Word (.docx)
Acrobat (.pdf)
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.
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.
- 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 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.
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.
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.
Related Courses
Related Access Points
Related Resources
Formative Assessments
Image/Photograph
Lesson Plans
Original Student Tutorials
Perspectives Video: Teaching Ideas
Problem-Solving Tasks
Virtual Manipulative
MFAS Formative Assessments
Students partition three different circles into two, three, and four equal parts and consider what fraction each part represents.
Students partition a rectangle into four equal parts and consider what fraction represents the whole.
Original Student Tutorials Mathematics - Grades K-5
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.
It's time for cake! Learn to partition cakes into thirds in this interactive student tutorial.
It's time for pie! Learn to partition circular pies into fourths in this interactive student tutorial.
Learn to partition circular and rectangular pizzas into halves in this interactive tutorial.
It's Thanksgiving and time for pie! Learn to partition rectangular pies into fourths in this interactive student tutorial.
Student Resources
Original Student Tutorials
It's time for cake! Learn to partition cakes into thirds in this interactive student tutorial.
Type: Original Student Tutorial
Learn to partition circular and rectangular pizzas into halves in this interactive tutorial.
Type: Original Student Tutorial
It's time for pie! Learn to partition circular pies into fourths in this interactive student tutorial.
Type: Original Student Tutorial
It's Thanksgiving and time for pie! Learn to partition rectangular pies into fourths in this interactive student tutorial.
Type: Original Student Tutorial
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.
Type: Original Student Tutorial
Problem-Solving Tasks
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.
Type: Problem-Solving Task
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.
Type: Problem-Solving Task
Virtual Manipulative
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
Type: Virtual Manipulative
Parent Resources
Image/Photograph
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
Problem-Solving Tasks
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.
Type: Problem-Solving Task
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.
Type: Problem-Solving Task
Virtual Manipulative
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
Type: Virtual Manipulative
