3RD HERD

Kentucky Down Under - Olssen

Invented Strategies - The "Matthew" Plan

On the first day of teaching subtraction with regrouping, one student began explaining his own way of solving problems so that he didn't have to regroup - he could use mental strategies instead. I listened intently as he showed us how he worked through a problem. At first, I thought it was a fluke! Then, I realized this strategy would work well with almost any subtraction problem. The students have loved Matthew's method! In Matthew's strategy, he makes the initial problem easier to solve by forcing his first answer to be a "nice" number. From there, he uses several different strategies including counting up, counting down, and mental math. This plan works best with 2 and 3 digit numbers because the subtraction becomes difficult with more complex numbers.

Subtraction Strategies - Modeling the Process

This video shows the "Modeling" method for solving subtraction problems. This strategy is great for students who are moving from concrete learning (using manipulatives) to more abstact learning. In this method, students draw pictures to represent the highest number, then begin taking away the smaller number. Children can "see" the steps of traditional regrouping. This helps build number sense because students are visualizing the base ten representation of numbers. This is not the most effecient means to solve a subtraction problem, but it effective. One word of caution - your child does not have a "picture" to use for numbers larger than 4 digits.

Invented Strategies - Partial Differences

In this method, students use the expanded form of numbers to create simpler subtraction problems and avoid regrouping. One of the most common problems students face in solving problems is that they want to begin on the left and work to the right. In the traditional regrouping method, this is not possible and leads to errors. In the partial difference method, students can work left to right, leading to fewer errors. The students have enjoyed this method because of the exposure to negative numbers. If an answer is a negative number, the student puts a minus sign in front of it. If the answer is a positive number, the student puts a plus sign in front. Students must be flexible in their thinking and be able to do mental computations.

Empty Number Line Strategy

The empty number line strategy helps students visualize the "counting back" nature of subtraction. This strategy allows students to break the problem down into more manageable steps and to solve easier problems. This method can take up a LOT of space! Students continue to improve their number sense by utilizing this strategy. It also allows students to solve from left to right.