3.OA.2 - About the Math, Learning Targets, and Rigor

Full Standard

Interpret whole-number quotients of whole numbers (e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.

 

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 division.

 

Learning Targets

• Use division to determine the size of each group when the number of groups is known (partitive, i.e. 12 apples in 3 bags. How many are in each bag?)
• Use division to determine the number of groups when the size of each group is known. (quotative or measurement, 12 apples with 4 in each bag. How many bags?)
• Represent division with models and drawings.
• Write an equation for a division situation.
• Describe how partitive and measurement division are different.

 

About the Math

Division can be thought of in two ways. It is critical that students understand both ways deeply. Students do not need to know the names of these two ways. 

• Use division to determine the size of each group when the number of groups is known (partitive, i.e. 12 apples in 3 bags. How many are in each bag?)

Division can be used to determine the size of group. If someone has 12 apples in 3 bags we can determine the size of the group by dividing. Here the total is 12. The number of each groups is 3. The bag is a group.

• Use division to determine the number of groups when the size of each group is known. (quotative or measurement, 12 apples with 4 in each bag. How many bags?)

Division can be used to determine the number of groups. If someone has 12 apples with 4 apples in each bag we can divide to find how many bags they have or how many bags are needed. The total is 12 apples. The size of the group is 4 apples. 4 apples can fit in each bag. The number of groups is unknown. 

• Represent division with models and drawings.

Students must be able to represent division with a range of models including counters, color tiles, base ten blocks, and more. Students should also be able to represent division with a drawing. Drawings and phsyical models should be connected to the problem and a division equation.

• Write an equation for a division situation.

Students must be able to write an equation and explain how it connects to a problem or representation. Students should be able to use a multiplication chart and the relationship to division to find unknown quotients. Keep in mind that repeated subtraction can be used to find a quotient but, like multiplication, repeated subtraction must not be the core understanding for our students.

• Describe how partitive and measurement division are different.

Students should work with word problems that promote both types of division. Students should be able to answer "are we finding the number of groups?" or "are we finding the group size?" each time they solve a division word problem.

Consider these 2 problems:

1. Maria cuts 12 feet of ribbon into 3 equal pieces so she can share it with her two sisters. How long is each piece?
2. Maria has 12 feet of ribbon and wants to wrap some gifts that need 3 feet of ribbon each. How many gifts can she wrap using the ribbon?

Instructional note: Students should first work with division situations in which there is no remainder. In time, students should be presented problems in context in which there is a remainder. Discussion should be had about the meaning of the remainder and how we note it. Pictures and representations should be used to support this discussion. Remainders should not be recorded as fractions in this grade. 

 

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

  The video to the right describes the Two Kinds of Division Links to an external site..

 

 

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
	Use division to determine the size of each group when the number of groups is known (partitive, i.e. 12 apples in 3 bags. How many are in each bag?) Use division to determine the number of groups when the size of each group is known. (quotative or measurement, 12 apples with 4 in each bag. How many bags?) Represent division with models and drawings. Write an equation for a division situation. Describe how partitive and measurement division are different.

 *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 5
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)	Interpret a fraction as division (5.NF.3) Interpret multiplication as scaling (resizing) (5.NF.5) Word problems with x of fractions (5.NF.6)

 

 

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Tasks

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

• Provide students cups and counters (cubes, lima beans, two-color counters, etc.). Present students with a problem such as 21 divided into equal groups of 3. Have students model the problem by placing the correct number of counters into each cup. Connect to the matching equation. Repeat with other examples. 
• Provide students with counters. Pose scenarios that will highlight both partitive and quotative division. Students should use the counters to show a representation that matches the problem. Two example problems could include: The teacher has 28 pencils and wants to have 4 pencils in each baggie, how many baggies will be needed? and The teacher has 28 pencils and shares them with 4 students, how many pencils will each student get?
• I have 24 total marshmallows divided into more than one bag. Each bag has the same amount. How many bags could I have? How many would be in each bag?
• How many ways can I share 36 equally?
• Explain the relationship between multiplication and division? Use models, drawings, and/or examples to support your answer.
• Think of an example in life when 42 ÷ 6 would be used with the sharing method of division (42 into 6 equal groups) and when it would be used with the measurement method (42 divided into groups of 6). Note: students do not need to know the vocabulary of sharing and measurement methods, but should be exposed to both.
• If the quotient is 6, what could your possible one-digit dividend and one-digit divisor be? List 3 different possibilities.
• How many people could share 32 M&M’s equally? Explain all possibilities.
• Show the equation 28 ÷ 7 = 4.  What does the 28 represent?  What could the 7 represent?  What about the 4?
• 48 books will be put onto 6 shelves, with the same number of books on each shelf.  How many books will go on each shelf?  Show how you know.  What if you have 8 shelves to place the books on?  How will this change the number of books on each shelf?  How would the equations look for each situation?

 

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.

 

Additional Tasks

  These links provide instructional ideas connected to this standard. 

• Knotty Rope Links to an external site. (3 Act Task, G.Fletcher)
• Sharing Pumpkin Seeds Links to an external site.(Georgia Department of Education, pages 98-103)

 

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) 92-93 (Expanded Lesson: Learning About Division)
	Hands on Standards	3-4	Lessons 11-15
	Math Intervention: Building Number Power 3-5	3-5	85-88 95-98 113-117
	The Super Source: Color Tiles   The Super Source: Snap Cubes	3-4	58-61 34-37
	Math In Practice Teaching Third-Grade Math	3	Module1

 

More Ideas

• More Ideas Inspired by Teaching Student-Centered Mathematics

 

 

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Centers

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

• Bar Diagrams: Division Download Bar Diagrams: Division
  (HCPSS-adapted resource)
• Fair Tickets Download Fair Tickets
  (HCPSS-adapted resource)
• Division Sort Download Division Sort
  (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.

• Represent Division Links to an external site.
• Represent Division on a Number Line Links to an external site.
• Quotative Division Links to an external site.

• Represent with Objects and Equations (performance task) Links to an external site.
• Represent with Base Ten Blocks (performance task) Links to an external site.
• Represent with Picture/Equation Links to an external site.
• Represent Division in Multiple Ways Links to an external site.
• Match Equation to Pictorial Representations Links to an external site.
• Determine Number of Groups Links to an external site.
• Determine Number of Groups_2 Links to an external site.
• Determine Size of Groups Links to an external site.
• Write Story Problem to Match Equation Links to an external site.

 

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Learning Targets

• Use division to determine the size of each group when the number of groups is known (partitive, i.e. 12 apples in 3 bags. How many are in each bag?)
• Use division to determine the number of groups when the size of each group is known. (quotative or measurement, 12 apples with 4 in each bag. How many bags?)
• Represent division with models and drawings.
• Write an equation for a division situation.
• Describe how partitive and measurement division are different.

 

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 Links to an external site.

 

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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