Fraction Conversion

Abstract

Students will learn how to convert between fractions and decimals using a computer applet and the concept of money.

Objectives

Upon completion of this lesson, students will:

  • practice converting fractions to decimals
  • understand the numeric value of various equivalent representations simple fractions and decimals

Standards Addressed

Grade 3

  • Numeration

    • The student demonstrates conceptual understanding of simple fractions with denominators 2, 3, 4, or 10.

Grade 4

  • Numeration

    • The student demonstrates conceptual understanding of fractions with denominators 2 through 12.

Grade 5

  • Numeration

    • The student demonstrates conceptual understanding of positive fractions with denominators 1 through 12 and 100 with proper and mixed numbers and benchmark percents (10%, 25%, 50%, 75%, 100%).

Grade 6

  • Numeration

    • The student demonstrates conceptual understanding of fractions (proper or mixed numbers), decimals, percents (whole number), or integers.
    • The student demonstrates conceptual understanding of fractions, mixed numbers, or percents.

Grade 7

  • Numeration

    • The student demonstrates conceptual understanding of rational numbers (fractions, decimals, percents, or integers).
    • The student demonstrates conceptual understanding of positive fractions, decimals, or percents.

Grade 8

  • Numeration

    • The student demonstrates conceptual understanding of real numbers.
    • The student demonstrates conceptual understanding of rational numbers (fractions, decimals, or percents including integers).

Grade 9

  • Estimation and Computation

    • The student accurately solves problems (including real-world situations).

  • Numeration

    • The student demonstrates conceptual understanding of real numbers.

Grade 10

  • Estimation and Computation

    • The student accurately solves problems (including real-world situations).

  • Numeration

    • The student demonstrates conceptual understanding of real numbers.

Grade 4

  • Number Sense

    • 1.0 Students understand the place value of whole numbers and decimals to two decimal places and how whole numbers and decimals relate to simple fractions. Students use the concepts of negative numbers

Grade 5

  • Number Sense

    • 1.0 Students compute with very large and very small numbers, positive integers, decimals, and fractions and understand the relationship between decimals, fractions, and percents. They understand the relative magnitudes of numbers

Third Grade

  • Number and Operations-Fractions

    • Develop understanding of fractions as numbers.

Fourth Grade

  • Number and Operations-Fractions

    • Extend understanding of fraction equivalence and ordering.
    • Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
    • Understand decimal notation for fractions, and compare decimal fractions.

Fifth Grade

  • Number and Operations in Base Ten

    • Perform operations with multi-digit whole numbers and with decimals to hundredths.

Grades 3-5

  • Numbers and Operations

    • Compute fluently and make reasonable estimates

3rd Grade

  • Number and Operations

    • The student will demonstrate through the mathematical processes an understanding of the representation of whole numbers and fractional parts; the addition and subtraction of whole numbers; accurate, efficient, and generalizable methods of multiplying whole numbers; and the relationships among multiplication, division, and related basic facts.

4th Grade

  • Number and Operations

    • Standard 4-2: The student will demonstrate through the mathematical processes an understanding of decimal notation as an extension of the place-value system; the relationship between fractions and decimals; the multiplication of whole numbers; and accurate, efficient, and generalizable methods of dividing whole numbers, adding decimals, and subtracting decimals.

7th Grade

  • Number and Operations

    • The student will demonstrate through the mathematical processes an understanding of the representation of rational numbers, percentages, and square roots of perfect squares; the application of ratios, rates, and proportions to solve problems; accurate, efficient, and generalizable methods for operations with integers; the multiplication and division of fractions and decimals; and the inverse relationship between squaring and finding the square roots of perfect squares.

Elementary Algebra

  • Elementary Algebra

    • Standard EA-2: The student will demonstrate through the mathematical processes an understanding of the real number system and operations involving exponents, matrices, and algebraic expressions.

5th Grade

  • Number and Operation

    • The student will develop number and operation sense needed to represent numbers and number relationships verbally, symbolically, and graphically and to compute fluently and make reasonable estimates in problem solving.

