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I love vacation, but it’s GREAT to be back home!  So, somewhere on a trail in the mountains of Georgia, I got to thinking about open number lines.  That’s a math buzz word you hear a lot these days, but what exactly is an open number line?  Well, it’s a number line with no numbers or tick marks.  Open number lines are great models for working with place value or, in the case below, addition.  In previous posts I’ve talked about mental strategies for addition.  The number line is a fantastic way to record the different strategies used by students. The three number lines below all show strategies for adding 37 + 48.  Look at each one and see if you can explain how the addition was done in each case.

1. Number Line 1: This student added the tens (30 + 40) and then the ones (7 + 8).  The number line starts at 30 (the tens from the first number) and adds on the 4 tens from the second number, landing on 70.  The student then added 7 + 8 to get 15 and added that to the 70 to get 85.
2. Number Line 2:  This student left 37 whole and added on the 4 tens from the second number.  He then broke the 8 ones into 3 + 5 and used the 3 ones to make 80.  Finally, he added on the remaining 5 ones.
3. Number Line 3:  This student took 3 of the 8 ones from the second number to get make a ten out of the 37 (37 + 3 = 40).  Then, she jumped on the 4 tens to get to 80.  Last, she added the remaining 5 ones.
Notice the number sense required for this type of math.  Students have to be able to think flexibly about numbers, understand place value, and decompose numbers.  This might be out of your comfort zone!  If so, try some problems on your own.  When you do this with your class, it is a good idea to anticipate the strategies students might use, so you’ll be ready to draw them.
Here’s a little freebie you can use with your class. 