Strand: NUMBER AND OPERATIONS IN BASE TEN (5.NBT)

Understand the place value system (Standards 5.NBT.1-4). Perform operations with multidigit whole numbers and with decimals to hundredths (Standards 5.NBT.5-7).
• 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.
• Base 60: Babylonian Decimals
An Annenberg Learning Math video introduces students to the Babylonian number system in base 60. In the classroom activity they review base 10 and apply their understanding to write numbers in base 60. 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 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.
• 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.
• 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.
• 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)
• 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.
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 1: Order of Operations & Whole Numbers (Georgia Standards)
In this unit students will solve problems by representing mathematical relationships between quantities using mathematical expressions and equations. Use the four whole number operations efficiently, including the application of order of operations. Write, evaluate, and interpret mathematical expressions with and without using symbols. Apply strategies for multiplying a 2- or 3-digit number by a 2-digit number. Develop paper-and-pencil multiplication algorithms (the U.S. traditional algorithm is not an expectation) for 3- or 4-digit number multiplied by a 2- or 3-digit number.
• Grade 5 Unit 2: Adding and Subtracting with Decimals (Georgia Standards)
In this unit students will solve problems by understanding that like whole numbers, the location of a digit in a decimal number determines the value of the digit. Understand that rounding decimals should be sensible for the context of the problem. Understand that decimal numbers can be represented with models. Understand that addition and subtraction with decimals are based on the fundamental concept of adding and subtracting the numbers in like position values.
• Grade 5 Unit 3: Multiplying and Dividing with Decimals (Georgia Standards)
General methods used for computing products of whole numbers extend to products of decimals. Because the expectations for decimals are limited to thousandths and expectations for factors are limited to hundredths at this grade level, students will multiply tenths with tenths and tenths with hundredths, but they need not multiply hundredths with hundredths.
• IXL Game: Mixed Operations
This game will help fifth graders understand how to add, subtract, multiply, and divide decimals. This is just one of many online games that supports the Utah Math core. Note: The IXL site requires subscription for unlimited use.
• 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.
• 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.
• 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.
• Number and Operations in Base Ten (5.NBT) - 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 in Base Ten (5.NBT)
• 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).
• 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.
• 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.

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.