Multi-Digit Addition and Subtraction Strategies

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Not Teaching Second graders "How to Subtract"

I have been working hard on a lot of place value up to 1000 concepts with my second graders as well as two digit addition and subtraction.  To ties some of this work together, I wanted to investigate our unifix cubes. 

When we purchased the unifix cubes, there were 1000.  I told my students this and dumped them out. I wanted to know how many I still had (it has been at least 7 years!)  I really didn't know how many were there.

We started by trying to estimate how many cubes there were.  This was REALLY hard!  It helped a lot when a student suggested that we take out 100 as a benchmark.  The estimates ranged from 500-1001. The kids organized them into 100's 10's and 1's and we figured out that there were 658 cubes.  We wrote the number in expanded form and talked about how that matched the picture and what it meant.  Then......

A student said, "Wow! You are missing a lot of cubes!"

and another replied "I think it is over 400!"

and then they all wanted to figure it out.  YESSSSS!!!!!

I gave them a few quiet minutes to figure out how many they thought were missing.  They had no pencil/paper etc during this part.  After everyone was giving me the ready signal, I gave them white boards and had them record what they thought the answer was and how they knew they were right.  WOW was I impressed!  It is amazing how many strategies they had and how many correct answers I saw.  And this is all before anyone has "taught" them how to do 1000-658!

Let me show you some of the strategies!

This student added the 100's, 10's and 1's separately and then knew 900+90+10=1000

This student started by adding 2 to 658 to get to a friendly 10 (660) and then added 40 more to get up to 700 and then added 300 to get up to 1000.  This reminds me of how we "Teach" kids to use the number line to add up at our school!

This student used sketching of base 10 pieces along with horizontally written number sentences

This student (and several others) got the answer wrong.   They added up to 10, 100 and 1000 but forgot to take into consideration the tens and hundreds that get traded up.  They looked at 658 and wanted to add 400 + 50 +2.  Their final answer is 110 off and you can see why!

This lesson really opened my eyes to the importance of letting students create their own strategies and letting them share those strategies with neighbors and the class.  This lets everyone learn and compare and contrast strategies.  I think even I learned a thing or two!