Comparing and ordering decimals was the focus of today's lesson. We took additional notes today as we learned the process. I began by having students restate what they learned about decimals yesterday. They did a very good job! They reminded me that when moving to the right in our place value system we are dividing by 10. They explained that we can think of the tenths place as a dime, the hundredths place as a penny, and the thousandths place as an amount smaller than a penny.
I explained that knowing this information would help when it came to comparing and ordering decimals. I asked that they write the most important rule of working with decimals:
ALWAYS line up decimal points!
Next, we discussed using t-charts to help us line up our decimal points. On the left side of the t-chart is where we place whole numbers. The right side is where we place the decimal numbers. The decimal itself is on the line that separates these two parts of our number.
Once we have placed our numbers on the t-chart we can use place value to compare. I covered the decimal portion of the t-chart and we focused on the whole numbers. Today I made it a little easier, all the whole numbers were the same! Once we realized that the whole numbers were no help in determining which number was larger (since they were all 7s), we moved to the next place... the 10ths place. Now we were able to look at the three digits in this place. This is where thinking of 10ths as dimes was helpful. They realized that a 5 in this place was less than an 8. Once we determined the smallest digit in the tenths place we moved to hundredths. Again, thinking of the digits as pennies proved helpful. Finally, we moved to the thousandths place and compared any remaining digits.
We also discussed that we can "add" a zero to the end of a decimal number to give it an equivalent number of digits to the other numbers being compared. I emphasized that we can add or take away zeroes at the END of decimal numbers, but NEVER add or remove zeros elsewhere in the number!
We reviewed our place value knowledge by working with a dry erase marker on our desk (always a favorite)! I asked the kids to write the number one hundred billion on their desks. This caused a little consternation until we realized that we can determine the number of zeroes needed by being aware of the meaning of the commas.
Once we had this large number (all the way to thousandths), we worked with changing the digits in the places. Again, there was consternation because I did this out of any identifiable order:
· change the 0 in the tens place to 1
· change the 0 in the ten thousands place to 7
· change the 0 in the ten millions place to 3
· change the 0 in the tenths place to 5
· Change the 0 in the ones place to 9
· Change the 0 in the hundred thousands place to 5
· Change the 0 in the billions place to 8
· Change the 0 in the thousandths place to 4
· Change the 0 in the millions place to 2
· Change the 0 in the ten billions place to 7
· Change the 0 in the hundreds place to 6
When finished, I asked the students to tell me if their table group all had the same number. None did. I asked them to discuss what we might have done to this number to help us. After a few minutes of discussion, every group had similar answers: we need to label the periods and places of our number! After rewriting one hundred billion (and going to the thousandths place), they labeled the number's periods and places and we tried again. This time with much more success!
I asked what we learned from this. Most students agreed that it is important to take the little extra time and effort to use the models and labels we practice in class to help us solve problems! Lesson learned!
Homework: Edmodo: Decimals (Day 2)