Heavy Cookies, Undervalued Coins, and Misconceptions
Simple question to get us started…
Which is worth more?
And of course the answer is, “The quarters, because 50¢ is more than 20¢,” right? But not to a kindergarten student or a pre-schooler who hasn’t yet learned how much coins are worth. A young student might argue, “Four is more than two.”
Why didn’t the quarter follow the nickel when he rolled himself down the hill?
Because the quarter had more cents.
Recently, I was asked to review an educational video for kindergarten math that had a similar question.
The video stated, “Can you tell the green, yellow, and orange cookies are heavier? That makes sense, doesn’t it? Because there are more of them!”
This is the same logic that would lead one to claim that the value of four nickels is greater than the value two quarters because there are more nickels. It’s a huge misconception for students to focus on number rather than value. So it’s very frustrating to see this video reinforce that misconception.
For example, if each green, yellow, or orange cookie weighs 3 ounces, but each blue or purple cookie weighs 5 ounces, then the left pile would weigh 6 × 3 = 18 ounces, and the right pile would weigh 4 × 5 = 20 ounces, so the right side would be heavier. (Then again, are there really 6 cookies on the left and 4 on the right, or are some cookies hidden? Hard to tell.)
As far as I’m concerned, the only acceptable answer is that the pile of green, yellow, and orange cookies must be heavier — assuming, of course, that the balance scale isn’t malfunctioning — because the pans are tipped in that direction.
All of this reminds me of the poem “Smart” by Shel Silverstein.
My dad gave me one dollar bill
‘Cause I’m his smartest son,
And I swapped it for two shiny quarters
‘Cause two is more than one!
And then I took the quarters
And traded them to Lou
For three dimes — I guess he don’t know
That three is more than two!
Just then, along came old blind Bates
And just ’cause he can’t see
He gave me four nickels for my three dimes,
And four is more than three!
And I took the nickels to Hiram Coombs
Down at the seed-feed store,
And the fool gave me five pennies for them,
And five is more than four!
And then I went and showed my dad,
And he got red in the cheeks
And closed his eyes and shook his head–
Too proud of me to speak!