Fifth grade word problem from Singapore: Jim and Dan have $24 altogether. If Jim gives $2 to Dan, he will have three times as much money as Dan. How much money does Jim have?
Observe the mighty bar diagram in action:
The kid thinks, "I can see that $24 will be divided into four equal groups of $6. Jim will have 3 groups of 6...that's $18.
Method #2
Let j be Jim's money and d be Dan's money: j + d = 24; j - 2 = 3*(d + 2) so j = 3(d + 2) + 2 substitute in to the first equation: 3(d+2)+2 + d = 24 simplify: 4d + 8 = 24, solve: d = $4; j = $20.
They both have their charms.
multimedia learning (Catherine)
A bar model!
ReplyDeleteI'm so happy!
I read an interesting paper on multimedia learning the other day, one I think probably holds water.
The researcher argues that you should always try to have a visual and a verbal representation - he's found that's most effective. (These folks are talking about PowerPoint, that kind of thing.)
I suspect that all along I've probably just been talking about something as "simple" as visual AND verbal.
I'll find his paper and post a link.
Kids these day.
ReplyDeleteBack in my day, we didn't have any of those fancy-schmancy 'bar models'. We had to solve it the old fashioned way - by entering it into our TI-82s, and getting 'Syntax Error' for an answer. And by gosh, we loved it!
And no one has pointed out that the answers differ. Too kind. One is $18 and the other is $20. *L*
ReplyDeleteShould I edit it and fix it or let it stand?
IG ---
ReplyDeleteROFL!!!!!!
Myrtle - well I of course didn't manage even to notice the error ..... whatever that tells you!
ReplyDeleteActually, the bar model solution (#1) and the algebraic solution (#2) answer slightly different questions.
ReplyDelete#1 tells you how much Jim will have after he gives $2 to Dan.
#2 tells you how much Jim has now, which more closely matches the question (the giving is hypothetical - "If Jim gives $2 to Dan, he will have..."
Thus showing the importance of languange skills when doing math.
Thank you, Myrtle, for this illustration.
ReplyDeleteI’ve been paying little attention to the bar models Singapore uses, and this was a quick way to learn what it’s about.
I love it!