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A Decimal Counting and Adding Methods

Notes

Terminology: A decimal count in the following lessons means a whole number given in decimal form. A decimal fraction in this section means a mixed number in which the fraction part consists of tenths, hundredths and so on. Both decimal counts and decimal fractions provide examples of decimals.

Lessons 1 to 8:

The webvideos in each are usually two to several minutes long. Please read the words in each page before starting the video, or while waiting for it load, or while watching the video. Each video can be played full screen.

• Lesson 1 - Counting Theory. Why do we take 1 + 1 = 2? How is the addition table justified? Lesson 1 explains why 3 +5 = 8. It is convention made in recognition of a pattern met in counting objects or counting on fingers. This convention is founding practice for counting and arithmetic with counts. This founding convention or practices yields the addition table for single digit decimal numbers 1 to 9 and beyond in elementary school, and it also provides a simple to the question why is 1 + 1 = 2?
  
• Lesson 2 - A Decimal Counting Principle/Practice - the basis for decimal addition methods. Lesson 2 explains how the number of ones, ten, hundreds and so on in decimal-based count of number of objects should not depend on the order in which the objects are counted. The acceptance of this assumption is another founding practice for counting and arithmetic with counts using decimals. This counting practice or principle is the basis for addition first with out carries and then with carries. Exercises involving additions without carries are introduced here.
  
• Lesson 3 - How to Add with Decimals when carries or conversion are not needed. Lesson 3 continues with examples of how counting in groups of ones, tens, hundreds and so on leads to addition methods or practices without carries/conversions. A few more exercises related to addition without carries appear here.
  
• Lessons 4 & 5 - How to Add with Carries/Conversions. Lessons 4 & 5 give more and more examples of place or column methods for addition of decimal counts - those without Examples range from cases with no conversions (no carries) to multiple conversions (er carries). All exercises but one (an oversight) involve no decimal points.
  
• Lesson 6. Addition of Amounts, Measures and Quantities involving mixed units. Lesson 6 gives several examples of addition of mixed unit of measures for money, length, time, working hours, and angles. Column methods for addition of decimals are extended here to arithmetic with mixed units. Exercises are included. Teachers might extend these exercises to includes days (work days) that are 8 hours long, and weeks (work weeks) that are 40 hours long. The numbers 8 and 40 represent economic culture in some work places, not all. Column calculations involving regular and overtime hours could also be included.
  
• Lessons 7 - How to Add Decimal Fractions with decimal points. Lessons 7 give more and more examples of place or column methods for addition of decimals representing whole numbers (decimal counts), or mixed numbers (decimal fractions) involving tenths and hundredths. Examples range from cases with no conversions (no carries) to multiple conversions (er carries).
  
• Lesson 8 - What addition arithmetic teachers, parents and students should expect and demand from themselves or others. The video in this lesson speaks to teachers, but in retrospect it should also address tutors, parents and students as well. It outlines the decimal addition practices that students should master in elementary school and not forget later.

Arithmetic - Ages 10+
1. Deciml Place Value - fun
2. Decimals for Tutors
3. Prime Factors - quickly
4. Fractions + Ratios
5. Arith with units - science