“True scholarship consists in knowing not what things exist, but what they mean; it is not memory but judgment.” -James Russell Lowell

Do any of you remember being thrilled about learning how to simplify fractions? I memorized some rules for how to do it and used these rules to complete worksheets filled with fractions. My brain didn’t crave memorization of rules. My brain needed something that helped me understand!

I worked with a group of 4th graders a few weeks ago. In Tabor Rotation, this whisper grouping might occur during Teacher Time on Days 2 & 3 or during Readiness Grouping on Days 4 & 5. I was differentiating instruction based upon readiness after I quickly pre-assessed what the students knew about GCF and simplifying fractions. I was differentiating based on learning style by having students manipulate number cards and yarn to create a factor rainbow.

My assigned job was to help them complete a worksheet on simplifying fractions. They told me that their teacher hadn’t really explained how to do it, or why they were doing it. They just knew that simplifying fractions was on the state test and they’d better learn it.

For the two overachievers in the group, the knowledge that it was on the upcoming state test was enough to get and keep their attention. The others in the group needed more. I asked them if they knew what a GCF was. No one did. That gave me a starting point. I opened my rolling case of math tools. This time I was reaching in for hands-on activities for factorization.

As I pulled the hands-on activities out of the case, one of the children commented that I was like Mary Poppins when she opened her suitcase and pulled out so many items. I consider this a great compliment since I’ve admire the way Mary Poppins transformed children. The children learned while having fun—just the way I like it!!!

I told them we were going to make a Factor Rainbow and by doing that we would learn what GCF meant. Each pair of students took pieces of brightly colored yarn and made rainbow in front of them. They then took an envelope with a number on it and the factors of that number inside of the envelope. The first pair to make the factor rainbow correctly would win that round and select the next set of envelopes.

The first set of envelopes had the number 16 on it. The pairs laughed as they placed the number 16 at the top of the rainbow and the factor pairs of 1, 16, 2, 8, and 4 to form the rainbow. In less than a minute, everyone has their factor rainbows made and their hands on their shoulders. Each pair explained how they placed their factors and how they knew that the numbers in the rainbow represented all the factors for 16.

The fastest pair chose the number 12 envelopes for the next round of the game. I asked them to place this new “12” Factor Rainbow next to the “16” Factor Rainbow. As before, the pairs laughed as they placed the factors and gave each other “high-fives” when they finished. Another discussion of what they were thinking as they created the second factor rainbow followed.

I asked them to look at each of the Factor Rainbows and find the factors that the two numbers had in common. We put buttons next to these common factors. I asked them to find the factor that each had in common that was the greatest and hold it up. Everyone held up the number 4. I asked them if 4 was the greatest common factor of 16 and 12. I wrote greatest common factor on a white board sitting next to me.

That’s when the “lightbulb” moment happened! One of the girls in the group yelled out, “That’s GCF! We found the GCF! GCF stands for greatest common factor!”

With much enthusiasm and curiosity, the group and I created Factor Rainbows and found the GCF of 3 more pairs of numbers. Now, we were ready to use this information to simplify fractions. The students in that group will never forget what a GCF is.  PRICELESS!!!

(What does this have to do with simplifying fractions? Read next Friday’s Games Blog and find out what happened next!)

“My life has no purpose, no direction, no aim, no meaning, and yet I’m happy. I can’t figure it out. What am I doing right?” -Charles Schulz, creator of the Peanuts comic strip