I have been thinking a lot lately about multidigit addition and subtraction. A few weeks ago I wrote
this post about work I am doing with my second graders around addition and subtraction strategies. This week, I have moved onto decimal addition and subtraction (in and out of the context of money) with my fourth graders. Today we did some problems pencil and paper free to start class. They were subtraction of money problems. It was so interesting to see the some of the same misconceptions and some of the same strategies that I saw in grade 2 with whole numbers.
Let's take a look

This was the problem and the four solutions that kids gave me. When asking for answers, I never acknowledge the correct answer, I just keep asking "does anyone have a different answer?" REMEMBER that the kids did not have pencil paper for this task. They did all of this "in their head". The things I wrote on the board were an attempt to capture different strategies. Some kids were able to correct their answer while explaining their thinking! 

This person decided that $3 was really close to $2.95 so they subtracted $3 from 10. They took 5 cents to much so then they add it back. Very efficient strategy for solving this type of problem where the amount of cents being taken away is almost a full dollar. 

This kid did a number line in his head. He thought about adding 5 cents to get up to $3, and then needed to add $7 to get up to $10. 

This young lady decided to subtract $2 first and then subtract the 95 cents from the result. 

This student did the opposite of what the last student did. She took away 95 cents and then took 2 dollars from the result. 
I was really impressed by how many different strategies my students had to solve this problem! I also loved how by explaining their thinking aloud to the class they were able to find and fix mistakes (either alone or with the help of classmates).
I was loving how this was going, so I posted another problem.

Check out the answers I got to this problem. You can see where the misconceptions are based on the way they answered! Below I am going to highlight a few different strategies that students used. 

This student used adding up to find the answer. He started at 55 cents and added 45 cents to get up to $1. He then added the $1 to the $4 and then knew he needed to add up 5 more dollars. 

This student subtracted in parts. First she took away the dollars and then the cents. 

This student also subtracted in parts but first took away the cents and then the dollars. 

This student used the visual model of the number line to add up in his head. He started at $4.55 and added 45 cents to get to $5. He then had to add 5 more dollars to get up to 10. 
What strategies do your students bring to decimal subtraction? Are you giving students a chance to think for themselves without paper and pencil?
I love the way you have demonstrated these strategies so clearly. Thanks for sharing these ideas with us.
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