Math - Fifth Grade

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5th Grade
Instructional Tasks

Stand alone tasks are organized to support learning of content standards. These tasks can be used as initial instruction or to support students who are struggling with a particular topic.

 

Strand: MATHEMATICAL PRACTICES (5.MP)
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Strand: OPERATIONS AND ALGEBRAIC THINKING (5.OA)
Write and interpret numerical expressions (Standards 5.OA.1–2)
  • Bowling for Numbers
    The purpose of this game is to help students think flexibly about numbers and operations and to record multiple operations using proper notation.
  • Comparing Products
    The purpose of this task is to generate a classroom discussion that helps students synthesize what they have learned about multiplication in previous grades.
  • Seeing is Believing
    The purpose of this task is to help students see that 4×(9+2) is four times as big as (9+2).
  • Using Operations and Parentheses
    The purpose of this task is to give students a chance to work creatively with three of the four fundamental arithmetic operations (addition, subtraction, and multiplication). It is well suited for helping students develop fluency with addition, subtraction, and multiplication of single digit numbers.
  • Video Game Scores
    This task asks students to exercise two complementary skills, writing an expression in part and interpreting a given expression.
  • Watch Out for Parentheses 1
    This problem asks the student to evaluate six numerical expressions that contain the same integers and operations yet have differing results due to placement of parentheses. It helps students see the purpose of using parentheses.
  • Words to Expressions 1
    This problem allows student to see words that can describe the expression from part (c) of "5.OA Watch out for Parentheses." Additionally , the words (add, sum) and (product, multiply) are all strategically used so that the student can see that these words have related meanings.
Analyze patterns and relationships (Standard 5.OA.3)
  • Sidewalk Patterns
    This purpose of this task is to help students articulate mathematical descriptions of number patterns.
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Strand: NUMBER AND OPERATIONS IN BASE TEN (5.NBT)
Understand the place value system (Standards 5.NBT.1–4)
  • Are these equivalent to 9.52?
    The purpose of this task is to help students develop the understanding that a single base-ten number can be represented in many different ways.
  • Comparing Decimals on the Number Line
    This task involves using number lines to compare decimal numbers. The numbers selected in this task are purposefully chosen to target student misconceptions.
  • Drawing Pictures to Illustrate Decimal Comparisons
    The purpose of this task is for students to compare decimal numbers using pictures or diagrams. Using such visual representations helps develop a deep understanding of the base-ten system and underscores that the relative place value of the digits can be more important than the value of the digits as numbers between 0 and 9.
  • Kipton's Scale
    The task allows students to explore both the structure of our place value system and how we use that to efficiently multiply and divide powers of 10.
  • Marta's Multiplication Error
    This task highlights a common misconception among students deriving the rules for multiplying a number by a power of 10. It could be used to ground a classroom discussion during the first day of multiplying decimals by powers of 10 or would also be appropriate for a formative assessment to check for student understanding of this pivotal transition from whole number reasoning to decimal reasoning.
  • Millions and Billions of People
    The purpose of this task is to help students understand the multiplicative relationship between commonly used large numbers (millions and billions) by using their understanding of place value.
  • Multiplying Decimals by 10
    The purpose of this task is to help students understand and explain why multiplying a decimal number by 10 shifts all the digits one place to the left.
  • Placing Thousandths on the Number Line
    Though this task primarily deals with comparing decimal numbers on a number line, it also requires students to draw upon what they know about the base ten system.
  • Rounding to Tenths and Hundredths
    The purpose of this task is for students to use the position of a number on the number line to round the number without knowing its exact value. Though this task deals most directly with rounding, it also requires students to understand or figure out that one tenth of 0.1 is 0.01.
  • Tenths and Hundredths
    The purpose of this task is for students to explore the relationship between tenths and hundredths (as well as the relationship between tens and hundreds).
  • Which number is it?
    The purpose of this task is to help students understand the fact that the value of a digit in one place is ten times the value of the same digit in the place to the right.
Perform operations with multidigit whole numbers and with decimals to hundredths (Standards 5.NBT.5–7)
  • Determining Surface Area with Unit Blocks, Rulers, and Nets
    In this video students are shown how to calculate the surface area of a prism. The classroom activity in the lesson requires that students apply this knowledge and measure the surface areas of real 3-Dl objects. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
  • Elmer's Multiplication Error
    This task has students explore a very common multiplication error that occurs when using the standard algorithm - it is easy to forget a step or misalign the addends if you aren't thinking about the value of a particular digit. This task is designed to help students catch these kinds of errors.
  • Games for Decimals
    This Teaching Channel video and lesson plan will help students understand tenths and hundredths with the game "Fill Two". (4 minutes)
  • Minutes and Days
    This task requires division of multi-digit numbers in the context of changing units. In addition, the conversion problem requires two steps since 2011 minutes needs to be converted first to hours and minutes and then to days, hours, and minutes.
  • The Value of Education
    The purpose of this task is for students to add, subtract, multiply, and divide decimal numbers in a real-world context.
  • 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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Strand: NUMBER AND OPERATIONS - FRACTIONS (5.NF)
