MA.2.FR.1.2

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Partition rectangles into two, three or four equal-sized parts in two different ways showing that equal-sized parts of the same whole may have different shapes.

Examples

A square cake can be cut into four equal-sized rectangular pieces or into four equal-sized triangular pieces.
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

  • Rectangle

 

Vertical Alignment

Previous Benchmarks

 

Next Benchmarks

 

Purpose and Instructional Strategies

The purpose of this benchmark is to build understanding that figures can be partitioned in multiple ways, the parts can look different but they still represent an equal amount of the whole.
  • Instruction includes the use of manipulatives including geoboards, fraction circles, pattern blocks or color tiles. 
  • Instruction includes the idea of part-whole relationship if supported by a model. 
  • 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.

 

Instructional Tasks

Instructional Task 1 (MTR.2.1) 

Provide students with multiple copies of a three-unit by four-unit array. 
  • Part A. Shade the array to show how it can be partitioned into two, three and four equal- sized pieces in as many ways as possible. 
  • Part B. Discuss with a partner or in a group why the parts look different but still represent the same equal-sized part of the whole. 

 

Instructional Task 2 (MTR.4.1) 

Given the images below, discuss why these are divided into three equal parts.

 

Instructional Items

Instructional Item 1 

Four friends will share a large rectangular pizza. Show several ways they can cut the pizza to show four equal-sized pieces. 

Instructional Item 2
Select all the rectangles that are partitioned into thirds.
rectangles

 

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

Related Courses

This benchmark is part of these courses.
5012040: Grade Two Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 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 - 2024, 2024 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
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

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Formative Assessments

Different Halves:

Students consider if two different shaped halves of the same rectangle represent equal shares.

Type: Formative Assessment

Different Fourths:

Students consider if two different shaped fourths of the same rectangle represent equal shares.

Type: Formative Assessment

Image/Photograph

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.

Type: Image/Photograph

Lesson Plans

Drone Zones:

Students will explore the division of a square into equal parts in multiple ways and interpret tally marks within a table to help a city develop a plan to inspect roadways after a hurricane using drones.

This is an open-ended engineering design lesson where students will develop a model to help them solve a problem. There are no “right” answers as the lesson is focused on the process of developing a solution and the skills and reasoning behind the process. Students should be given the freedom to interpret the problem and parameters in unique ways to pursue their own lines of thinking in producing a solution.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

Perspectives Video: Teaching Idea

Exploring Fractions with Pattern Blocks:

Unlock an effective teaching strategy for using pattern blocks to explore fraction concepts in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

MFAS Formative Assessments

Different Fourths:

Students consider if two different shaped fourths of the same rectangle represent equal shares.

Different Halves:

Students consider if two different shaped halves of the same rectangle represent equal shares.

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

Image/Photograph

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.

Type: Image/Photograph