Mathematics Grade 5
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)
Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
Grade 5 Mathematics 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 Mathematics 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.
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.
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.
Number and Operations in Base Ten - 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)
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).
Unit 1: Order of Operations & Whole Numbers
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.
Unit 2: Adding and Subtracting with Decimals
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.
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 Specialist -
and see the Mathematics - Elementary website. For
general questions about Utah's Core Standards contact the Director
- Jennifer Throndsen .
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