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Mathematics - Elementary Curriculum Mathematics Grade 5
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Strand: OPERATIONS AND ALGEBRAIC THINKING (5.OA)

Write and interpret numerical expressions (Standards 5.OA.12), and analyze patterns and relationships (Standard 5.OA.3).
  • 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.
  • Finding Patterns to Make Predictions
    This activity asks students to identify and contemplate mathematical patterns that we see around us. They are asked to represent them in a table and predict the pattern to the 7th, 9th, and nth terms. 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 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 6: Problem Solving with the Coordinate Plane (EngageNY)
    In this 40-day module, students develop a coordinate system for the first quadrant of the coordinate plane and use it to solve problems. Students use the familiar number line as an introduction to the idea of a coordinate, and they construct two perpendicular number lines to create a coordinate system on the plane. Students see that just as points on the line can be located by their distance from 0, the planes coordinate system can be used to locate and plot points using two coordinates. They then use the coordinate system to explore relationships between points, ordered pairs, patterns, lines and, more abstractly, the rules that generate them. This study culminates in an exploration of the coordinate plane in real world applications.
  • 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 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 7: Geometry and the Coordinate Plane (Georgia Standards)
    Students should be actively engaged by developing their own understanding. Mathematics should be represented in as many ways as possible by using graphs, tables, pictures, symbols, and words. Appropriate manipulatives and technology should be used to enhance student learning. Students should be given opportunities to revise their work based on teacher feedback, Peer feedback, and metacognition which includes self-assessment and reflection. Students need to write in mathematics class to explain their thinking, talk about how they perceive topics, and justify their work to others.
  • IXL Game: Algebra: Write equations to represent word problems
    This game will help fifth graders write equations to represent word problems. This is just one of many online games that supports the Utah Math core. Note: The IXL site requires subscription for unlimited use.
  • Operations and Algebraic Thinking (5.OA) - 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 - Operations and Algebraic Thinking (5.OA)
  • 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.
  • Patterns in Pascal's Triangle
    This lesson is designed to show students that patterns exist in the Pascal's Triangle, and to reinforce student's ability to identify patterns.
  • Petals Around the Rose
    This lesson plan involves the playing of a dice game in which students must use problem-solving skills in order to discover the non-standard pattern in the dice rolls.
  • Picturing Factors in Different Orders
    The purpose of this task is to help students picture the multiplicative structure of the number 30 in different ways.
  • 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).
  • Sidewalk Patterns
    This purpose of this task is to help students articulate mathematical descriptions of number patterns.
  • 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.
  • Why Do We Need an Order of Operations?
    The purpose of this task is to help students think about the reason for the mathematical convention known as the "order of operations." The task could be used in two ways: to present an apparently unresolvable mathematical situation that can lead to a classroom discussion about the need for an order of operations, or to help students who know already know the order of operations to pause and think more deeply about why they are necessary.
  • 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.
  • 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 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.