Place Value: Key to Making Sense of Numbers EDN 322

Four characteristics of our Hindu-Arabic Number System Place value – The position of the digit represents its value Base of ten – Base meaning a collection. Use of zero – A symbol for zero exists and allows us to represent symbolically the absence of something. Additive property – Numbers can be summed with respect to place value For example, the 2 in $23 names “twenty” and has a different mathematical meaning form the 2 in $32, which names “two.” Place value is an essential feature of our number system and should be developed early. In our system, 10 is the value that determines a new collection, and the system has ten digits 0-9. For example 205 shows the absence of tens in a number containing hundreds and ones. For example, 123 names the number that is the sum of 100 + 20 + 3. These properties make our number system efficient and contribute to the development of number sense. That is, once these characteristics are understood, the formation and interpretation of numbers – either large or small – is a natural development.

Modeling Hands-on experience with manipulatives (models) is essential in establishing and developing the concept of place value. All models are based on groups of 10. Proportional models Nonproportional models Proportional models – base 10 blocks, bean sticks Nonproportional models – abacus, money

Developing Place Value Counting and Patterns Regrouping and Renaming Estimation and Rounding The importance of clearly understanding the regrouping process cannot be overstressed. Counting and Patterns – Calculators are useful in counting and pattern recognition. (Wipe Out) Seeing each value displayed on the calculator helps students develop important insight into what digits are changing and when. There are many patterns involved with counting, but of the most important is observing what happens when the number after 9 (or 19, or 29) is modeled. Regrouping and place value are intertwined in later development of computation. Whenever trading or regrouping occurs, there are changes in how the number is recorded. Estimation and Rounding help develop good number sense. Rounding rules may vary from text to text for numbers ending in 5 – round up; increase the previous digit by 1 for numbers ending in 5 – if the number preceding the 5 is even, do nothing; round up if the number preceding the 5 is odd, increase the previous digit by 1