Grade 3: Place Value to 999,999: When Students Ask

Place Value to 999,999: When Students Ask

Why should I bother learning about place value?
Explain to students that place value will help them learn the value of numbers. Write the digit 1 in the ones place on a place-value chart.
Ask: What is the value of the digit 1? (1) Below that, write the digit 1 in the hundred thousands place, followed by zeros.
Ask: What is the value of the digit 1 in this number? (100,000) This demonstration should clearly show that the place of a digit can make a big difference in the value of a number.
When I compare numbers, do I have to compare the digits in every place?
Give students several examples such as the following to illustrate the answer to this question.

42,683	<	72,993	You only need to compare the ten thousands.
928,771	>	915,560	You need to compare the hundred thousands and the ten thousands.
8,624	<	8,627	You need to compare the thousands, hundreds, tens, and ones.

When will I ever use rounded numbers?
Students can discover the answer to this question by looking for rounded numbers in the newspaper. They will see a variety of situations in which rounded numbers are used. Explain to them that they will also use rounded numbers when they estimate answers in addition and subtraction.
Why do I have to start at the left to compare numbers? Why can't I start at the right?
Point out to students that they compare numbers starting with the greatest place, since that is a more efficient way of comparing numbers. If one number has 7 thousands and the other number has only 2 thousands, it is not necessary to look at the rest of the digits in the number to know which is greater. However, if one number has 8 ones and the other has 6 ones, you can't tell which number is greater without comparing all the other digits. The greatest place is the place on the far left.