MAE3270 Module 3 - Lecture 1: Fractions and division

Chapter 1: Introduction

  • Introduction to division structures

  • Division requires equal sharing between a given number of portions

  • Example: Sharing 20 marbles equally between 4 children

  • Two interpretations of division: equal sharing and inverse of multiplication

Chapter 2: Addition And Division

  • Division can be related to repeated subtraction

  • Example: How many sets of 4 marbles can be made from a set of 20 marbles

  • Inverse operation of division is multiplication

  • Division can also be related to repeated addition

  • Example: How many sets of 4 are needed to get a set of 20

  • Division problems can be solved by repeated subtraction using a number line

  • Introduction to ratios for comparing two quantities

Chapter 3: Equal Size Parts

  • Comparison of earnings using subtraction and division

  • Scale factor used to determine how many times greater one quantity is compared to another

  • Introduction to different representations and models for division

  • Area model, discrete model, and number line

  • Caution against favoring one model over the others

Chapter 4: Write The Number

  • Introduction to representing fractions using models

  • Partitioning objects and number lines to represent fractions

  • Conversion of fractions to decimals and percentages

  • Useful interactive number line tool

Chapter 5: Write Equivalent Fractions

  • Equivalent fractions have the same value

    • Example: 1/2 = 2/4

    • Use a ruler to line up equivalent fractions

  • Visualize and understand equivalent fractions using manipulatives and diagrams

  • Move from concrete to abstract understanding

  • Select a number to multiply both the numerator and denominator to write an equivalent fraction

Chapter 6: A Whole Number

  • Select a number to multiply both the numerator and denominator to find an equivalent fraction

    • Example: 1/3 x 3/3 = 3/9

  • Convert improper fractions to mixed numerals and vice versa

  • Improper fraction: numerator > denominator

  • Mixed numeral: whole number + proper fraction

Chapter 7: A Mixed Number

  • Divide circles into equal parts to represent fractions

  • Convert improper fractions to mixed numerals

    • Example: 7/3 = 2 1/3

  • Convert mixed numerals to improper fractions

    • Example: 1 3/4 = 7/4

Chapter 8: Utilize A Number

  • Visuals and number lines can be used to understand fractions

  • Divide the numerator by the denominator to find the whole number and remainder

    • Example: 7/3 = 2 1/3

Chapter 9: Conclusion

  • The number 3 goes into the number 7 twice, making it the whole number.

  • The remaining 1 becomes the numerator.

  • The denominator remains the same.

How a mixed numeral becomes 7 4ths:

  • Using a diagram or area model:

    • Multiply the whole number (1) by the denominator (4) to get 4.

    • Add the numerator (3) to the result (4) to get 7.

  • In abstract:

    • Multiply the whole number (1) by the denominator (4) to get 4.

    • Add the numerator (3) to the result (4) to get 7.

    • The resulting 7 becomes the numerator.

    • The denominator remains the same.