Counting and Estimating Routines Part 2

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If you missed part one of this series.  Click here to check it out!  Part 1 is an estimating and counting routine I use with young (K-1) children.

This counting and estimating routine is packed full of great math ideas.  I do this routine (with some variations!) from late grade 1 up through grade 6.  The following took place in a third grade classroom.  Because the common core wants second graders to be familiar with numbers up to 1000, this was a great way for me to review and reinforce number concepts up to 1000 as well as building skip counting strategies and multi-digit computation.

I started by dumping out my entire tub of 2 color counters.  The container says 1000, but it has been around for a few years and I recently lent a handful out to another teacher so I knew there was short of 1000 remaining in the container.

All the kids and myself are sitting in a circle on the floor and the materials get dumped in the middle.  I ask kids to think about how many are there and then turn and tell a partner what their estimate is.  This is a VERY challenging estimate for students to make and I heard estimates ranging from 200-1000.

I then asked kids to share ideas about how we would figure out how many we had.  Most ideas centered around us each taking some.  Many kids thought we could take 50 but some thought we should just start with 20 each.  (There were 15 of us in the circle) One student suggested that we each take 25 and since I know there are kids in this group who need practice counting by 25's I agreed that we should start there.

I modeled how to estimate 25 counters and pull them into my own space.  I then asked for ideas about how to organize them so that anyone in the circle could just look and know I had 25.  The consensus was putting them in piles of 10 with 5 left over.  I then sent half of the kids into the circle at a time to estimate and pull about 25 counters out.  Then the other half the kids got their chance.

A peek at several students' piles of 25

When kids all had 25 counters in front of them, we went around the circle counting by 25's to figure out how many we already had.  This was a great way to practice counting by 25.  We started at several different spots in the circle to see if we would get the same number every time.  We did of course :)  The number we got to was 375.  I asked kids to think about their estimate and perhaps change it based on what they had seen so far.  Again they shared their estimates with a partner and this time they were much more reasonable.
I then asked the students to think about how many more we should each take.  Many kids suggested 25.  I asked students how many counters we would need altogether if we each took another 25.  This lead to a great discussion about how to figure out 375 + 375.

A look at a students' pile of 50

 Once each student had 50 counters, our pile was MUCH smaller

We decided to each take 10 more.  Once we all had 60 total, there were only 14 left in the circle.

Each person ended with 60 in front of them

Since these students are just starting third grade, they are not quite ready to count by 60's.  They are also not able to think about 15 X 60.  Later in third grade, and if I do this routine in fifth grade these are both ideas I would pursue.  Instead we counted by 50's and then each added 10 more  (adding 10 to any number under 1000 is also a big idea in the common core)

Our grand total: 914

The next question: If there are supposed to be 1000, how many are missing?

I gave students about 3 minutes to think to themselves (no pencil and paper!) and then had them turn and talk to a neighbor.  When we came back together, I had kids raise their hands if they did it a different way than their partner.  I then called on certain kids and had them explain how their partner solved the problem.  Here is a peak at a few of the students' strategies as I tried to capture them on the white board.

This student pretended that 914 was 915 because "it is a friendlier number".  He said, " it is easy to know that 915 + 85 = 100."  He then used the idea of compensation to take one from the first addend and give it to the second addend.  This is a big idea in addition and I was so happy to see one of my students using it!

This student thought about how 900 + 100 = 1000.  She then knew she had 14 of the last 100 to make 1000 so she did 100 -14.  When I pressed her for details she said first she took away 10 from 100 then she took away 4 more.  

This student used two equations to add up from 914 to 1000.  First he added 6 to get to a "friendly 10" and then he added 80 more.  He knew in all he added 86.

This final strategy was given by a student who really struggles with math.  She was able to identify that she needed to find what went with 14 to make 100.  She used the 100 bead strings available in the classroom to figure out what went with 14 to make 100.  

Do you notice that all of my students used counting up or adding up strategies?  None of them subtracted.  I think (hope!) that the reason they chose this over subtraction is because the numbers 914 and 1000 are close together.  If the numbers are farther apart I am curious to see if they would solve it differently..... something I will try to work into my lessons this week!!!

Click here to head to part 3!

How do you use counting and estimating routines in your classroom?  Let me know in the comments below!