Standard #: MA.2.FR.1.1


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Partition circles and rectangles into two, three or four equal-sized parts. Name the parts using appropriate language, and describe the whole as two halves, three thirds or four fourths.


Clarifications


Clarification 1: Within this benchmark, the expectation is not to write the equal-sized parts as a fraction with a numerator and denominator.

Clarification 2: Problems include mathematical and real-world context.



General Information

Subject Area: Mathematics (B.E.S.T.)
Grade: 2
Strand: Fractions
Standard: Develop an understanding of fractions.
Date Adopted or Revised: 08/20
Status: State Board Approved

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

 

Terms from the K-12 Glossary

  • Circle 
  • Rectangle

 

Vertical Alignment

Previous Benchmarks

 

Next Benchmarks

 

Purpose and Instructional Strategies

The purpose of this benchmark is to extend the work from grade 1 of partitioning circles and rectangles. At this grade level, students will partition into three equal-sized parts, name the parts as three thirds and describe the whole (MTR.5.1).
  • Instruction includes the use of manipulatives such as geoboards, fraction circles, pattern blocks or color tiles, along with contextual sharing situations. 
  • Instruction includes the idea of part-whole relationships as supported by a model. 
  • Naming the parts is based on the number of equal parts that make the whole. 
  • Students are not expected to use formal fraction notation until grade 3.

 

Common Misconceptions or Errors

  • Students may have difficulty partitioning into equal-sized parts. 
  • Students may not understand that the parts can be equal parts even if they do not look identical.

 

Strategies to Support Tiered Instruction

  • Instruction includes geoboards to partition rectangles and circles into thirds.
  • Instruction includes graph paper to divide shapes into equal parts when given part of a whole by counting the units inside the shape. 
    • For example, the shape is a total of 30 units and one equal part is given. Students partition the shape into 3 equal parts using the knowledge that one part is equal to 10 units. 
graph paper
  • Teacher provides opportunities to use fraction manipulatives to develop understanding of thirds in circles and rectangles. 
    • For example, teacher provides pictures of circles and rectangles (of the same size as the manipulatives) on a sheet of paper. Students then use the “thirds” manipulatives to trace the thirds into the circles and rectangles, so they develop an understanding of how to partition these shapes into thirds. 
  • Teacher provides opportunities to use a pre-partitioned shape on graph paper to count units and determine if the different sized parts are equal. 
    • For example, the shape is partitioned into two parts. Students may count to determine if they are equal parts.

pre-partitioned shape on graph paper

 

Instructional Tasks

Instructional Task 1 (MTR.2.1) 

Provide students with paper copies of circles and rectangles. 
  • Part A. Cut or fold the figures to determine how one can create two, three or four equal- sized parts. 
  • Part B. Use mathematical language to describe the parts created in Part A.

 

Instructional Items

Instructional Item 1 

Is Shape A or Shape B partitioned into four fourths? Explain your thinking.

Shape A and Shape 2

 

Instructional Item 2 

Below is one-half of a whole. Draw two halves to make a whole. Encourage students to provide two different ways to make a whole. 

rectangle

 

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.


Related Courses

Course Number1111 Course Title222
5012040: Mathematics - Grade Two (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7712030: Access Mathematics Grade 2 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012005: Foundational Skills in Mathematics K-2 (Specifically in versions: 2019 - 2022, 2022 and beyond (current))


Related Access Points

Access Point Number Access Point Title
MA.2.FR.1.AP.1 Partition rectangles into two or four equal-sized parts in two different ways showing that equal-sized parts of the same whole may have different shapes.


Related Resources

Formative Assessments

Name Description
How Many Fourths Are in a Whole?

Students partition a rectangle into four equal parts and consider what fraction represents the whole.

Halves, Thirds, and Fourths

Students partition three different circles into two, three, and four equal parts and consider what fraction each part represents.

Image/Photograph

Name Description
Clipart ETC Fractions

Illustrations that can be used for teaching and demonstrating fractions. Fractional representations are modeled in wedges of circles ("pieces of pie") and parts of polygons. There are also clipart images of numerical fractions, both proper and improper, from halves to twelfths. Fraction charts and fraction strips found in this collection can be used as manipulatives and are ready to print for classroom use.

Lesson Plans

Name Description
Partition the Flag

In this Math and Social Studies Civics lesson plan, students will use their mathematical knowledge of fractions as equal groups, and knowledge of wholes, and fourths. Additionally, students will use two interrelated symbols representing Florida, to design a new Florida State Flag into four equal parts. Students will discuss and reason why Marjory Stoneman Douglas and the Florida Everglades were chosen as symbols of Florida, and brainstorm other possible symbols that could be used based on their personal experiences. As students design their flag, they will determine the best way to partition the rectangular shape into fourths, so that the four areas are equal-sized parts.

Equal Shares: I Care

Students will understand the concept of halves, thirds and fourths through the exploration of circles, squares and rectangles. Students will recognize that a half of a circle may not look like a half of a square or a rectangle. Also, students will demonstrate that halves, thirds and fourths of different sizes of circles, squares and rectangles will not look the same.

Who gets the bigger share?

Use this interactive lesson to help your students learn about fractions by partitioning circles and rectangles into two, three, or equal-sized parts and by using a real life scenario.

Thirds

In this lesson, students will gain experience partitioning rectangles and circles into equal shares of halves, thirds, and fourths.

Original Student Tutorials

Name Description
Partitioning Cakes: Thirds

It's time for cake! Learn to partition cakes into thirds in this interactive student tutorial.

