The sixth graders in my class were having trouble with absolute value. I went to the internet to see what others had to say. I found a post by MTBos blogger, Growing Exponentially called The Absolute Value Project. (She was inspired by Dan Meyer’s Guess the Eggs post.)
Not having jelly beans on hand, I put 195 unifix cubes in a container that had been hanging around in a back closet.
My students were excited to find this “game” as their warm-up activity first thing on a Friday morning. In under 3 minutes they all had their guesses written on an index card for me to review. I was somewhat gleeful that all but one guess below the actual number of cubes.
Then I asked them to calculate the difference between their estimate and the actual number of cubes. (We were able to preview that vocabulary word, difference, as the expressions and equations unit is coming up next.)
Then I started a number line with 195 in the middle, indicating it had a zero difference. 195-195=0. We started to record their guesses, -61, -103, … then came -98. Where does -98 go on the number line? As we went through each guess, determining which negative integer was larger allowed me to assess who had mastered this concept and who still needed some work. Finally we got to the one person that over-estimated with 400 and a positive 205 difference.
The students could tell the estimate of 165 with a difference of -30 was the closest to zero. It had the smallest distance from zero.
Then the connection was made, absolute value measures distance from zero. It’s not an abstract concept only found in math homework, it’s something we use!