MAE3270 Module 3 - Lecture 1: Fractions and division

Chapter 1: Introduction

  • The lecture focuses on fractions and division

  • Key understandings include:

    • Sequence of number development

    • Fractions as part of a whole

    • Unit fractions

    • Counting by unit fractions

Chapter 2: Consecutive Whole Numbers

  • Students learn to count by unit fractions

  • Decimal fractions and comparisons

  • Equivalent fractions and conversions

Chapter 3: The Whole Determines

  • Fractions involve dividing an object or collection into equal parts

  • Using diagrams and manipulatives to understand fractions

  • Partitioning the whole determines the fraction

  • Examples of partitioning and equal parts

  • Misconception about the size of sections based on the denominator

Chapter 4: Division And Fractions

  • Fraction terminology

    • The numerator is the top number

    • The denominator is the bottom number

    • Separated by a horizontal bar

    • Another representation for fractions is division

  • Division and fractions are interchangeable

    • Numinator and denominator can be replaced with dots to represent division

    • Encourage students to always write fractions with a horizontal line to remind them of the interchangeability

  • The denominator names the family of fractions

    • 1 third is 1/3

    • 1 fifth is 1/5

    • 1 eighth is 1/8

Chapter 5: Conclusion

  • When writing a quantity as a fraction, use whole numbers as the numerator and denominator

  • Fractions over fractions or decimals over decimals should be avoided

  • Fractions are sometimes called rational numbers

  • Numbers that can't be expressed as fractions are called irrational

  • Example of an irrational number is pi

  • Comparison between 2 thirds and 1 quarter

    • 2 thirds means dividing a whole into 3 equal parts and considering 2 of those parts

    • 1 quarter means dividing a whole into 4 equal parts and considering 1 of those parts