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Investigating Fraction Relationships with Relationship Rods

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Investigating Fraction Relationships with Relationship Rods

Grade Levels

3rd Grade, 4th Grade, 5th Grade

Course, Subject

Related Academic Standards
CC.2.1.3.C.1 CC.2.1.3.C.1
Explore and develop an understanding of fractions as numbers.
CC.2.1.4.C.1 CC.2.1.4.C.1
Extend the understanding of fractions to show equivalence and ordering.
CC.2.1.5.B.1 CC.2.1.5.B.1
Apply place value to show an understanding of operations and rounding as they pertain to whole numbers and decimals.
CC.2.1.5.B.2 CC.2.1.5.B.2
Extend an understanding of operations with whole numbers to perform operations including decimals.
M03.A-F.1.1.1 M03.A-F.1.1.1
Demonstrate that when a whole or set is partitioned into y equal parts, the fraction 1/y represents 1 part of the whole and/or the fraction x/y represents x equal parts of the whole (limit denominators to 2, 3, 4, 6, and 8; limit numerators to whole numbers less than the denominator; and no simplification necessary).
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  • Big Ideas
    Measures can be estimated by using known referents.
    Numbers, measures, expressions, equations, and inequalities can represent mathematical situations and structures in many equivalent forms.
    Numerical quantities and calculations can be estimated by using numbers that are close to the actual values, but easier to compute.
    Patterns exhibit relationships that can be extended, described, and generalized.
    Some attributes of objects are measureable, e.g., length, mass, capacity, and can be quantified.
    The base-ten number system is a way to organize, represent, and compare numbers using groups of ten and place value.
    The same number sentence (e.g., 12 - 4 = 8) can be associated with different concrete or real world situations, AND different number sentences can be associated with the same concrete or real world situation.
    There are some mathematical relationships that are always true and these relationships are used as the rules of arithmetic and algebra and are useful for writing equivalent forms of expressions and solving equations and inequalities.
    Two- and three-dimensional objects can be described, classified, and analyzed by their attributes, and their location can be described quantitatively.
  • Concepts
    Base Ten System: Place value - base 10 system to 100,000s place
    Division: Understanding of strategies, fluency
    Equations and Inequalities: Use patterns, models, and relationships
    Estimation: Products, sizes, distance
    Fractions and Decimals: Addition and subtractions
    Fractions and decimals: Develop basic understandings
    Multiplication and division of whole numbers and the relationship between operations
    Perimeter: Units, tools, strategies to measure
    Surface Area and Volume: Units, strategies and tools to find measurements; and the development of formulas
  • Competencies
    Apply increasingly sophisticated strategies to solve multiplication and division problems that include, and go beyond, basic facts and one-digit multiplier problems, using properties of addition and multiplication. Select and apply appropriate strategies to estimate and/or solve a variety of problems, including problems involving addition and subtraction of decimals and of fractions with like denominators.
    Develop an understanding of and fluency with addition and subtraction of fractions and decimals (models, place value, properties of addition and subtraction of decimals) to solve problems in a variety of contexts, including measurement. Develop understanding of negative integers using concrete objects.
    Develop an understanding of multiplication and division of whole numbers by building on knowledge of the base ten system/operations and through the use of representations (e.g., equal-sized groups, arrays, area models, equal "jumps" on number lines, successive subtraction, partitioning, and sharing) in order to describe relationships, make estimations, and solve problems.
    Develop an understanding of the size, meaning, and uses of fractions to represent parts of a whole, parts of a set, or points/distances on a number line, and that fractions are used to represent numbers that are equal to, less than, or greater than one
    Develop fluency with and an understanding of efficient strategies for division (models, place value, properties of operations, and the relationship between multiplication and division) and use them to solve problems.
    Read, represent, interpret the representation, compare, and order fractions in various forms (e.g., area model, fraction of a set, fraction notation). Relate understandings of fractions to reading and writing of decimals and understand decimal notation as an extension of the base-ten system.

Description

Students use relationship rods to explore fraction relationships. This work with relationships lays the foundation for work with more challenging fraction concepts.  Relationship rods are wooden or plastic rods in ten different colors. They range in length from one to ten centimeters. Each length is a different color.

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Investigating Fraction Relationships with Relationship Rods

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Illuminations

 

Illuminations is a project designed by the National Council of Teachers of Mathematics (NCTM) and supported by the Verizon Foundation.  Illuminations works to serve you by increasing access to quality standards-based resources for teaching and learning mathematics, including interactive tools for students and instructional support for teachers.

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