Trading Up to One

Summary

Students will use various coin denominations to explore the concept of fractions.

Objectives

Students will demonstrate an understanding of the fractions 1/2 (50 cents), 1/4 (25 cents), 10ths (10 cents) and 20ths (5 cents) by using fraction circle pieces to create whole units (1 dollar).

Subject Area

  • Math

Grades

  • 3rd
  • 4th
  • 5th

Class Time

  • Total Time: 0-45 minutes

Materials

  • Fraction circles:  whole circle, half, quarters, tenths and twentieths
  • Coin pictures (half dollar, quarter, dime, and nickel)
  • Fraction and coin dice (or spinner)

Lesson Steps

  1. Divide the students into pairs. Give each student a complete set of fraction circles (whole, half, quarters, tenths, twentieths). The object of the activity is to see who can create a whole unit (or $1.00) first.
  2. Have the students place their whole circle in front of them and take turns rolling the fraction or money dice or spinning the spinner. They then place the corresponding fraction piece onto their whole piece if they can. As they go, the players should trade down their fraction parts (2 dimes and a nickel for a quarter, 2 quarters for a half dollar, and so on).
  3. Let the play continue until someone wins by creating a whole unit or exactly $1.00.

Assess

Use observation to see which student pairs understand the fraction concepts, and which pairs are having difficulty. After everyone is comfortable with the rules and the fractions, the students should be able to finish a whole unit (1 dollar).

Common Core Standards

Discipline: Math
Domain: 2.OA Operations and Algebraic Thinking
Grade(s): Grade 2
Cluster: Add and subtract within 20
Standards:

  • 2.OA.2. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, eg, by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Discipline: Math
Domain: 3.NF Number and Operations: Fractions
Grade(s): Grade 2
Cluster: Develop understanding of fractions as numbers
Standards:

  • 3.NF.1. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
  • 3.NF.2. Understand a fraction as a number on the number line; represent fractions on a number line diagram.
    • Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.
    • Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.
  • 3.NF.3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
    • Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
    • Recognize and generate simple equivalent fractions, eg, 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, eg, by using a visual fraction model
    • Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.
    • Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, eg, by using a visual fraction model

National Standards

Discipline: Mathematics
Domain: 3-5 Number and Operations
Cluster: Compute fluently and make reasonable estimates.
Grade(s): Grades 3–5
Standards:

In grades 3–5 all students should

  • develop fluency with basic number combinations for multiplication and division and use these combinations to mentally compute related problems, such as 30 × 50;
  • develop fluency in adding, subtracting, multiplying, and dividing whole numbers;
  • develop and use strategies to estimate the results of whole-number computations and to judge the reasonableness of such results;
  • develop and use strategies to estimate computations involving fractions and decimals in situations relevant to students' experience;
  • use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals; and
  • select appropriate methods and tools for computing with whole numbers from among mental computation, estimation, calculators, and paper and pencil according to the context and nature of the computation and use the selected method or tools.

Discipline: Mathematics
Domain: 3-5 Number and Operations
Cluster: Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
Grade(s): Grades 3–5
Standards:

In grades 3–5 all students should

  • understand the place-value structure of the base-ten number system and be able to represent and compare whole numbers and decimals;
  • recognize equivalent representations for the same number and generate them by decomposing and composing numbers;
  • develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers;
  • use models, benchmarks, and equivalent forms to judge the size of fractions;
  • recognize and generate equivalent forms of commonly used fractions, decimals, and percents;
  • explore numbers less than 0 by extending the number line and through familiar applications; and
  • describe classes of numbers according to characteristics such as the nature of their factors.

Discipline: Mathematics
Domain: All Problem Solving
Cluster: Instructional programs from kindergarten through grade 12 should enable all students to
Grade(s): Grades 3–5
Standards:

  • Build new mathematical knowledge through problem solving
  • Solve problems that arise in mathematics and in other contexts
  • Apply and adapt a variety of appropriate strategies to solve problems
  • Monitor and reflect on the process of mathematical problem solving

Discipline: Mathematics
Domain: All Communication
Cluster: Instructional programs from kindergarten through grade 12 should enable all students to
Grade(s): Grades 3–5
Standards:

  • organize and consolidate their mathematical thinking through communication 
  • communicate their mathematical thinking coherently and clearly to peers, teachers, and others;
  • analyze and evaluate the mathematical thinking and strategies of others; and
  • use the language of mathematics to express mathematical ideas precisely.