My son has had no formal instruction in fractions. Children are naturally curious. He quickly was able to figure out the value of each colored fractional piece by using concrete materials.
I asked what is one of those pieces worth? Two of the pieces? Etc…
Then I asked him if we could cut the black “candy bar” into 100 pieces?
“Yep” he said. He instantly grabbed the pen and started to try to show me the size of what one hundredth would look like?
This stumped him for a bit. He made it into 20 equal parts, then tried to cut the 20th into parts. After cutting it into 80ths, he said, “Oh, boy… I needed to draw one more line…” he did and then he said, “These are the approximate size of a hundredth, mom.”
I then asked, “What are you noticing about the half and the hundredth?
He said, “The half is much larger.” So, I asked… “what is happening when we cut the candy bar into pieces?” He said, “The more pieces there are, the smaller the part.”
“Give me more mom!”
I grabbed the 1/2 piece. How many ways can you make 1/2? He instantly went to work. He found 2/4, 3/6, 4/8, 5/10, 6/12. Wrote each of them like: 1/2 = 2/4.
I then circled all the denominators of the equivalent fractions. I asked, “What do you notice?” He said, “2, 4, 6, 8, 10, 12! They are counting by twos!”
Yes. What else do you know about those numbers?
Long pause.
Hmmmmm…
…
I waited.
…
“They are even!”
Yes! I said. Now what if we cut this candy bar up into sixteenths? I wrote: 1/2 = /16. What would make an equivalent fraction?
“8/16ths!”
“Give me more mom!”
So I wrote: /20 , /100…
“Too easy mom…come on! 10/20ths and 50/100ths. You are going to have to do harder than that!”
So I wrote: /80 , /150, /96.
Handed him the pen. And watched. He put 40 above the 80 and 75 above the 150… instantly. Then paused at the /96. In about 5 seconds he wrote 48/96.
I asked, “How did you figure the last one out?”
He said, “Well, I broke the 96 up. First I thought of 80. Half of 80 is 40. Then I took half of 10, that is 5, then I just had 6 left. Half of that was 3. Soooo…. 40 + 5 + 3 = 48! Half of 96 is 48, so 48/96ths = 1/2″
(80 + 10 + 6 = 96)… He took half of each of those and added.
I did not directly teach him one thing. He made the connections and the discoveries with my guidance. Took all of 25 minutes! Asking the right questions is the gateway to a child’s natural propensity for curiosity.
RIGOR
VS.
VIGOR
Passionately Submitted,
RAZ ON FIRE
IGNITE! ... Fire is Catching 
Hello! I was inspired by your ingenious twist on CC to Curiosity and Creativity, as well as your use of rigor vs. vigor to develop a chart comparing the characteristics of each. This is just a draft, and I would appreciate your feedback. When it’s finalized I would like to distribute it in my state (RI). I would like to acknowledge that your original ideas sparked my thinking. Please let me know what you think. Sorry that the formatting didn’t work well when copying and pasting, but I think you can see what I mean. Thanks!
“A Tale of Two Teaching Paradigms”
CC (Common Core) CC (Curiosity/Creativity)
Standardized input for all Varied input according to student interests and needs
Rigor—death of imagination Vigor—nourishing of imagination
Prescribed texts and scripted questions and answers/dead end learning Flexibility in curriculum, open ended questions and answers/exploration
Produces disengaged youth Empowers engaged youth
No space for student voice Encourages student voice
Pushes out art, music, drama, phys. Ed Embraces art, music, drama, phys. Ed
Competition Cooperation
Demeans teachers’ professionalism Acknowledges teachers’ professionalism
Goal of workforce training Goal of self-actualized participants in a rapidly changing world
Overuse and misuse of mass administered standardized testing Diagnostic assessments to improve teaching methods to meet individual needs
Intrusive data collection that parents cannot control, released to 3rd parties for “research” or marketing Data kept within the school for necessary educational purposes and not released to 3rd parties for “research” or marketing
“personalization” via computer algorithms with adults to monitor performance Personalization from experienced, knowledgeable, and dedicated human teachers who interact compassionately with students
Putting children in front of computer screens/hand-held devices for more and more of their “learning” time Encouraging children to examine and explore the natural world and interact with each other and their communities
Exposing children both in school and at home to potentially toxic levels of wifi radiation from hand-held devices Limiting screen time and using the new technologies in exciting and creative ways
Molds students to become self-centered Opens students to empathize with others
Which do you choose for your child? Stand up for your children’s right to an enriching public school education!
LikeLiked by 1 person
Hi Sheila! I am so glad your thinking was “sparked”… This is my purpose for my blog. To spark knowledge. To spark ideas. And to hold a torch for our children… and our teachers… and our public schools. I like your ideas of the comparison. Really powerful. I would love to see it in its formatting! I would be wonderful to post it on my blog too! I would honor you as a guest author… piggy backing on ideas is beautiful thinking! Thank you for taking the time to share with me. My email address is: (for now) razmathr118@yahoo.com mailto:razmathr118@yahoo.com
My very best to you Sheila as you Crusade for our Children. Keep the Fire Burning!
-Raz
LikeLike
Great! Thanks so much! I’m going to finalize it with my group and then email the final version to you. You definitely are a divine spark!
LikeLike
Thank you Sheila! I’m looking forward to seeing what the contrast between Common Core and Curiosity and Creativity looks like…
-Raz
LikeLike