Strand: OPERATIONS AND ALGEBRAIC THINKING (5.OA)

Write and interpret numerical expressions (Standards 5.OA.1–2), and analyze patterns and relationships (Standard 5.OA.3).

Standard 5.OA.1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

• 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.
• 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 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.
• Order of Operations
Arithmetic operations where there are no parentheses are the focus of this video as students learn about the order of operations. Note: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Order of Operations: PEMDAS
A Flocabulary rap song instructs students on the order of operations and then they apply that knowledge to 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.
• USBE Core Guide (5OA1)
This core guide was developed by USBE and Utah educators.
• 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.
• 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.

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 - Shannon Ference and see the Mathematics - Elementary website. For general questions about Utah's Core Standards contact the Director - DIANA SUDDRETH .
Email:  diana.suddreth@schools.utah.gov

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