![]() ![]() ![]() While this above strategy makes sense when calculating via paper-and-pencil, it might not be helpful for our students to develop number sense, or in this case, maintain magnitude. The problem is recomposed into (40-10) + (12-9) ![]() Take a look: 52 is decomposed into 40+10+2 The traditional algorithm suggests that we decompose 52-19 based on the value of each column, making sure that each column can be subtracted 1 digit at a time… In this case, the question would be recomposed into (40-10)+(12-9). Understanding how numbers are decomposed and recomposed can help us make sense of subtraction when we consider 52-19 as being 52-10-9 or 52-20+1 or (40-10)+(12-9) or 49-19+3 (or many other possibilities)… Let’s take a look at how each of these might be used: For example, the number 10 can be thought of as 2 groups of 5, or 5 groups of 2, or a 7 and a 3, or two-and-one-half and seven-and-one-half… Decomposing and Recomposingįoundational to almost every aspect of mathematics is the idea that things can be broken down into pieces or units in a variety of ways, and be then recomposed again. In this post, I’d like to help us think about how and why we use visual representations and contexts to help our students make sense of the numbers they are using. I plan on writing a few articles in the next while to discuss a few of these areas. Throughout mathematics, the idea that objects and numbers can be decomposed and recomposed can be found almost everywhere. ![]()
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