Subtraction Strategies

Today my MT added a math computation segment to the morning's agenda. Because the class is scheduled for "specialists" (P.E., Library, Art, Music and Computer Lab) most days between approximately 9:30 and 10:30 AM, we lose an hour's prime instructional time in the morning. (Scheduling for specialists rotates from year to year so as to be fair.) This means that we have only about 2 hours each morning in the classroom, and that includes "early work," paper collection, etc.

The fifth and sixth grades must agree as a team about the timing of reading, writing and math instructional periods so as to accommodate ELL and special ed schedules. This year the team agreed to teach reading and writing in the morning and math and science/social studies in the afternoon. Our class has a math block from about 1-2:15 each day and this time is devoted to the Connected Math curriculum. My MT is squeezing some extra computational work into the morning periodically.

Today the kids were presented with several multi-digit subtraction problems, all of which required regrouping. While a number of the kids were proficient, others were confused about the process of solving such problems. I worked for about ten minutes with one rather bright boy, who had his own strategy. Unfortunately, it was flawed and cumbersome. He had clearly thought about the process of subtraction and conceptualized the need to "borrow" from a higher place value to solve problems. However, he sometimes tried to borrow "50" for example, which didn't work. In another case, he used an extended sort of subtraction that involved subtracting thousands from thousands, for example, but also involved using a lot of negative numbers and was prone to errors.

I told him that it was great to think creatively about solving math problems, but that it was also useful to know the standard ways of solving problems. In explaining, why it worked to borrow 10, but not 50, I asked if he had ever worked with unit blocks (although I didn't call them by this name). He said that he had, and was able to relate to my pictures of such blocks, to conceptualize trading or borrowing. He'll need practice, but given his accuracy in verbalizing the process, I think he should be able to successfully employ the standard method for subtraction when called upon to do so.