 Mathematics Grade 4

Strand: NUMBER AND OPERATIONS - FRACTIONS (4.NF)

Extend understanding of equivalence and ordering of fractions (Standards 4.NF.1�2). Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers (Standards 4.NF.3�4). Understand decimal notation to the hundredths and compare decimal fractions with denominators of 10 and 100 (Standards 4.NF.5� 7). Denominators for fourth grade are limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100.
This problem simply asks students to add the tenths and hundredths together.
• Addition of Fractions Using a Visual Model
Adding two fractions with unlike denominators is the focus of this video lesson. Students will learn how to use a visual model to work with these fractions. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Comparing Fractions Using Benchmarks Game
The goal of this task is to determine appropriate benchmarks for fractions with a focus on providing explanations that demonstrate deep conceptual understanding.
• Comparing Fractions with Lines
This lesson will help students simplify fractions, compare and order them on a number line, and estimate their value.
• Comparing Sums of Unit Fractions
The purpose of this task is to help develop students' understanding of addition of fractions; it is intended as an instructional task.
• Comparing Two Different Pizzas
Students are given the example of two whole pizzas, one large and one medium. They must determine what fraction of the two pizzas has been eaten if someone eats 2 slices of the medium pizza. They must explain their reasoning and draw a picture to illustrate their solution.
• Cynthia's Perfect Punch
The purpose of this task is for students to estimate and compute sums of mixed numbers in the context of a student making a punch recipe.
• Dimes and Pennies
This task asks: "A dime is 1/10 of a dollar and a penny is 1/100 of a dollar. What fraction of a dollar is 6 dimes and 3 pennies? Write your answer in both fraction and decimal form."
• Doubling Numerators and Denominators
The purpose of this task is to assess whether students understand the meaning of the numerator and the denominator in a fraction. This task is not appropriate for a high-stakes summative assessment, but it could be very helpful in gauging students' flexibility with the meaning of fractions.
• 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.
• Expanded Fractions and Decimals
The purpose of this task is for students to show they understand the connection between fraction and decimal notation by writing the same numbers both ways.
• Explaining Fraction Equivalence with Pictures
The purpose of this task is to provide students with an opportunity to explain fraction equivalence through visual models in a particular example.
• Extending Multiplication From Whole Numbers to Fractions
This task can be used at the beginning of a fourth grade unit on multiplication with fractions to evaluate what students know about multiplication.
• Fraction Conversion 2 (with percents)
When completing this lesson students will understand how to convert fractions, decimals, and percentages.
• Fraction Equivalence
Students are given this task: "Explain why 6/10=60.100. Draw a picture to illustrate your explanation."
• Fraction King
This is a lesson plan to help students compare two fractions and understand the addition and subtraction of fractions.
• Fractions and Rectangles
The primary goal of this task is for students to use pictures to explain the equivalence between 3/12 and 1/4.
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 4 Mathematics Module 5: Fraction Equivalence, Ordering, and Operations
In this 40-day module, students build on their Grade 3 work with unit fractions as they explore fraction equivalence and extend this understanding to mixed numbers. This leads to the comparison of fractions and mixed numbers and the representation of both in a variety of models. Benchmark fractions play an important part in students ability to generalize and reason about relative fraction and mixed number sizes. Students then have the opportunity to apply what they know to be true for whole number operations to the new concepts of fraction and mixed number operations.
• Grade 4 Mathematics Module 6: Decimal Fractions
This 20-day module gives students their first opportunity to explore decimal numbers via their relationship to decimal fractions, expressing a given quantity in both fraction and decimal forms. Utilizing the understanding of fractions developed throughout Module 5, students apply the same reasoning to decimal numbers, building a solid foundation for Grade 5 work with decimal operations.
• Grade 4 Unit 3: Fraction Equivalents (Georgia Standards)
In this unit students will understand representations of simple equivalent fractions and compare fractions with different numerators and different denominators.
• Grade 4 Unit 4: Operations with Fractions (Georgia Standards)
In this unit students will identify visual and written representations of fractions, understand representations of simple equivalent fractions, understand the concept of mixed numbers with common denominators to 12, add and subtract fractions with common denominators, add and subtract mixed numbers with common denominators and convert mixed numbers to improper fractions and improper fractions to mixed fractions.
