Strand: NUMBER AND OPERATIONS - FRACTIONS (5.NF)

Use equivalent fractions as a strategy to add and subtract fractions (Standards 5.NF.1–2). Apply and extend previous understandings of multiplication and division to multiply and divide fractions (Standards 5.NF.3–7).

Standard 5.NF.4

Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

• Area Model for Multiplication of Fractions
In this lesson and activity students will use area models of fractions to understand how to multiply them. They will also make predictions about results, reduce answers to their simplest forms, and note any patterns they observe. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Banana Pudding
The purpose of this task is to provide students with a concrete situation involving a recipe that they can model by dividing a whole number by a unit fraction.
• Calculator Trouble
In this task students are told "Luke had a calculator that will only display numbers less than or equal to 999,999,999." They are then given a list of multiplication problems and asked which of them his calculator would display and they must explain their answer.
• Chavone's Bathroom Tiles
• Comparing a Number and a Product
The purpose of this task is for students to compare a number and its product with other numbers that are greater than and less than one. As written, this task could be used in a summative assessment context, but it might be more useful in an instructional setting where students are asked to explain their answers either to a partner or in a whole class discussion.
• Connecting the Area Model to Context
This task is designed to assess students conceptual understanding of the area model (one of the visual fraction models referred to in the standard for multiplying fractions).
• Connor and Makayla Discuss Multiplication
The purpose of this task is to have students think about the meaning of multiplying a number by a fraction and use this burgeoning understanding of fraction multiplication to make sense of the commutative property of multiplication in the case of fractions.
• Converting Fractions of a Unit into a Smaller Unit
In this task each of these problems students are given a set of a specified size and a specified number of subsets into which it is to be divided. The questions ask the student to find out the size of each of the subsets.
This task is designed to introduce students to an area representation for multiplying a fraction by a fraction.
• Cross Country Training
This task was designed to provide students with opportunities to extend their understanding of whole number multiplication to multiplication with fractions.
• Dividing a Whole Number by a Unit Fraction
In this lesson a visual model is used to help students learn how a fraction can be used to divide a whole number. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Dividing by One-Half
This task requires students to recognize both "number of groups unknown" and "group size unknown" division problems in the context of a whole number divided by a unit fraction.
• Drinking Juice
This is the question for this task: "Alisa had 1/2 a liter of juice in a bottle. She drank 3/4 of the juice that was in the bottle. How many liters of juice did she drink?"
• Folding Strips of Paper
The purpose of this task is to provide students with a concrete experience they can relate to fraction multiplication. The task also purposefully relates length and locations of points on a number line, a common trouble spot for students. This task is meant for instruction and would be a useful as part of an introductory unit on fraction multiplication.
• Fundraising
This task reads "Cai, Mark, and Jen were raising money for a school trip. Cai collected 2/12 times as much as Mark. Mark collected 2/3 as much as Jen. Who collected the most? Who collected the least? Explain."
• Grade 5 Math Module 4: Multiplication and Division of Fractions and Decimal Fractions (EngageNY)
Grade 5's Module 4 extends student understanding of fraction operations to multiplication and division of both fractions and decimal fractions. Work proceeds from interpretation of line plots which include fractional measurements to interpreting fractions as division and reasoning about finding fractions of sets through fraction by whole number multiplication. The module proceeds to fraction by fraction multiplication in both fraction and decimal forms. An understanding of multiplication as scaling and multiplication by n/n as multiplication by 1 allows students to reason about products and convert fractions to decimals and vice versa. Students are introduced to the work of division with fractions and decimal fractions. Division cases are limited to division of whole numbers by unit fractions and unit fractions by whole numbers. Decimal fraction divisors are introduced and equivalent fraction and place value thinking allow student to reason about the size of quotients, calculate quotients and sensibly place decimals in quotients. Throughout the module students are asked to reason about these important concepts by interpreting numerical expressions which include fraction and decimal operations and by persevering in solving real-world, multistep problems which include all fraction operations supported by the use of tape diagrams.
• Grade 5 Math Module 5: Addition and Multiplication with Volume and Area (EngageNY)
In this 25-day module, students work with two- and three-dimensional figures. Volume is introduced to students through concrete exploration of cubic units and culminates with the development of the volume formula for right rectangular prisms. The second half of the module turns to extending students understanding of two-dimensional figures. Students combine prior knowledge of area with newly acquired knowledge of fraction multiplication to determine the area of rectangular figures with fractional side lengths. They then engage in hands-on construction of two-dimensional shapes, developing a foundation for classifying the shapes by reasoning about their attributes. This module fills a gap between Grade 4's work with two-dimensional figures and Grade 6's work with volume and area.
