division Word Problems:

 

 

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Assessment

Learning Targets


  • Represent a multiplication or division word problem with models, drawings, and equations.
  • Solve word problems with multiplication or division.
  • Use estimation or related facts to determine if answers are reasonable.

 

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.  

 

 

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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.