• Grade 4 Unit 5: Fractions and Decimals (Georgia Standards)
In this unit, students will express fractions with denominators of 10 and 100 as decimals, understand the relationship between decimals and the base ten system, understand decimal notation for fractions, use fractions with denominators of 10 and 100 interchangeably with decimals and express a fraction with a denominator 10 as an equivalent fraction with a denominator 100.
• Histograms and Bar Graphs
This lesson will introduce students to histograms and bar graphs and help them understand the difference between them.
• How Many Tenths and Hundredths?
In this task students are given a list of equations such as "1 tenth + 4 hundredths = ______________ hundredths" and asked to finish the equations to make true statements.
• IXL Game: Add and Subtract Fractions
This game helps fourth graders understand how to compare two fractions with different numerators and different denominators. This is just one of many online games that supports the Utah Math core. Note: The IXL site requires subscription for unlimited use.
• Listing fractions in increasing size
This activity asks students to order a group of fractions from smallest to largest and explain their reasoning.
• Making 22 Seventeenths in Different Ways
This is a straightforward task related to adding fractions with the same denominator. The main purpose is to emphasize that there are many ways to decompose a fraction as a sum of fractions, similar to decompositions of whole numbers that students should have seen in earlier grades. It is suitable for assessment or, with opportunity for classroom discussion, it could also be useful in instruction.
• Money in the piggy bank
Students are given the scenario of a student opening a piggy bank and finding an array of coins. They must determine the number of coins, what fraction is made up of dimes and the total value of the coins.
• Multiply Fractions Jeopardy
This game can be played by one or two players as they solve multiplication problems with fractions.
• Number and Operations - Fractions (4.NF) - Fourth Grade Core Guide
The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for Fourth Grade Mathematics - Number and Operations - Fractions (4.NF)
• Peaches
This task provides a context where it is appropriate for students to subtract fractions with a common denominator; it could be used for either assessment or instructional purposes.
• Plastic Building Blocks
The purpose of this task is to have students add mixed numbers with like denominators when given a problem in the context of two students building a castle out of building blocks.
• Rational Number Project
This portal leads to 28 lesson plans designed to help students understand the four operations with fractions.
• Running Laps
The purpose of this task is for students to compare two fractions that arise in a context. Because the fractions are equal, students need to be able to explain how they know that.
• Single Fraction Finder
In this lesson students will practice dividing a whole into a fraction and visualize fractions on a number line.
• Subtraction of Fractions Using a Visual Model
Students will learn how to subtract fractions with unlike denominators by using a visual model. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Sugar in Six Cans of Soda
In this task students are given the statement "For a certain brand of orange soda, each can contains 4/15 cup of sugar." They are asked to calculate how many cups of sugar are in six cans and then draw a picture representing the answer.
• Using Benchmarks to Compare Fractions
This task is intended primarily for instruction. The goal is to provide examples for comparing two fractions, 1/5 and 2/7 in this case, by finding a benchmark fraction which lies in between the two.
• Using Place Value
Each part of this task highlights a slightly different aspect of place value as it relates to decimal notation. More than simply being comfortable with decimal notation, the point is for students to be able to move fluidly between and among the different ways that a single value can be represented and to understand the relative size of the numbers in each place.
• 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)
• Writing a Mixed Number as an Equivalent Fraction
This task relates to writing a mixed number as an equivalent fraction. The purpose of this task is to help students understand and articulate the reasons for the steps in the usual algorithm for converting a mixed number into an equivalent fraction, 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 Specialists - Trish  French or Molly  Basham and see the Mathematics - Elementary website. For general questions about Utah's Core Standards contact the Director - Jennifer  Throndsen.

These materials have been produced by and for the teachers of the State of Utah. Copies of these materials may be freely reproduced for teacher and classroom use. When distributing these materials, credit should be given to Utah State Board of Education. These materials may not be published, in whole or part, or in any other format, without the written permission of the Utah State Board of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah 84114-4200.