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Mathematics - Elementary Curriculum Mathematics Grade 5
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Convert like measurement units within a given measurement system (Standard 5.MD.1). Represent and interpret data (Standard 5.MD.2). Understand concepts of geometric measurement and volume, as well as how multiplication and addition relate to volume (Standard 5.MD.3-5).
  • An Introduction To Volume
    This lesson plan is designed so that students will count volume in cubic units, estimate volume, and use multiplication to find volume.
  • 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.
  • Breaking Apart Composite Solids
    The purpose of this task is to help students see different ways of breaking a solid into right rectangular prisms and to relate volume to the operations of multiplication and division.
  • 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.
  • 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.
  • 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.
  • Geometry and Classification of 2D Figures: Bianca Busts a Move
    After breaking a friend's table while dancing on it, Bianca must use her knowledge of measurement and geometry to get a piece of wood to fix it. In the classroom activity students create tabletop designs in order to use their knowledge of perimeter and area. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
  • Grade 5 Math Module 1: Place Value and Decimal Fractions
    In Module 1, students understanding of the patterns in the base ten system are extended from Grade 4s work with place value of multi-digit whole numbers and decimals to hundredths to the thousandths place. In Grade 5, students deepen their knowledge through a more generalized understanding of the relationships between and among adjacent places on the place value chart, e.g., 1 tenth times any digit on the place value chart moves it one place value to the right. Toward the modules end students apply these new understandings as they reason about and perform decimal operations through the hundredths place.
  • Grade 5 Math Module 2: Multi-Digit Whole Number and Decimal Fraction Operations
    In Module 2 students apply patterns of the base ten system to mental strategies and a sequential study of multiplication via area diagrams and the distributive property leading to fluency with the standard algorithm. Students move from whole numbers to multiplication with decimals, again using place value as a guide to reason and make estimations about products. Multiplication is explored as a method for expressing equivalent measures in both whole number and decimal forms. A similar sequence for division begins concretely with number disks as an introduction to division with multi-digit divisors and leads student to divide multi-digit whole number and decimal dividends by two-digit divisors using a vertical written method. In addition, students evaluate and write expressions, recording their calculations using the associative property and parentheses. Students apply the work of the module to solve multi-step word problems using multi-digit multiplication and division with unknowns representing either the group size or number of groups. An emphasis on the reasonableness of both products and quotients, interpretation of remainders and reasoning about the placement of decimals draws on skills learned throughout the module, including refining knowledge of place value, rounding, and estimation.
  • 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.
  • Grade 5 Unit 6: Volume and Measurement (Georgia Standards)
    In this unit students will change units to related units within the same measurement system by multiplying or dividing using conversion factors, use line plots to display a data set of measurements that includes fractions, use operations to solve problems based on data displayed in a line plot and recognize volume as an attribute of three-dimensional space.
  • 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)
  • IXL Game: Measurement: Convert customary units involving fractions
    This game will help fifth graders understand how to convert customary units involving fractions. This is just one of many online games that supports the Utah Math core. Note: The IXL site requires subscription for unlimited use.
  • Living Wages in CA: Ratio and Rate in the Real World
    The use of infographics helps us understand the costs of basic living expenses. The classroom activity has students look at real-life examples and data to calculate whether the minimum wage in their state can be a living wage. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
  • Measurement and Data (5.MD) - 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 - Measurement and Data (5.MD)
  • 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.
  • 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.
  • Standard Measures and Conversions within a System: Solve the Measurement Problem!
    In this video a group of friends must follow a recipe to cure a friend. They must not only find standard measures to use but also make the dosage stronger. Students then use measuring tools to create a classroom conversion chart. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
  • Standard Measures and Conversions: Liquid Volume, Milliliters and Liters
    These videos help students learn about measuring liquid volume and the units, milliliters and liters, used in the calculation. Students then demonstrate this understanding by creating a classroom conversion chart. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
  • Surface Area and Volume
    An online activity is the focus of this lesson plan to help students understand the concepts of surface area and volume.
  • Understanding Concepts of Volume and Measurement: Bianca's Babysitting Blues
    Bianca the babysitter has a dilemma, she has two differently shaped bottles to feed the twins. How can she determine the volume of them so that she can give the babies equal amounts of formula? 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.

UEN logo - 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.