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.”
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?
“They are even!”
“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.
RAZ ON FIRE