MAE3270 Module 4 - Lecture 1: Decimal and percentages

Chapter 1: Introduction

  • Decimals and percentages in the real number system

  • Sequence of learning for decimals:

    • Year 4: Understanding place value after the decimal point (tenths and hundredths)

    • Year 5: Comparing, ordering, and representing decimals

    • Year 6: Adding, subtracting, multiplying, and dividing decimals; making connections between fractions, decimals, and percentages

  • Real numbers include whole numbers, fractions, and negative numbers

  • Real numbers can be represented on a number line

Chapter 2: Decimal place value

  • Year 4 students learn about place value after the decimal point (tenths and hundredths)

  • Decimal notation requires multiplicative thinking

  • Place value decreases by a factor of 10 for each digit moved to the right

  • Decimal point separates the whole number part from the decimal part

  • Left side of the decimal point: multiply by place value

  • Right side of the decimal point: divide by place value

Chapter 3: Consecutive Whole Numbers

  • There are an infinite number of numbers between consecutive whole numbers

  • Numbers between consecutive whole numbers can be written as fractions or decimals

  • Example: 4.6 is the same as 4 6/10

  • Fractions and decimals are interchangeable

  • Decimals can be partitioned like whole numbers

  • Example: 0.74 can be written in different ways

Chapter 4: Writing Decimals

  • There are different ways to write decimals

    • 0.7 can also be written as 0.3 and 0.44

  • Decimals can be written as fractions

    • 0.7 can be written as 7 tenths + 4 hundredths or 74 hundredths

    • 74 hundredths is the same as 74 divided by 100 or 740,000 divided by 1000

  • Using a calculator to divide the numerator by the denominator helps understand decimal conversion

  • Fractions, decimals, and percentages can be converted between each other

  • Common fraction, decimal, and percentage conversions

    • Half = 0.5 = 50%

    • Quarter = 0.25 = 25%

    • Three quarters = 0.75 = 75%

    • One tenth = 0.1 = 10%

  • Understanding how to convert between fractions, decimals, and percentages is important

  • To convert a decimal to a fraction, identify the place value of the digit after the decimal point

    • 0.7 is in the 10ths column, so the fraction will have a denominator of 10 and a numerator of 7

  • To convert a decimal to a percentage, multiply by 100

Chapter 5: Conclusion

  • Multiplying by 100 moves the decimal point 2 places to the right

  • 0.7 is the same as 70% when multiplied by 100

  • Representations for teaching decimals

    • Place value mat with hundreds, tens, and ones

    • Base 10 blocks

    • 1 whole can be partitioned into 1,000ths, 10 100s, or 10 tenths

    • 100th grid number lines

    • Tens frame

  • Representation of 0.8