The sixth graders in Ms. Chanales's math class have skipped several years of schooling and have received their doctorates in mathematics. Imaginary students from around the world write to them, seeking their advice and guidance on how to solve problems or their wisdom for explanations about why some of their favorite rules and algorithms work. The goal of this assignment is to help students move beyond using standard algorithms to compute. We want them to understand how these procedures developed and why they work. The students have done an exceptional job stepping into the role of Dr. Math and their ability to both understand and explain math is amazing! Feel free to send us your own math queries.
Here is a sample of some letters and their responses:
Dear Zero Hero,
Your thought is a common one and I would like to help you resolve it. You are correct that 0.8 is the same as 0.80. This applies only to decimals and not numbers higer than 1.00. If you would "add" a zero to 800 you would get 8000. The reason that you can "add"a zero (change its place) to decimals is that you are not changing its value.You see,decimals are like fractions. For this particular question you have to divide the following (0.8) 8/10=.80 and (0.80) 80/10=.80. After dividing it becomes clear that they are equal. Also, your teacher is correct that you aren't really adding zeros. The value of 0.80 and 0.8000 are the same. While the value of 80 and 8000 aren't. I hope this helps make your head less fuzzy. Sincerely, Dr. Math (Binyamin)
Your thought is a common one and I would like to help you resolve it. You are correct that 0.8 is the same as 0.80. This applies only to decimals and not numbers higer than 1.00. If you would "add" a zero to 800 you would get 8000. The reason that you can "add"a zero (change its place) to decimals is that you are not changing its value.You see,decimals are like fractions. For this particular question you have to divide the following (0.8) 8/10=.80 and (0.80) 80/10=.80. After dividing it becomes clear that they are equal. Also, your teacher is correct that you aren't really adding zeros. The value of 0.80 and 0.8000 are the same. While the value of 80 and 8000 aren't. I hope this helps make your head less fuzzy. Sincerely, Dr. Math (Binyamin)
Dear Missing the Point,
You are missing the point here. The reason you line up the decimals is so that you can add thousandths with thousandths and hundredths with hundredths and tenths with tenths and ones with ones and tens with tens and hundreds with hundreds... you get the point. if you didn't line up the decimals you'd be adding tens with hundreds and ones with tenths and everything would be messy because each of those are different sizes. That's why it's so important to line up the decimals.
-Dr. Math (Eitan)
You are missing the point here. The reason you line up the decimals is so that you can add thousandths with thousandths and hundredths with hundredths and tenths with tenths and ones with ones and tens with tens and hundreds with hundreds... you get the point. if you didn't line up the decimals you'd be adding tens with hundreds and ones with tenths and everything would be messy because each of those are different sizes. That's why it's so important to line up the decimals.
-Dr. Math (Eitan)
Dear Borrower Worrier,
First of all it's not like borrowing sugar from your neighbor. This borrowing is if you have a number 800.5-6.7 you have to take the 800 and change that to a 700 so you can make the next number 10 tens. Which equals a hundred , which is the hundred that we took off from the 800 to make it 700. Then you have the next column. you just added a ten for the tens column but there's nothing to subtract there. But then you look at the next column and you see that the bottom number is bigger then the top number. So you take 10 and make it a 9 and you cross out the 0 and make it a ten because ten ones are equal to one ten. So now you can subtract those two numbers. But than you have to do the same thing for the next column to make sure that you can subtract the top number to the bottom.
From,
Dr.Math. (Eli)
First of all it's not like borrowing sugar from your neighbor. This borrowing is if you have a number 800.5-6.7 you have to take the 800 and change that to a 700 so you can make the next number 10 tens. Which equals a hundred , which is the hundred that we took off from the 800 to make it 700. Then you have the next column. you just added a ten for the tens column but there's nothing to subtract there. But then you look at the next column and you see that the bottom number is bigger then the top number. So you take 10 and make it a 9 and you cross out the 0 and make it a ten because ten ones are equal to one ten. So now you can subtract those two numbers. But than you have to do the same thing for the next column to make sure that you can subtract the top number to the bottom.
From,
Dr.Math. (Eli)