Partitioning Pizzas: Halves

Learn to partition circular and rectangular pizzas into halves in this interactive tutorial.

Partitioning Circular Pies: Fourths

It's time for pie! Learn to partition circular pies into fourths in this interactive student tutorial. 

Partitioning Rectangular Pies: Fourths

It's Thanksgiving and time for pie! Learn to partition rectangular pies into fourths in this interactive student tutorial.

Chocolate Partitioning!

Learn to partition a rectangular chocolate bar into equally sized pieces by making rows and columns in this interactive tutorial. 

 

Note: This tutorial extends beyond partitioning a rectangle into 4 equal sized shares and explores partitioning into higher numbers.

Perspectives Video: Teaching Ideas

Name Description
Using Manipulatives to Add Fractions

Unlock an effective teaching strategy for teaching adding fractions in this Teacher Perspectives video for educators.

Making Connections Between Partitioning Circles and Circle Graphs

Unlock an effective teaching strategy for connecting partitioning circles and circle graphs in this Teacher Perspectives video for educators.

Decomposing Fractions in Multiple Ways

Unlock an effective teaching strategy for decomposing fractions in multiple ways in this Teacher Perspectives video for educators.

Problem-Solving Tasks

Name Description
Which Pictures Represent One Half?

The purpose of this task is for students to see different ways of partitioning a figure into two or more equal shares, by which we mean decomposing the figure into "pieces" with equal area.

Representing Half of a Rectangle

This task is for assessment purposes, providing a context for indentifying different ways of representing half of an object, a rectangle in this case. The task may also be used for instructional purposes but if so the teacher may wish to introduce some other ways of showing one half of the rectangle, such as dividing along a diagonal (and shading in one piece) or dividing it into four equal pieces, shading in two pieces that only touch at a corner.

Virtual Manipulative

Name Description
Build a Fraction


This virtual manipulative will help the students to build fractions from shapes and numbers to earn stars in this fraction lab. To challenge the children there are multiple levels, where they can earn lots of stars.
Some of the sample learning goals can be:

  • Build equivalent fractions using numbers and pictures.
  • Compare fractions using numbers and patterns
  • Recognize equivalent simplified and unsimplified fractions

Student Resources

Original Student Tutorials

Name Description
Partitioning Cakes: Thirds:

It's time for cake! Learn to partition cakes into thirds in this interactive student tutorial.

Partitioning Pizzas: Halves:

Learn to partition circular and rectangular pizzas into halves in this interactive tutorial.

Partitioning Circular Pies: Fourths:

It's time for pie! Learn to partition circular pies into fourths in this interactive student tutorial. 

Partitioning Rectangular Pies: Fourths:

It's Thanksgiving and time for pie! Learn to partition rectangular pies into fourths in this interactive student tutorial.

Chocolate Partitioning!:

Learn to partition a rectangular chocolate bar into equally sized pieces by making rows and columns in this interactive tutorial. 

 

Note: This tutorial extends beyond partitioning a rectangle into 4 equal sized shares and explores partitioning into higher numbers.

Problem-Solving Tasks

Name Description
Which Pictures Represent One Half?:

The purpose of this task is for students to see different ways of partitioning a figure into two or more equal shares, by which we mean decomposing the figure into "pieces" with equal area.

Representing Half of a Rectangle:

This task is for assessment purposes, providing a context for indentifying different ways of representing half of an object, a rectangle in this case. The task may also be used for instructional purposes but if so the teacher may wish to introduce some other ways of showing one half of the rectangle, such as dividing along a diagonal (and shading in one piece) or dividing it into four equal pieces, shading in two pieces that only touch at a corner.

Virtual Manipulative

Name Description
Build a Fraction:


This virtual manipulative will help the students to build fractions from shapes and numbers to earn stars in this fraction lab. To challenge the children there are multiple levels, where they can earn lots of stars.
Some of the sample learning goals can be:

  • Build equivalent fractions using numbers and pictures.
  • Compare fractions using numbers and patterns
  • Recognize equivalent simplified and unsimplified fractions


Parent Resources

Image/Photograph

Name Description
Clipart ETC Fractions:

Illustrations that can be used for teaching and demonstrating fractions. Fractional representations are modeled in wedges of circles ("pieces of pie") and parts of polygons. There are also clipart images of numerical fractions, both proper and improper, from halves to twelfths. Fraction charts and fraction strips found in this collection can be used as manipulatives and are ready to print for classroom use.

Problem-Solving Tasks

Name Description
Which Pictures Represent One Half?:

The purpose of this task is for students to see different ways of partitioning a figure into two or more equal shares, by which we mean decomposing the figure into "pieces" with equal area.

Representing Half of a Rectangle:

This task is for assessment purposes, providing a context for indentifying different ways of representing half of an object, a rectangle in this case. The task may also be used for instructional purposes but if so the teacher may wish to introduce some other ways of showing one half of the rectangle, such as dividing along a diagonal (and shading in one piece) or dividing it into four equal pieces, shading in two pieces that only touch at a corner.

Virtual Manipulative

Name Description
Build a Fraction:


This virtual manipulative will help the students to build fractions from shapes and numbers to earn stars in this fraction lab. To challenge the children there are multiple levels, where they can earn lots of stars.
Some of the sample learning goals can be:

  • Build equivalent fractions using numbers and pictures.
  • Compare fractions using numbers and patterns
  • Recognize equivalent simplified and unsimplified fractions


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