## Sunday, September 29, 2013

### Estimating and Counting Routines Part 3

Click HERE to start at part 1 or HERE to check out part 2!

Today's estimating and counting routine was done with students who are about 1 month into grade 3.  This is also an excellent routine do with kids from K up to grade 4.  The strategies and efficiency will vary greatly among the grades but there is something different you can bring to each level.

This routine was not done as a whole group lesson but rather in small groups of 2-3 students.  I gave each students a scoop of dominoes and asked them to spread them out on the table in front of them with the dot side up.  I gave them about 15 seconds to look at the dominoes and come up with an estimate about how many dots they think are there.  Then one person in the group covered the dominoes with a student sized white board and each person wrote down their estimate.
 The dominoes awaiting estimation

 A group of students record their estimates

Once students were done estimating, their job was to figure out how many dots there actually were.  I did not provide parameters about how this had to be done or make suggestions about ways to do it efficiently.  It was late on a Friday afternoon however, and they knew if they had any time left before end of the day pick up, they got to play with the dominoes so they were super motivated to do this task efficiently.

Here is a look at some of their strategies.

 This team was grouping by 10's but had several dominoes that did not fit into their schema.  The black and blue one in the upper left corner got pushed together to make a group of 20.  The two black and one yellow one above those they figured out by imagining breaking apart the dots on the center domino and giving one to each of the top and bottom of the domino on the left and 2 to the yellow domino.  then they had 30 and 5 left over.  From 35 they simply counted on by tens touching the group of 20 twice.

 This group had some simple combinations (silly teacher forgot to put some double 9 dominoes into this cup!)  This activity done this way without the double 9's would be great in K or grade 1 as a way to practice combinations of ten and counting by tens.  You could even contrive exactly which dominoes go into a cup and really push on the idea of 10.
 This group started by putting some dominoes together to make 10's but had more that could not make a friendly ten and they did not think about going farther and trying to make 20 or imagine moving dots to make tens.  They pulled out the 100 bead strings to help them when they got stuck adding unfriendly numbers.

 Here is a look at a group of 2 kids estimates and the real answer.  As you can see, kids still need more practice with estimating.  My next question as usual when they finish is how far were you off by?  This often leads to a lot of discussion about adding up versus subtracting.  On this particular day we were running behind so this part got a little shortchanged.
I closed this session by having each team share their strategy for figuring out how many dots and telling how well their strategy worked and if they thought it was an efficient way to do it.  I am always amazed at how perceptive kids are about their own struggles and successes.

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What is your favorite math manipulative to use for estimating?  Respond in the comments below!