 Mathematics Grade 3

Strand: NUMBER AND OPERATIONS - FRACTIONS (3.NF)

Develop understanding of fractions as numbers. Denominators are limited to 2, 3, 4, 6, and 8 in third grade.
• Closest to 1/2
In this task students are given a number line and a choice of fractions. They must identify which of the choices is closest to 1/2.
• Comparing Fractions
The purpose of this task is for students to compare fractions using common numerators and common denominators and to recognize equivalent fractions. Students need to represent their answers with both symbols and pictures, so that the visual representation can help students make meaning of the more abstract symbolic representations.
• Comparing Fractions Game
The goal of this task is to compare fractions with a focus on providing explanations that demonstrate deep conceptual understanding.
• Comparing Fractions with a Different Whole
This task is meant to address a common error that students make, namely, that they represent fractions with different wholes when they need to compare them.
• Comparing Fractions with Lines
This lesson will help students simplify fractions, compare and order them on a number line, and estimate their value.
• Comparing Fractions with the Same Denominator, Assessment Variation
This task is part of a set of three assessment tasks for 3.NF.3d. This part of the standard is about comparing two fractions with the same numerator or the same denominator by reasoning about their size, and understanding that such comparisons are valid only when the fractions refer to the same whole.
• Comparing Fractions with the Same Numerators, Assessment Variation
This task is part of a set of three assessment tasks for 3.NF.3d. This part of the standard is about comparing two fractions with the same numerator or the same denominator by reasoning about their size, and understanding that such comparisons are valid only when the fractions refer to the same whole.
• Equivalent Fractions Finder
Students doing this lesson will visually experiment with the relationship between the value of fractions and areas within a square or a circle. In doing so they will practice simplifying fractions and compare fractions.
• Equivalent Fractions Pointer
This lesson will help students understand how to simplify and compare fractions as well as place them in order on a number line.
• Find 1
The purpose of this task is to assess whether students understand fractions as being built from unit fractions and whether they can accurately locate fractions on the number line.
• Find 1 Starting from 5/3, Assessment Variation
This is the third of three summative assessment tasks for 3.NF.2 that progress in difficulty. Each requires that students "understand a fraction as a number on the number line" and "represent fractions on a number line diagram."
• Find 1/4 Starting from 1, Assessment Version
This is the first of three summative assessment tasks for 3.NF.2 that progress in difficulty. Each requires that students "understand a fraction as a number on the number line" and "represent fractions on a number line diagram."
• Find 7/4 starting from 1, Assessment Variation
This is the second of three summative assessment tasks for 3.NF.2 that progress in difficulty. Each requires that students "understand a fraction as a number on the number line" and "represent fractions on a number line diagram."
• Finding 2/3
This simple-looking problem reveals much about how well students understand unit fractions as well as representing fractions on a number line.
• Fraction Comparisons With Pictures, Assessment Variation
This task is part of a set of three assessment tasks for 3.NF.3d. This part of the standard is about comparing two fractions with the same numerator or the same denominator by reasoning about their size, and understanding that such comparisons are valid only when the fractions refer to the same whole.
• Grade 3 Math Module 5: Fractions as Numbers on the Number Line (EngageNY)
In this 35-day Grade 3 module, students extend and deepen second grade practice with "equal shares" to understanding fractions as equal partitions of a whole. Their knowledge becomes more formal as they work with area models and the number line.
In order to assist educators with the implementation of the Common Core, the New York State Education Department provides curricular modules in Pre-K-Grade 12 English Language Arts and Mathematics that schools and districts can adopt or adapt for local purposes.
• Grade 3 Unit 5: Representing and Comparing Fractions (Georgia Standards)
In this unit, students will develop an understanding of fractions, beginning with unit fractions. View fractions in general as being built out of unit fractions, and they use fractions along with visual fraction models to represent parts of a whole. Understand that the size of a fractional part is relative to the size of the whole. For example, 1/2 of the paint in a small bucket could be less paint than 1/3 of the paint in a larger bucket, but 1/3 of a ribbon is longer than 1/5 of the same ribbon because when the ribbon is divided into 3 equal parts, the parts are longer than when the ribbon is divided into 5 equal parts. Students are able to use fractions to represent numbers equal to, less than, and greater than one.
• Halves, thirds, and sixths
The purpose of this task is for students to use their understanding of area as the number of square units that covers a region, to recognize different ways of representing fractions with area, and to understand why fractions are equivalent in special cases.
• IXL Game: Compare Fractions
This game helps the third grader compare two fractions with the same numerator or the same denominator by reasoning about their size. This is just one of many online games that supports the Utah Math core. Note: The IXL site requires subscription for unlimited use.
• Jon and Charlie's Run
The purpose of this task is to present students with a context where they need to explain why two simple fractions are equivalent and is most appropriate for instruction.
• Locating Fractions Greater than One on the Number Line
Given a number line and a list of fractions, students must mark and label each fraction on the line.
• Locating Fractions Less than One on the Number Line
In every part of this task, students must treat the interval from 0 to 1 as a whole, partition the whole into the appropriate number of equal sized parts, and then locate the fraction(s) on a number line.
• Naming the Whole for a Fraction
The goal of this task is to show that when the whole is not specified, which fraction is being represented is left ambiguous.
• Ordering Fractions
The purpose of this task is to extend students' understanding of fraction comparison and is intended for an instructional setting.
• Single Fraction Finder
In this lesson students will practice dividing a whole into a fraction and visualize fractions on a number line.
• Single Fraction Pointer
This activity was designed to help students better understand fractions by practicing dividing a whole into a fraction and visualizing fractions on a number line.
• Snow Day
The purpose of this task is for students to investigate a claim about a comparison of two fractions in a context. This particular task helps students to construct viable arguments and critique the reasoning of others. Students are asked to critique the reasoning of Alec's claim that his school day was shorter than his brother's in the scenario given.
• What Fraction of this Shape is Red?
This Teaching Channel video shows how students can explore part and whole by creating pattern block designs. (4 minutes)
• Which is Closer to 1?
In this problem students are given 2 fractions and asked to determine which of them is closest to 1. http://www.uen.org - in partnership with Utah State Board of Education (USBE) and Utah System of Higher Education (USHE).  Send questions or comments to USBE Specialist - Shannon Olson and see the Mathematics - Elementary website. For general questions about Utah's Core Standards contact the Director - Jennifer Throndsen .

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