“As long as algebra is taught in school, there will be prayer in school. ” -Cokie Roberts

“It is hard to convince a high-school student that he will encounter a lot of problems more difficult than those of algebra and geometry.” -Edgar Watson Howe

I woke up this morning and looked at the stuffed animal my parents brought back from Germany a few years ago. It’s a purple cow. I know, you’re probably saying the purple cow poem in your head. I love the cow, not because it’s purple, but because it has been a perfect tool to introduce algebraic thinking to many groups of students. When you squeeze its stomach it moos 3 times.

Here’s how I do it. Before I begin the lesson, I place the cow in a large, brown shopping bag with the top folded down. I call this The Mystery Bag. The Mystery Bag The children use deductive reasoning to guess what is in the bag. I can only answer questions that can be answered with yes or no. I only allow 10 questions, so the students have to work in groups to develop the questions that will best guide them to what is in the bag.

After the students have guessed what is in the bag, I squeeze the cow. The cow moos 3 times per squeeze. I ask the students to think about how many moos the cow will make if I squeeze it 3 times. I have counters, pencil and paper, and calculators available to each group.

After I have given each group enough time to think about it, I record their responses on the board. I also ask them to share with the whole group how they thought about the answer. Sharing their thinking is very important because it gives the students the chance to hear how others think. It also is a time to “think about your thinking.”

I ask the students if there is a way to write about the squeezes and the moos. The students come up with many ways to do this. After recording each of these on the board, I ask them if there is an shortened way to write 1 squeeze = 3 moos. The students eventually determine that 1s = 3m is the shortest way to record it.

I then write 3s = _m and 5s = _m on the board. I ask the groups to think about what number would go in each blank and why. After giving think time, I ask several students to share how they determined the answer.
I then write _s = 18m and ask them to determine how what will go in the blank. Within just a few minutes the children have been able to determine the answer.

The activity continues with the students generating problems, writing them on the front of a folder, placing the answer inside, and passing them to the next group to solve.

At the end of the lesson we talk about the fact that we have just “thought like a high schooler.” They are THRILLED with themselves and are encouraged to go home and tell someone they were doing algebra.

You can study for years about algebraic thinking. Every article you read about the topic will include a bibliography with more articles about it. My primary goal with elementary level students and teachers is to remove the intimidation of algebra. Hopefully, after reading this post, you heart won’t start beating faster thinking about x and y. Remember, it’s really just a squeeze and three moos!

“The most difficult thing is to just start the ball rolling. Once it starts, it’s actually more difficult to stop it.” -Butch Lovelace

By the way, Gelet Burgess, author of “The Purple Cow,” hopes to be remembered by all his other works. He also says he wished he’d never written the one that all of us can quote…