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Explaining subtraction word problem
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My son(8) understands basic subtraction word problems like this: “Frank had 15 oranges and gave 5 to Charles: how many did Frank then have?”
But for these he has a real hard time understanding how to work: “I sold a ball for 12 cents, which cost me 8: how much did I gain?” He keeps telling me he has 12 cents since that is how much it sold for and I am having a hard time explaining that you have to take away the original cost of the ball to you in order to find out your profit. Any thoughts on how I can use manipulatives or something visual to explain this? I’m not coming up with anything that is working well.
It seems like the issue is the order in which the events happened. Maybe if you discussed the sequence of events first, then acted it out. For example, What three things are happening in this scenario? In the word problem the order they are mentioned is: Sell the ball, buy the ball yourself, figure gain/profit. But which one actually happened first? (Can you sell the ball if you haven’t bought it first?) Next? Last? Now let’s act it out with a ball and 12 pennies. Would something like that help him think it through?
Thank you Sonya, I hadn’t thought of the order of events because he was still focusing on the fact that he sold the ball for 12 cents so that had to be how much he made. I think I will give him 10c to start with and have him buy the ball, then sell it and see that he has more money. Then when he understands the whole process I can show him that he can get the same answer by just subtracting the cost from the profit.
There is a lot complicated with that word problem….
1) the concept of “gain” or profit
2) the order of information given is out sequence
3) the answer isn’t the “final state”
Now, there isn’t anything wrong with any of those things – but if he is used to “you start with this, something happens to change it, what do you end up with” – and then gets this problem – yes, he is going to struggle with it…. having 3 complications thrown at him at once….
He needs to start off with things that have just one complication… like….
Bob started out with a number of balls. He was given 3 more, and now he has 5. How many did he start with. (complication 3)
or
Bob was given 3 balls. He started with 2. How many does he have now? (complication 2)
eventually that can move to ones that have a couple of complications…
Bob has 5 balls today. Yesterday he had 2. How many was he given? (complication 2 and 3)
And I’m not sure how to explain “gain”….
Are there other questions like this he has to answer? If not – I’d just skip this one for now….
Suzukimom, he has had several of the type of problem you mention and not had to much problem with them. It does take him a bit longer to think it through, but he does eventually get it without any help. These questions with finding the profit are the only ones he has big problems with. The profit problems are usually stated as I alread mentioned or switched around with the purchase first then the sale. There are maybe 2 problems out of 10 that are like this. The biggest problem he has is focusing on the fact that if he sold if for 12c then he thinks that is how much money he made. He isn’t understanding that you have to factor in the purchase of the item to get the profit. Hopefuly if he acts it out a few times he will see why he has to factor in the purchase and will better understand these problems.
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