# Teaching Inverse Operations to Challenging Learners

Last weekend I was looking ahead at the math skills that I had to teach my 3rd graders and based on what I saw I had to teach them how recognize that multiplication and division were inverses of one another. So, yesterday I was teaching teaching my students how to subtract 2 digit numbers with regrouping using a place value chart while teaching my lesson I had an AHA! moment. First, I realized that I could introduce the concept of inverse operations while teaching subtraction because subtraction is the inverse of addition. Modeling the inverse concept was very simple and didn’t take much time. While I was modeling trading a ten from the tens place and regrouping it as 10 ones, I asked my students this question,”In addition problems how do we trade?” Their answers were, ” We trade 10 ones for a group of ten.” At that moment I introduced the term inverse operation. I then went on to explain that an inverse operation is when we do the opposite for subtraction than we do for addition. One of my students responded as if a light turned on, “It’s backwards?” I said yes it’s backwards! When he said that I instantly realized that he was attempting to make the connection and put it into his own words. I was so excited because I had finally found a picture and a conceptual approach that I could use to explain what an inverse operation looks like. After I introduced the concept of inverse operation, I then used it as an anchor to teach the students how to trade a 10 from the tens place and trade/regroup it as a group of 10 ones. Teaching complex concepts to my students is very challenging because the they lack the literacy proficiency that is needed for them to grasp the concept.

When I know that I have to introduce a skill or concept that will be difficult for my students to understand I follow these steps:

1. Connect a previous lesson to the new skill or front load my instruction with the foundation skill

2. Teach the new skill from simple to complex (begin with conceptual then move to the abstract)

3. Use a think aloud to explain my thought process

4. Look for patterns in the process that will support acquisition of the new skill

I often see the fact family concept taught to students in 1st and 2nd grade with the numbers, but I sometimes wonder how the teacher introduced the concept to their students. Fact families are an example of inverse operations on a simpler level. The facts 2+3=5 and 5-3=2 are inverses of each other because the student has to put 2 parts plus 3 parts to equal 5 parts and in the subtraction fact a student would have to begin with the total (which is the opposite) and then subtract 3 parts. Teaching the inverse operation concept to struggling learners can be a challenge for any teacher, but if you remember to begin with a picture it will make your life much easier! If you are in need of a lesson to teach multiplication and division inverses I have a complete lesson plan in my store.