Magical2017
DIS Veteran
- Joined
- Jul 2, 2016
- Messages
- 2,057
Yes, and 34-19= 15. I can use an algorithm, including the US standard algorithm to solve this efficiently and accurately, which is why it is a standard in the CCSS-M. I love algorithms and there are many algorithms in the world that are fast and efficient. However, before teaching these algorithms, it is interesting to allow children to come up with a strategy on their own. "How would you approach this?" I might put it in a context I have 34 pencils and give 19 to a friend. Now how many pencils do I have? Some students are at the concrete stage and require counters. Some will use drawings. Some will be at the abstract stage. As a student, I can decompose by place value, or compensate by changing one of the numbers to easily calculate. This involves using the properties of operations, such as the commutative and associative properties. These are not new to the Common Core.2 + 2 = 4.
If I use the standard algorithm and regroup (or borrow and carry), I am essentially recomposing the problem as 20 + 14 minus 10 + 9. I can now subtract either the ones form t he ones or the tens from the tens. Understanding several ways to approach a problem allow a student to better understand the steps in algorithms. Most students will not automatically attempt to subtract the ones places before the tens place. They will intuitively try to work with the tens place first.
Another example is comparing fractions. Before teaching students to find common denominators, a good class discussion might center around deciding which is larger, 3/5 or 4/10, and proving to a partner why we are correct. If I think about the fact that 3/5 is greater than one half and 4/10 is a bit less than a half, then I am building conceptual understanding. Students can then be taught to find common denominators using a procedure if they don't automatically make the connection to multiplication, but this can be taught after the conceptual understanding is there.