Use equivalent fractions as a strategy to add and subtract fractions (Standards 5.NF.1–2)
  • 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.
  • 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.
  • 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.
  • Egyptian Fractions
    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.
  • 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.)
  • Jog-a-Thon
    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.
  • Making S'Mores
    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.
  • 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.
  • Salad Dressing
    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.
  • Sharing Chocolate
    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.
  • Sharing Lunches
    This task requires students to think about how a single situation involving fractions can be accurately represented using addition or multiplication.
  • 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.
Apply and extend previous understandings of multiplication and division to multiply and divide fractions (Standards 5.NF.3–7)
  • 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
    This task helps students link the concepts of multiplication and area.
  • 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.
  • 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.
  • Cornbread Fundraiser
    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."
  • Grass Seedlings
    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.
  • Making Cookies
    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.
  • 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.
  • 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.
  • 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?"
  • Salad Dressing
    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).
  • Sharing Chocolate
    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.
  • 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, 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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Strand: MEASUREMENT AND DATA (5.MD)
Convert like measurement units within a given measurement system (Standard 5.MD.1)
  • 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.
  • Minutes and Days
    This task requires division of multi-digit numbers in the context of changing units. In addition, the conversion problem requires two steps since 2011 minutes needs to be converted first to hours and minutes and then to days, hours, and minutes.
Represent and interpret data (Standard 5.MD.2)
  • 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.
Understand concepts of geometric measurement and volume, as well as how multiplication and addition relate to volume (Standard 5.MD.3-5)
  • Box of Clay
    This task provides an opportunity to compare the relative volumes of boxes in order to calculate the mass of clay required to fill them.
  • Calculating Volume: Tunnel Construction
    Engineers used volume calculations in the planning for a tunnel in Boston's Big Dig project. Students will see the process they used in this video. Students will then measure the volume of irregular objects in the classroom activity. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
  • Cari's Aquarium
    This task asks students to use the volume formula and conceptual understanding to solve real-world problems.
  • How Many Peas Fill the Classroom?
    This Teaching Channel video has students estimate and measure peas and room size to learn about volume. (6 minutes)
  • Representing Volume and Surface Area of Right Rectangular Prisms with Unit Cubes
    This video is a demonstration of calculating the volume of a right rectangular prism. It also explains the "true meaning" of volume with unit cubes. Students are then asked to create various structures with the same volume but differing surface areas. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
  • Using Volume to Understand the Associative Property of Multiplication
    The purpose of this task is for students to use the volume of a rectangular prism to understand the associative property of multiplication.
  • Volume of Right Rectangular Prisms
    This video demonstrates for students how unit cubes can be used to model the formula for calculating the volume of right rectangular prisms. The students then build prisms from unit cubes in the classroom activity. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
  • Volume of Shapes Composed of Right Rectangular Prisms
    This video shows students how to find the volume of right rectangular prisms by using unit cubes. They then apply this understanding to classroom activities. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
  • You Can Multiply Three Numbers in Any Order
    The purpose of this task is for students to use the volume of a rectangular prism to see why you can multiply three numbers in any order you want and still get the same result.
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Strand: GEOMETRY (5.G)
Graph points on the coordinate plane to solve real-world and mathematical problems in quadrant one (Standards 5.G.1–2)
  • Coordinate Plane
    Definition with Examples
  • Meerkat Coordinate Plane Task
    The purpose of this task is for students to answer questions about a problem situation by drawing and interpreting the meaning of points that are in the first quadrant of the coordinate plane.
Classify two-dimensional figures into categories based on their properties. (Standards 5.G.3–4)
  • Always, Sometimes, Never
    The purpose of this task is to have students reason about different kinds of shapes based on their defining attributes and to understand the relationship between different categories of shapes that share some defining attributes.
  • An Introduction To Quadrilaterals
    In this lesson the student is introduced to parallelograms, rectangles, and trapezoids and practices creating various types of quadrilaterals.
  • What do these shapes have in Common?
    This task asks students to classify shapes based on their properties. The task itself is straightforward, but there are a number of opportunities to present this task in class and push the level of discussion and reasoning.
  • What is a Trapezoid? (part 2)
    The purpose of this task is for students to compare different definitions for trapezoids.
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