Mathematics Grade 5
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)
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.
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.
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.
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
This task helps students link the concepts of multiplication and area.
Commutative and Associative Equations
This lesson focuses on how to rearrange and combine parts of algebraic expressions by using the commutative and associative properties of addition. 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 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.
Comparing Heights of Buildings
The goal of this task is to compare three quantities using the notion of multiplication as scaling. Students will recognize (5.NF.B.5) that the Burj Khalifa is taller than the Eiffel tower and that the Eiffel Tower is shorter than the Willis Tower using the size of the given multiplicative scalars.
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.
Do These Add Up?
This set of questions is designed to enhance a student's understanding of when it is and is not appropriate to add fractions.
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?"
Because the Egyptians represented fractions differently than we do, this task can help students understand that there can be many ways of representing the same number. This helps prepare them for writing algebraic expressions in 6th grade.
Finding Common Denominators to Add
This task asks students to find and use two different common denominators to add two given fractions. It also ask students to draw pictures to help them to see why finding a common denominator is an important part of solving the given addition problems.
Finding Common Denominators to Subtract
Part of this task asks students to use two different denominators to subtract fractions. The purpose of this is to help students realize that any common denominator will work, not just the least common denominator. They are also asked to draw pictures to help them see why finding a common denominator is important.
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.
This lesson plan uses an online game to teach students how to perform the four basic operations on fractions.
Fractions on a Line Plot
The purpose of this task is for students to add unit fractions with unlike denominators and solve addition and subtraction problems involving fractions that have more than one possible solution.
Fractions with Borrowing
This Teaching Channel video shows how students use decomposition to subtract fractions and mixed numbers. (14 min.)
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 3: Addition and Subtraction of Fractions (EngageNY)
In Module 3, students' understanding of addition and subtraction of fractions extends from earlier work with fraction equivalence and decimals. This module marks a significant shift away from the elementary grades' centrality of base ten units to the study and use of the full set of fractional units from Grade 5 forward, especially as applied to algebra.
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 Mathematics
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 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.
This task reads "The students in Raul’s class were growing grass seedlings in different conditions for a science project. He noticed that Pablo’s seedlings were 1 1/2 times a tall as his own seedlings. He also saw that Celina’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 Marbles?
This task presents this problem: "Julius has 4 blue marbles. If one third of Julius' marbles are blue, how many marbles does Julius have? Draw a diagram and explain."
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 a÷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.
The purpose of this task is to present students with a situation where it is natural to add fraction with unlike denominators; it can be used for either assessment or instructional purposes.
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.
The purpose of this instructional task is to motivate a discussion about adding fractions and the meaning of the common denominator. The different parts of the task have students moving back and forth between the abstract representation of the fractions and the meaning of the fractions in the context.
This task could form part of a classroom activity where students are encouraged to find as many different ways as possible to make different fractions such as 1/12 and then share their methods.
Mixed Numbers with Unlike Denominators
The purpose of this task is to help students realize there are different ways to add mixed numbers and is most appropriate for use in an instructional setting.
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.
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)
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.
Reasoning about Multiplication
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?"
The purpose of this task is to have students add fractions with unlike denominators and divide a unit fraction by a whole number. This accessible real-life context provides students with an opportunity to apply their understanding of addition as joining two separate quantities.
Scaling Up and Down
This task is structured so that a teacher can diagnose the depth of a students understanding of what it means to multiply a number by a fraction, specifically in terms of scaling (as such it can be used formatively or summatively).
This task was designed to include specific features that support access for all students and align to best practice for English Language Learner (ELL) instruction.
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.
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.
To Multiply Or Not to Multiply, Variation 2
This task was written as part of a collaborative project between Illustrative Mathematics, the Smarter Balanced Digital Library, and the Teaching Channel.
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.
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