Solving Addition and Subtraction Problems

The second grade math students have been learning to solve addition and subtraction problems using a variety of strategies. Making sense of a problem situation, developing strategies for solving the problem, and communicating their solutions and strategies orally and in writing are the three major tasks involved.

The students progress through the following strategies for solving addition and subtraction problems (Investigations, 2008):

Counting All  

Some students need to build a model or draw a picture to visualize the problem and model the action. For example, in a problem about birds flying away (25-11),  they may draw 25 birds or tallies and cross out 11 of them and count the number left. These students see the problem as a collection of ones. The goal is for them to develop mental representations that allow them to work with groups.

Counting On or Back

These students can keep a quantity in their mind and count on for addition or count back for subtraction. This requires the child to keep track of the numbers she is counting and how many numbers she has counted. For example 25 + 11  count 26, 27, 28, 29, 30...35, 36  or 25 -11  count 24, 23, 22, 21 20...14.

Numerical Strategies

Counting on or back eventually leads to more efficient strategies as students learn to count on / back in chunks. 25 + 10 = 35 + 1= 36.  As students gain more understanding of the place value system, they apply this knowledge as they add and subtract. For example, in 25 +11, the students learn to break apart numbers into 10s and 1s (20 + 5 + 10 + 1), combine like parts (20 + 10 = 30, 5 + 1 = 6), and then combine 30 + 6 = 36. This place value strategy is often done mentally as students become more fluent with number combinations.

Notating strategies (showing their work) is an important extension of oral explanations. One thing I watch for is students who record a strategy because it is easy to show on paper or because they have seen someone else do it, but  are unable to explain it to me. For example, I’ve noticed some of the children have some understanding of exchanging or “borrowing and carrying,” as you and I were taught, but they show no clear understanding of the concept when asked to explain the process. In a problem like 25 + 18, a child will tell me, “First I added the 5 and 8 and I put the 3 here and then I put the one here.” When asked why, I often get a shrug. This tells me they have memorized an algorithm but have no understanding of the place value concept involved yet. I don’t know about you, but this is how I was taught math pretty much throughout my elementary years. In Investigations, the math program we adopted this year, the conventional or traditional strategies, including the U.S. standard algorithms for addition and subtraction, are taught in Grades 3, 4, and 5 along with a focus on achieving computational fluency. While introducing these strategies now may be right for your child, please check for understanding and just as important their ability to use another strategy to solve the problem. Some of them tend to stay with the one strategy that is comfortable for them without developing their skill with other problem- solving methods. For example, in the second semester, children solving addition or subtraction problems should have moved passed counting all and should be able to conserve the larger number and count on or back with ease; some will be working entirely with numerical strategies. 

The focus throughout is on how the students can represent their mathematical thinking and how different strategies are related.

This math program is new this year to teachers, students, and parents at our elementary school. We all have some new tricks to learn! I have included in today's Thursday envelope examples of a variety of ways the children are learning to problem solve. These are copied from the Investigations Student Handbook, which you may check out from me at any time. Please look through it and save it in your math file for future reference.

I hope this gives you more insight into the math your children are doing and why. Your help at home is always appreciated. Checking for understanding, using the “teachable moment,” or following up with enrichment activities are valuable ways to stay connected to your child’s progress.

Posted on February 7, 2008 12:42 PM | Permalink