Representations of Ten

Last week, while I was walking around helping the first grade students in my main placement with the math problems they had been assigned, I noticed that many of them were struggling with the “draw a picture” portion of their worksheets.

The lesson had been on determining the number of “tens” in a two digit number and the students seemed to be able to choose the correct answer from the listed choices, but then had difficulty representing it with a picture.  I puzzled over this as I heard the teacher explain to more than one student that they hadn’t finished the problem until they had drawn a picture to represent their answer.  Many of them had correctly identified that 7 “tens” were in the number 70, but they were having difficulty drawing seven towers of ten.  One student had small squares scattered across the allotted space.  Another had seven leaning towers of various heights.  Still another had drawn a tower of stacked squares, but none of them were the same size.  This puzzled me because I wasn’t sure if this was indicative of them not understanding the concept of the number of tens in a number or just of them “not being able to physically draw a picture to represent it”.    

 It seemed to me that that if the students were able to draw these groups of ten “correctly” it would help them determine their answers.  They had studied skip counting with tens and if they were able to draw distinct groups of ten they would be able to “count them” to arrive at their answer.  In my prior experience, drawing a picture had brought clarity.

Later, my master teacher and I discussed this and wondered if we should consider doing a “warm up” exercise where she’d model drawing towers of ten, giving the students step by step instructions.  Then we would give them an opportunity to practice this skill.  We had possibly moved too fast over this portion of the lesson and needed to slow down a bit, given the outcome of the assessment. 

Another idea we discussed, to see if they understood the concept of “tens,” was to have the students build the towers with manipulatives instead, rather than draw them.  Their ability (or inability) to do this would certainly shed light on their understanding of this concept.   This exercise of “troubleshooting” with my master teacher reinforced the idea that teaching math is definitely a dynamic process, an art rather than a science.  It reinforced the idea that there isn’t a “one size fits all solution” when teaching.