• Grade 5 Unit 4: Adding, Subtracting, Multiplying, and Dividing Fractions (Georgia Standards)
Students apply their understanding of fractions and fraction models to represent the addition and subtraction of fractions with unlike denominators as equivalent calculations with like denominators.
• Grass Seedlings
This task reads "The students in Raulâ€™s class were growing grass seedlings in different conditions for a science project. He noticed that Pabloâ€™s seedlings were 1 1/2 times a tall as his own seedlings. He also saw that Celinaâ€™s seedlings were 3/4 as tall as his own. Which of the seedlings shown below must belong to which student? Explain your reasoning."
• Half of a Recipe
Here is the question for this task: "Kendra is making 1/2 of a recipe. The full recipe calls for 3 1/4 cup of flour. How many cups of flour should Kendra use?"
• How Many Servings of Oatmeal?
This task provides a context for performing division of a whole number by a unit fraction.
• How Much Pie?
The purpose of this task is to help students see the connection between aÃ·b and a/b in a particular concrete example.
• IXL Game: Mixed operations: fractions and mixed numbers
This game will help fifth graders understand how to add, subtract, multiply, and divide fractions and mixed numbers. This is just one of many online games that supports the Utah Math core. Note: The IXL site requires subscription for unlimited use.
• Make Your Own Fractions Worksheet
This Teachers Corner page allows the teacher to create worksheets to give students practice with addition, subtraction, multiplication and division of fractions.
This task provides an opportunity to discuss unit conversion and rounding in a very realistic context.
• Modeling Fraction and Mixed Number Division Using Arrays
Students will learn how to solve word problems that involve dividing fractions and mixed numbers 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.
• Models for the Multiplication and Division of Fraction
This lesson plan shows students what happens when they multiply and divide fractions by using visual area models. The students can also create their own models based on problems they solve.
• Mrs. Gray's Homework Assignment
This task is intended to assess students ability to compare the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
• Multiply Fractions Jeopardy
This game can be played by one or two players as they solve multiplication problems with fractions.
• New Park
Part 1 of this task is designed to elicit student thinking about multiplication of fractions and the commutative property. Part 2 of the task uses the area of a rectangle to help students understand why the commutative property always holds.
• Number and Operations - Fractions (5.NF) - Fifth Grade Core Guide
The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for Fifth Grade Mathematics - Number and Operations - Fractions (5.NF)
• Origami Stars
The purpose of this task is to present students with a situation in which they need to divide a whole number by a unit fraction in order to find a solution. Calculating the number of origami stars that Avery and Megan can make illustrates students' understanding of the process of dividing a whole number by a unit fraction.
• Painting a Room
The purpose of this task is to provide students with a situation in which it is natural for them to divide a unit fraction by a non-zero whole number.
• Painting a Wall
The purpose of this task is for students to find the answer to a question in context that can be represented by fraction multiplication. This task is appropriate for either instruction or assessment depending on how it is used and where students are in their understanding of fraction multiplication.
• Product of a Whole Number and a Fraction
With the help of this video students will learn how to multiply a whole number and a fraction. A classroom activity involving money asks students practice this skill. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
In this task a rule is posited "When you multiply by a number, you will always get a bigger answer." Students are asked for what numbers will the rule work? For what numbers will the rule not work? Explain and give examples.
• Running a Mile
Students are given this statement "Curt and Ian both ran a mile. Curt's time was 8/9 Ian's time." They must determine who ran faster, explain their answer and draw a picture.
• Running to School
This task asks for the solution to this problem: "The distance between Rosa's house and her school is 3/4 mile. She ran 1/3 of the way to school. How many miles did she run?"
• Sharing Lunches
This task requires students to think about how a single situation involving fractions can be accurately represented using addition or multiplication.
• Standing in Line
The purpose of this task is for students to solve a problem in context that can be solved in different ways, but in particular by dividing a whole number by a unit fraction.
• To Multiply or Not to Multiply?
In this task students are given some problems which can be solved by multiplying 1/82/5, while others need a different operation. Students are to select the ones that can be solved by multiplying these two numbers and for the remaining, tell what operation is appropriate. In all cases they must solve the problem (if possible) and include appropriate units in their answer.
• What is 23 divided by 5?
This task involves whole number division problems which do not result in a whole number quotient. It is important for students to be able to decide whether the context requires the result to be reported as a whole number with remainder or a mixed number/decimal.

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.

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