NA3-4: Know how many tenths, tens, hundreds, and thousands are in whole numbers.

Elaboration on this Achievement Objective

This means students will develop a multiplicative view of whole number place value that involves more than knowing the significance of the position of digits in a whole number, for example In 239 456 the 3 means three ten thousands. Strategies for computation require a nested view of place value and understanding the scaling effect as digits move to the right and left in place value. This means that nested in the thousands are hundreds, tens and ones in the same way that nested in the tens are ones and tenths, for example 239 456 has 23 ten thousands, 2394 hundreds, and 23 945 tens, etc. An understanding of nested place value is best demonstrated by calculations where place value units must be constructed by combining or decomposing other place value units. For example, calculations like 2 004 - 700 = may require students to think of 1000 as ten hundreds. At Level Three students should connect the multiplicative value of the places, for example one hundred thousand is ten times as much as ten thousand, and one hundred is the result of dividing one thousand by ten. They should know the effect of multiplying and dividing by ten - 4200 is ten times more than 420 and 43 divided by ten is 4.3.