Natasha had \$8.72. She spent \$4.89 on a gift for her mother. How much money does Natasha have left?

• I gave this question to my 4th Grade class. (11 kids, one absent.) It was December, I had seen them do a variety of subtraction work. I knew that a lot of them could handle subtraction using something like the standard algorithm — though certainly not everyone — and I was wondering whether a money context would be easier or harder for them. Would you predict that \$8.72 – \$4.89 would be easier or harder than 872 – 489?
• What approaches would you predict kids to take for this money problem? What mistakes do you expect to see?

Take a look below, and then report back in the comments:

• Which student’s approach surprised you the most?
• Assume that you’ve got time in the curriculum to ask students to work on precisely one question at the beginning of class the next day. What question would you ask to address some of the ideas you see in their work below?

Student 1

Student 2

Student 3

Student 4

Student 5

Student 6

Student 7

Student 8

Student 9

Student 10

• bryandisqus

I’m curious what your method for scanning or uploading all the student work pages, is that a process you have streamlined well? Because I haven’t yet!

• Michael Pershan

My school has an awesome scanner. I can actually get the scanned files as jpeg. When I’m working with a scanner that doesn’t have that I use pdf2jpeg.net to create image files. And then I open everything in MS Paint and get rid of the names.

• Jennifer Yi

I’m definitely not surprised at student 1’s mistake. I see that pretty often with students that I work with and I think it’s the worst when you make a mistake because of some penmanship problems. The 9 was misinterpreted as a 4 and so the student did 12-4 on the very righthand side (ones place) when subtracting to get a 8 instead of the 3 he or she should have gotten.

I am most surprised at student 10’s answer because they gave two answers, which can’t be possible. Also, neither of them are correct. The student got -23 for one of the answers and instead of borrowing, the student chose to keep using the same 7, which was reduced to 6 and do 6-8 for the tens place, giving -2 instead of how it usually would have been to get 16-8 in the tens place (if that makes sense). The borrowing mistake is something I expected to see in this problem, since the decimal tends to confuse students because it might be new to them. But student 10’s borrowing mistake was interesting.

I would most likely ask student why they did the approach that they did. How did they come up with two answers, did they double check their work, and if they think it’s possible that Natasha can have two different amounts of money left.

• Candice Lundy

Student 4 and 8 surprised me the most. They have answers, but no work. I am wondering what process they used? Also, because the question did not say “show your work”, would you consider this correct? Would you consider it correct without the decimal in place? I would also say that it depends on how much work they have had with money in class, if not a lot then of course the decimal or even the money sign would confuse the children. With that said, how much experience has your class had with money work in class?

I really am not surprised that students would get confused with the decimal there. I can see why many of the students above took apart the problem into dollars and cents, that is what I have seen children do more than most other methods. This would explain the confusion that student #2 had. I think that it was really great information for the teacher, on student #2 answer, to see where the confusion was taking place. Also, that the student does understand that 100 cents is in a dollar and you need a dollar to pay for some form of cent amount. The confusion just came from the decimal, and for many students that was the issue.

• Valeria Calvario

Which student’s approach surprised you the most?

I really found student 7 to be surprising. The reason why they surprised me the most was the skill that they used to organized their work you can see that they spent \$4.89 and you need \$0.11 cents to make \$5.00. Then they logically thought if they had 5 dollars how many more would you need to get to \$8.00 which is \$3.00. Then if they now have \$8.00 how much do you need to get to \$8.72 which is \$0.72. It seems like they used the addition method to add \$0.11, \$3.00 and \$0.72 to get \$3.83. In my opinion the studen used their skills beautifully to solve the problem. I like how they simplified it and were able to reverse the problem to addition rather than multiplication.

Assume that you’ve got time in the curriculum to ask students to work on precisely one question at the beginning of class the next day. What question would you ask to address some of the ideas you see in their work below

I would ask them what does .89 and .11 mean? Does it mean 11 complete things or part of something. I definitely think that the decimal is throwing some of the children off since I don’t think they understand that .89 and .11 is not a whole of something its kind of thinking of it as a fraction. The kinds accidentally took .89 and .11 as dollars and didnt understand that there is 100 somethings in 1 dollar.

• Natalie Sit

What approaches would you predict kids to take for this money problem? What mistakes do you expect to see?

I would expect to see the student 6 and student 9 to take this money problem because they really did the great job on the standard algorithm that are exactly what I learned before. I expect to see someone who did the mistake like student 1. It always happens on careless children.

Which student’s approach surprised you the most?

Student 7 surprised me the most because I never think about this way that can get the answer. He did the calculation inversely and show each step clearly. It is easy to get understand what he is doing. However, it is only good for multiple choice or doing a sketch.He cannot get full points by this work,

Assume that you’ve got time in the curriculum to ask students to work on precisely one question at the beginning of class the next day. What question would you ask to address some of the ideas you see in their work below?

I would like to ask like that: I have \$10.00. How much do I spend If I have \$8.98? This question would see how clear do they understand on standard algorithm. This seems so easy but children have to think about it before starting.

• Thanh Dang

I noticed that some of the students disregarded the decimals and goes on and subtracts the number. I thought that student 7’s technique is pretty neat because she adds the numbers up to the next whole. I can understand how she got her answer because she added the numbers that were given to the next whole and add those numbers that she made the whole up and got her answer. She made it simply easier to recognize which are coins and which are dollars that she is adding. If I were to teach something like this in class I would ask the students what is their definition of a whole number and from that I would ask them how much more from .89 to get to a full dollar? It’s so interesting how different students had different ways to approaching the question.

• Marissa

It’s funny to me that the students who showed the least amount of work were the correct students. The work of these students definitely surprised me the most. I am wondering how they found these final answer if many of their other students shower their work and had a difficult time. Student number one had the right idea to create a standard algorithm, but failed in the process of adding decimals. We teach students that dollars and coins are separate entities, so I can understand the student though to starting by seeing what eight minus four is, and then finishing the problem. When I looked closer at the students work, I noticed a very common math mistake when students write out all of their work. I was a victim of this habit so often in elementary school, so I understand how this could happen. When I was nervous about finishing the test, I would be really sloppy with my numbers thinking that I could understand my own writing because it was my own writing. Student number one mistook his or her written nine as a four, and subtracted 4 from 12, which is 8. The student also though that 7 minus 4 is 2, not 3. These mistakes happen in math time and time again, so educators needs to urge their students, to write large, write legibly , and check over his or her work.

• Chauntelle

Looking through all student’s answers, what I got curiosity is about how did students can answer without writing down solutions. There were some students who were able to write answers correctly without demonstrating the solutions. Also for other students, some of them missed to put decimal place value. Even though students acknowledge of decimal points, there could be confusion when it comes to additions or subtractions of two decimal numbers. Therefore, students who put 383 rather than stating 3.83, indicates the importance of learning decimal points. If I have chance to teach them about standard algorithm using decimal numbers, I would like to teach how the decimal points should be matched and discussing about each place value.
Looking at those different answers from different students, I was able to gather information that how each student think differently with same concept and how they learn differently with multiple perspectives

• Laura Spencer

Sorry- I teach high school. I assume anyone who has the correct answer with no work cheated by copying the smart kid. I always have two versions (or sometimes 3 or 4). Just saying…