Addition Strategies
As a veteran teacher, I encountered several parents, over the years, who were confused about how we ask students to add and subtract because "we were not taught that way when we were in school". Additionally, the same parents show their children to add and subtract using the traditional algorithms in the early grades. Many of the students, who learn this method, especially when regrouping or "borrowing" is involved, are confused as to why they have to do so because their number sense is not developed enough. They simply do not understand, in a case like 509 - 345, that subtracting 0 - 4 in the tens place is the equivalent of 0 - 40 and that to regroup means to take a hundred (or 10 tens) and subtract 40 (or four tens) from it. I witnessed a great number of students who were taught to compute with the traditional algorithm at home or in earlier grades. They sometimes used it correctly one day and forgot how to use it the next. In second and third grade, most students are not all mathematically ready to calculate the "traditional way" and should be concentrating on manipulating numbers instead.
With 48 states officially adopting the "Common Core Standards" (http://www.corestandards.org/) the way we teach students to add and subtract will shift from learning a procedure to understanding the concepts and internalizing them. It all begins by asking students to invent their own strategies for adding and subtracting and sharing it with their peers. This way, we are exposing children to various ways to manipulate numbers. Teachers will also introduce different ways to add and subtract numbers that focus on number sense. Eventually students will be asked to choose one or two methods that suit them. Students will begin to learn to add and subtract using the “traditional way” in fourth grade. In the third grade Common Core Standards, it is mentioned that students will be evaluated, on the EOG, on understanding, using and analyzing different addition strategies.
All this does not mean that we leave students to their own devices. We DO teach them different strategies for adding that are based on place value and decomposing numbers. This week, your child will reflect on how they add numbers and will learn 3 strategies (shown below) that will help strengthen their number sense. They will practice them in class and in their homework. Do not be surprised to hear your child say “But it’s easier the traditional way”. To them it may seem “easier” but based on some classroom observations, many are making mistakes adding this way. It is my goal to discuss this with them this week; it may seem easier because it is does not take as much time but their results are often not accurate (especially with subtraction). For the students who want to practice the traditional way, it could be used as a way for them to verify their answers. Students have also been taught to check their work with the calculator.
#1 Place Value Addition
In the reading corner, there are 139 non-fiction books. Someone donated 206 nonfiction books to the classroom library. How many nonfiction books are there now?
139 + 206 =
100+200=300
30+0=30
9+6= 15
300+30+15=345 books
#2 Number Line Addition (including counting on by place value)
Mrs. Keller wants to find out how many students there are in buildings 400 and 600 combined. She knows that building 400 holds 235 students and building 600 hosts 248 students. How many students are in both buildings?
235 + 248 =
+200 +30 +8
235 435 475 483
# 3 Changing the ones
There are 178 fourth graders and 225 fifth graders on the playground. What is the total number of students on the playground?
178 + 225 =
I added 2 to 178 to get 180. I took the 2 from the ones place in 225.
Now I have 223.
I added 180 to 223 to get 403.