3rd Grade

  • Numbers and Operations

    • The student will develop number and operation sense needed to represent numbers and number relationships verbally, symbolically, and graphically and to compute fluently and make reasonable estimates in problem solving.

4th Grade

  • Number and Operation

    • The student will develop number and operation sense needed to represent numbers and number relationships verbally, symbolically, and graphically and to compute fluently and make reasonable estimates in problem solving.

7th Grade

  • Number and Number Sense

    • 7.1 The student will compare, order, and determine equivalent relationships between fractions, decimals, and percents, including use of scientific notation for numbers greater than 10.

4th Grade

  • Number and Number Sense

    • 4.2.c The student will relate fractions to decimals, using concrete objects.

5th Grade

  • Number and Number Sense

    • 5.2a The student will recognize and name commonly used fractions (halves, fourths, fifths, eighths, and tenths) in their equivalent decimal form and vice versa
    • 5.2b The student will order a given set of fractions and decimals from least to greatest. Fractions will include like and unlike denominators limited to 12 or less, and mixed numbers.

8th Grade

  • Computation and Estimation

    • 8.3 The student will solve practical problems involving rational numbers, percents, ratios, and proportions. Problems will be of varying complexities and will involve real-life data, such as finding a discount and discount prices and balancing a checkbook.
    • 8.3 The student will solve practical problems involving rational numbers, percents, ratios, and proportions. Problems will be of varying complexities and will involve real-life data,

6th Grade

  • Number and Number Sense

    • 6.1 The student will identify representations of a given percent and describe orally and in writing the equivalence relationships among fractions, decimals, and percents.
    • 6.4 The student will compare and order whole numbers, fractions, and decimals, using concrete materials, drawings or pictures, and mathematical symbols.

Textbooks Aligned

Grade Six

  • Bits and Pieces I

    • Investigation Four: From Fractions to Decimals
    • Investigation Five: Moving Between Fractions and Decimals

  • Bits and Pieces II

    • Investigation Three: Estimating with Fractions and Decimals

Book 2

  • Module 5 - Recreation

    • Section 4: Fractions to Decimals to Percents

Grade 5

  • Measure for Measure

    • Fraction/Decimal Equivalence

Grade 6

  • Fraction Times

    • Fraction/Percent/Decimal/Ration Relationships

  • More or Less

    • Fraction/Decimal/Percent Relationships

  • Ratios and Rates

    • Ratio/Fraction/Decimal/Percent Relationships

Student Prerequisites

  • Technological: Students must be able to:
    • perform basic mouse manipulations such as point, click and drag
    • use a browser for experimenting with the activities
  • Arithmetic: Students must be able to:
    • a basic understanding of fractions and what they represent

Teacher Preparation

Students will need:

  • access to a browser
  • pencil and paper

Key Terms

decimal

Short for the term "decimal fraction", a decimal is another way to represent fractional numbers. The decimal uses place value to express the value of a number as opposed to a fraction that uses a numerator and denominator.

fraction

A rational number of the form a/b where a is called the numerator and b is called the denominator

Lesson Outline

  1. Focus and Review

    Review prior fraction material. Lead into this lesson by:

    • explaining to students that there are other ways of representing fractional amounts besides with fractions
    • asking students if they are familiar with any other way of representing fractional amounts

  2. Objectives

    Let the students know what it is they will be doing and learning today. Say something like this:

    • Today we will be learning how to convert between fractions and decimals.

  3. Teacher Input

    • Lead a discussion on decimals.
    • Show the students how to convert from fractions to decimals by dividing the numerator by the denominator.

  4. Guided Practice

    • Open the Converter applet in a browser.
    • Work through a few simple conversions as a class, first guessing the answer before clicking on the button so that students can understand what the applet is doing.

  5. Independent Practice

  6. Closure

    • Discuss anything the students found interesting while answering the exploration questions.
    • Discuss why conversions between fractions and decimals are important in real life situations.
    • Review the steps used to convert between fractions and decimals.
    • Review any new vocabulary.

Suggested Follow-Up

This lesson can be followed up by Fraction Conversion II.