Tuesday, October 8, 2013

Multi-Digit Addition and Subtraction and the Common Core Part 2

If you missed part 1 of this series where I look at subtracting 2 and 3 digit numbers click here to check it out!

Over the next week and half, I will be seeing a class of third graders 3 separate times for about 40 minutes each.  In this time, my goal is to help move them from subtracting from 100 to subtracting from 1000.  I will be taking lots of pictures and sharing how I use problem strings to move kids forward in their thinking about place value and their own development of strategies for multi-digit subtraction.

Day 1
I started day 1 with a string of problems related to subtracting from 100.  The first few were subtracting just tens and the next few subtracting just ones.  I have done a great deal of work with this group as second and third graders with combinations of 100.  I started at this level to be sure kids were building on their prior knowledge and to make even the lowest students feel like this was something they could do.

 The first problem string.  At this point in the year with these third graders this went very quickly without much discussion.  My students were showing me they were ready quickly and fluently.  If I was doing this same string at this point in the year with first or second graders, I would expect a great deal of discussion around these problems and strategies for finding answers.   I expect third grade and up to be fluent with these ideas.

I quickly moved onto a second string of problems.  These were subtracting tens and ones from 100.  We had a bit more discussion about how kids knew they were right.  The two most common strategies in this class are subtracting tens and then ones or adding up.

 The second set of problems.  I expect third graders to be fluent with these problems as well.  Check out this post on how work with kids towards achieving fluency at this level.

After making sure kids were thinking about previous subtraction strategies they had developed, I upped the ante and we looked at a problem string that was all about subtracting from 1000.

 Our 1000 take away problem string.  Notice I start with just subtracting hundreds and then just tens before I start combining them.
Our first problem was 1000-200.  Some kids required a lot more think time than I was expecting to come up with the answer to this so we had a great deal of discussion about how various kids knew the answer.  I really liked that one student connected it to what he knew about 10 - 2 = 8.  He said, "I know 1000 is 10 hundreds and if you take 2 hundreds away from that then it is 8 hundreds."  I had him write this using words and numbers like this on the board

10 hundreds - 2 hundreds = 8 hundreds

Another kid wanted to come up to the board and added this:

100 - 20 = 80
10 tens - 2 tens = 8 tens

WOW!!  I loved this idea so I had to add my own to it

10 - 2 = 8
10 ones - 2 ones = 8 ones

This discussion REALLY helped kids get the big idea and further reinforced how important it is for kids to be fluent with combinations of 10.

Moving onto the next problem, we tried 1000-500.  The kids were much faster with this and were easily able to connect it to the last discussion so I decided to move on to subtracting some tens.

We looked at 1000 - 80.  Students were fairly fast to get this idea and several students talked about how they looked at 1000 as 900 + 100 and took the 80 out of the 100 part leaving 900 + 20 left.  Students were so quick with this idea, I decided to jump right to subtracting hundreds and tens.

We tried 1000-180.  Most students subtracted the 100 first and then the 80.  There were a few students who had some errors in their thinking such as thinking about 1000-100=900 and then subtracting 80 from 900 and coming up with 980.  Other students were quick to see and correct these mistakes.

We tried another problem subtracting tens and ones 1000-350.  Fifty is a really friendly number for kids and all students were able to agree on the correct answer for this.

I ordinarily would build up a bit more to my ultimate goal of subtracting a 3 digit number where none of the digits is zero but I was running short on time.  This entire lesson had been very teacher driven with lots of partner and whole group discussion and I was afraid I was losing the students' focus and they were due to leave for P.E. in about 6 minutes.  I decided to go for it and see how they would do with 1000-738.  This would give me a good idea of where kids were with their strategies and who could extend their previous understanding to a more challenging problem.

Students had about 4 minutes to think about this problem and as they were finishing up, I had them whisper the answer to me which is one of my favorite formative assessment strategies.  About half of the class got it correct and another fourth of the class was off by either 10 or 100.  The final fourth of the class was either way off or unable to come up with a solution in the time given.  This quick check in as students were lining up gave me good ideas about where to start the next lesson and who to target my instruction at.

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