There was a great question on social media today! The teacher posting knew this was not correct, but was asking what students should be able to do and explain. She asked about place value, and she was correct! This seemed to long to type, so I created a quick video. There are no bells and whistles, but I hope it is helpful!
The next day, she very politely responded with a question, and I realized I never answered what I expected the students to say! Sorry! I’ll add it to the video later, but here is how I typically handle that WHEN (not if) it happens!
When my students say, “I add a zero”, I ask them what adding a zero actually means. Then I give an example such as “What is 15+0?”. Then they have to explain what they are doing is not adding a zero, but placing a zero in the one place, because that is the only way to show you have tens. If you do not place a zero in the ones place, what would happen?
A question to ask would be “How do you write 4 tens, 15 tens, etc. in base ten format? Why?
The only reason the zero is needed is to show the new value of the digit. You can then discuss what would happen if they multiplied by hundreds, etc. I have them say this every time, because then when they multiply decimals, they can discuss why this is not needed. When I taught fourth grade students, I asked them if they thought that would always be true.
Another example I like to do is show them, especially when they are adamant about the ‘pattern’ of ‘adding a zero’, is ten quarters or ten dimes. They don’t know how to multiply decimals, but they do know money! When they see $0.25 x 10 = $2.50, they struggle with seeing their ‘rule’ does not work, but they do eventually make the connection.
I believe it is important to question them (rather than show or tell them) so they reach cognitive disequilibrium and are ready to learn a new idea. Spending time having the students figure it out can be challenging, and it requires a lot of patience. (Maybe I just don’t have much!) I have always found it to be worth it, though!
What are your thoughts and ideas? Please share!