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Need new ideas on how to see mult/div

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Arg. I'm so tired of struggling with this. My DD does wonderfully when her word problems in math are addition and subtraction. However, as soon as multiplication or division are involved, she just can't see what operation to use. She can solve multiplication and division problems just fine, she just doesn't get their application I guess.


I have shown her over and over how multiplication works with many groups of equal size, repeated addition, and arrays. I've shown her division is taking a large group and breaking it into smaller equal groups.


Is there any other way than just pressing on and doing the same thing over again? We do have the process skills books, but they just aren't helping with this particular struggle.

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I used flash cards.  Every word associated with multiplication and division (groups, between, split, etc.).  After a few rounds of the cards, I handed the child a highlighter to highlight all the math words in the story problem.  Numbers get circled or highlighted as well.  It's too easy for kids to get lost in the sentence if they're not practicing knowing what to look for.

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Where did you start with the process skills books?

I began with book one, even though the math was beneath him.  I sit with my son for each problem. We do it on the white board. If he needs my help, we rework the problem again the next day. If he completes it on his own, I put a check mark in the spot so we know to skip it in the future.  I sometimes have to prompt him to draw the problem, but the act of drawing the models can help him think through what needs to happen in the problem. Starting in those early books helped him learn how to think his way through by drawing the bar models. I do think memorizing that "of" means multiply is helpful.


I like c-rods for really understanding what multiplication and division do, but it sounds like that isn't really her issue.

Edited by sbgrace
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Very good ideas.  Thanks!


Is there a good listing of cue words to look for?  I know that method isn't foolproof because we tried it a few years ago, but it would be a start.


I usually have her draw what is happening in the problem, but she really dislikes it.  We started out in book 3 for the Process Skills books because her addition and subtraction word problems were fine.  Should we have started in book 1?  She does in general struggle with the bar method as well as when we use c-rods.  Other manipulatives seem to work better for her.  Maybe that signals that we should work on bar methods more, I don't know.


Multi-step problems are definitely an issue.  However, even more simple ones still stump her.  For example, she had a problem solving something like "Somebody needed 30 feet of rope.  The rope cost $1.25 per foot.  What is the cost of the rope?"

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For some kids the main issue is waiting for the problem to be completely understood before starting work on the arithmetic of it.


That was a biggie for my DD. 


I sat with her over and over and taught her a two column method of solving things.  On the right we would write down everything we knew from the way the problem was written.  This was done in the form of equations.  Every time she wrote down an equation, we would check to see whether it was correct, and then read the problem again to make sure that every piece of information in the problem was written as an equation.  If there was information that had not yet been expressed, she would write another equation, and then recheck.  It was the rechecking that made her finally able to do well on these kinds of problems.


Then on the left she would start solving equations together and checking her work using the other equations.


Then she would check to see whether the actual question had been answered exactly.


Here is a simple example:


Patty has 2 sheep.  Jerry has 4 sheep for every sheep that Patty has.  How many sheep does Jerry have?


On the right:

P=number of sheep for Patty=2 sheep

J=number of sheep for Jerry.

J also equals 4 sheep for every sheep of Patty's.  To write that as an equation:

J=4 x P

Checking back, all of the 'given' information for the problem has been expressed as an equation.


Then on the left:

J = 4x P = 4 x 2



Checking back, the question was how many sheep does Jerry have, and the answer is 8 sheep. 


The reason the two column approach helped DD, I finally figured out, is that it separated but did not confuse expressing the word problem as equations, and actually solving them.  DD always wanted to jump straight to solving the problem, and without this approach often got kind of lost in the middle of it.

Edited by Carol in Cal.
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