Place Value Patterns- Moving the Numbers!
Part of our curriculum in 5th grade is to recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. (Arkansas Mathematics Standards)
Students also need to understand why multiplying or dividing by a power of 10 shifts the value of the digits of a whole number or decimal and explain patterns in the number of zeros of the product when multiplying a whole number by powers of 10. This is not just for whole numbers but decimals place values up to the thousandths place.
This year we were working with a program called Eureka Math. They illustrated a great way of moving the numbers back or forth when multiplying and dividing instead of just moving the decimal, which is a quick short cut way that leads to misunderstanding.
So, until the students understood what was happening in actuality to the numbers in each place value, they had to draw the place value chart or lines to represent the different place holders in the chart. Once they could explain accurately what was happening to the numbers, most quickly figured out the short cut way of moving the decimal to the right or left.
I created an anchor chart (above) that helps the students to remember the patterns. This was easy for them to see and we also put a miniature version in our math notebooks.