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

Grade 3 Geometry

3.G.A.2

About the Math

Full Standard

Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

 

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 number and fraction concepts.

 

 

Learning Targets

  • Partition shapes into equal parts understanding that the parts have equal areas.
  • Write a unit-fraction or a non-unit fraction for partitioned shapes.

 

About the Math

  • Partition shapes into equal parts understanding that the parts have equal areas.

This standard introduces the beginning concepts of fractions. Instead, the focus should be on equal parts of a shape. Students need to know that when a shape is divided into four equal parts, one part is called one-fourth. Students should know that when you divide a shape into two parts, one part is called one-half. They should also know that when a shape is divided into three parts, one part is a third. Students should be given opportunities to experiment with cutting or drawing shapes into equal parts.

  • Write a unit-fraction or a non-unit fraction for partitioned shapes.

Once students show understanding of partitioning they should connect their recordings to the symbolic recording of a fraction explaining the number of partitions and the number of parts identified.

Essential vocabulary for this standard includes area, fraction, and partition.

 

 

 

 

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
 

 
  • Partition shapes into equal parts understanding that the parts have equal areas.
  • Write a unit-fraction or a non-unit fraction for partitioned shapes.

 

 

 

 

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

Partition circles and rectangles (2.G.A.3)

This concept is not taught after grade 3.  Students are expected to apply this skill proficiently.

 

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Instructional Tasks

Tasks

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

  • Print these equal/unequal cards Links to an external site. and provide one set for each group of 2 or 3 students. Prompt the students to sort the figures in any way they see fit. Then discuss how the different groups chose to sort. It is highly likely that one or more groups will have noticed the equal/unequal. Center your discussion around this fundamental idea for fractions.
  • Create a design in which a square represents ¼ of the area of the design.
  • Provide each student with 3 different, but identical rectangles. Can you break each rectangle into sixths- differently for each rectangle?
  • Using pattern blocks, show the students a triangle. If the triangle is ⅓, what does the whole look like? If the triangle is ⅛, what will the whole look like?
  • Provide students with a rectangle, a triangle and a square (sizes can vary). For the triangle, tell the students this represents one-fourth of the whole. Have them draw or make the whole. Repeat with rectangle and square.
  • Draw a small rectangle. Draw a bigger rectangle that the smaller one is a part of. Tell what fraction of the big rectangle the small one is.
  • Have students draw three rectangles, all different sizes.  Have them partition all three rectangles into fourths.  Ask students to explain how all of the parts can be ¼  even though they are all different sizes.
  • Show students two squares.  One square is large and divided into thirds.  The other square is smaller and divided in half.  Ask them why ⅓ is larger than ½ in this situation?  How can you use what you understand about fractions to explain why this happens?
  • Can you partition a triangle into thirds by drawing two lines across the shape?  What would you say to someone who says you can do this?

 

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 9 • Fractions (Representing)

Partitioning of Shapes:

 

 

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

 Teaching Student-Centered Mathematics   

 K-3

257 (Correct Shares, Activity 9.1)
257 (Finding Fair Shares, Activity 9.2)
258 (More, Less, or Equal to One Whole, Activity 9.3)
  Hands-On Standards 3-4 44 (Identify and Write Fractions)
46 (Fractional Pairs)
 
  Problem-Driven Math 3 93 - 95 (Robot Round-Up)
  Roads to Reasoning 3 40 and 53
  SuperSource: Color Tiles 3-4 46-49
  20 Thinking Questions for Fraction Circles 3-6  
  Brain-Compatible Activities for Mathematics 2-3 93 - 95 (Robot Round-Up)

Math In Practice

Teaching Third-Grade Math

 3 Module 8

 

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

Learning Targets


  • Partition shapes into equal parts understanding that the parts have equal areas.
  • Write a unit-fraction or a non-unit fraction for partitioned shapes.

 

Learning targets identify what students should be able to do.  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.