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Isolating A Variable Using Inverse Operations - CONCRETE STRATEGY

Student in fifth grade and up are dealing with the abstract concept of isolating variables using inverse operations. There will always be students that are having problems with this idea. If the book fails, then use the following method...

Write on the board the following for the objective:

Isolating Variables
Inverse Operations

Then for each word, break it apart on the board. Start with the word isolating. Many students don't know what isolate means. I use the word "alone" to describe isolate. Next, the word variables can be described as an "unknown." The word inverse is a tough one for students also. I usually show students my jacket and say, "the outside of my jacket is made of canvas while the inverse is made of whatever." They see that the word inverse means the "opposite." Lastly, I usually show the operations they are going to use like the addition, subtraction, multiplication, and division signs for now. Then draw an arrow from unknown to alone to opposite to the operations. See image below...

Say: "We are going to make the "unknown alone using the opposite operation." Just by saying this, students really start to understand what we are going to do today.

When you are ready to actually do the lesson (be sure not to skip other steps of the lesson like telling students why this is important and activating prior knowledge etc...) then it is time to tell a story.

Say: "Variable are loners, recluses, isolationists... (Explain what these are) They like to be alone. This variable lives in a house like you do. The variable is trying to be alone in his bedroom but the integer just won't leave him alone. In this problem, there is a 4 in his room. The X just wants him out. To kick out the 4 and to isolate the variable and make the unknown alone, we must do the opposite operation. So we need subtract the 4 because subtraction is the opposite of addition. But, the four didn't just disappear. It went into the living room. You must subtract the 4 in the living because that is where the 4 is going to hang out to leave the variable alone. Now the unknown, the X, the variable is happy. He is all alone in his room, just the way he likes it."

Are You Covering or Teaching?

It is apart of our American educational culture to talk about "covering material" in your classroom. Covering material, does not mean that you taught the material. You may be asking, "How can I tell if I'm really teaching?"

Teachers should check for understanding every 3-5 minutes of a lesson or more. If 80% have the concept, then you should move forward. If less that 80% have the concept then you should stop and reteach. Do not more on until 80% have the concept. Then, there should be built in time to deal with the 20% that did not grasp the idea. Checking for understanding is teaching...

What does checking for understanding look like?

  • hand gestures
  • mini white boards
  • choral responses to questions
  • think-pair-share
  • visual inspection of work
  • so many more!

  • Underused Resource for Teachers

    One underused resource for teacher is using the district or county office library. Librarians spend their whole day collecting, storing, organizing, and providing high quality standards based supplemental material for teachers and their students.

    For example, in 7th grade life science, we were in a unit about DNA. The school did not have the materials for the chapter lab from the book. So I visited my local county office library to see if they could help. It just so happened that they had a whole DNA lab kit. It wasn't the lab from the book, it was better! The lab was full of manipulatives and it provided a nice science lab booklet to guide our study. They also had nice books on DNA to supplement and provide students new books to read on DNA. Lastly, they had a DNA model that showed a magnified strand that stood 2 feet tall. Students actually said, "Today was so much fun!"

    Most district and county office libraries have an online system where you can order without traveling. Some will even deliver the order to your school site. Take advantage of these resources.

    The Power of 1, 2, 3

    When required to read from a textbook, students have a tendency to space out! To help prevent space out in text reading, teach students that at anytime they all may be required to read chorally. Practice choral reading together. One person may read, then you may prompt the class with 1, 2, 3. The whole class reads after 3. Mix it up so students never know if they will be called on to read together.

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