# Place Value Relationships

Hello All,

For the last few weeks, life has been all about Place Value in the 4th and 5th grade math room. Fourth graders have been exploring whole numbers, while fifth graders have been diving into decimals.

The fourth grade unit began with students estimating how long 100 centimeters would be and then building 100 centimeter strips to see how they compared to their estimates. Most students were surprised to see that the actual measurement was shorter than they estimated. They then made predictions to see where they thought a thousand centimeter strip would extend in the classroom. Again, they were surprised by their estimates. A thousand centimeters was a lot longer than they anticipated.

Building these strips helped lay the foundation for patterns in our place value system. We realized that 10 is ten times greater than 1; 100 is ten times greater than 10; 1000 is ten times greater than 100, and so on.

Fifth graders have also been exploring place value, but in relation to decimals. What they have discovered is that the same relationships occur even when we move beyond whole numbers. As we move to the right on the place value chart, the numbers get ten times smaller. As we move left each place, the numbers get ten times larger. They also realized that when we multiply whole numbers by a power of ten, the reason the zeroes occur is because the digits are shifting left.

This week and next, fifth graders are using this understanding of the shifting digits to help develop understandings in multiplying and dividing with decimals.

Enjoy your week!

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