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Kim F
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| Posted: Jan 16 2007 at 8:37am | IP Logged
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Not sure if Living Math is the correct place to say my 4th grader's math is "killing" me?? If anyone can help us I would greatly appreciate it. I probably should not be attempting to figure this out when I am this tired but she truly is not grasping the place values nor the order of operations for multi-digit multiplication. I can't seem to figure out the manipulatives involved for multiplying say a 3 digit number by a 2 digit number like 234 x 52?
We began with our manip's and did 234 x 2. That was easy. She made two groups of 4units, 2 groups of 3 tens, and 2 groups of 2 hundreds. What I can't figure out how to show her is how to progress to multiplying the 234 by the 5 tens. It requires way too many base ten blocks to show 50 sets of 4 units and 50 sets of 3 tens etc.
Leonie are you out there??
If anyone has the MUS explanation for this or any other tips I would greatly appreciate it!
Kim
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lilac hill
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| Posted: Jan 16 2007 at 8:56am | IP Logged
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Kim,
There is a very helpful Yahoo group of MUS users--they may better be able to answer this question, I know they helped me in the past.
Short MUS answer that I recall:
"Mittening"--when multiplying larger numbers that end in zeros, "mitten" or cover up the zero(s), do the multiplication and add the zero or zeros to the answer. Here I practiced/started with problems like 2x10 and 4x100, problems that we could do simply and with blocks or Momopoly $..
With my less that enthusiastic math minded DD we do keep the MUS steps (rather than doing the short cuts--for instance, right now she is using prime facotrization to reduce fractions instead of dividing by a common factor or the GCF) in place for a lot longer than I think she should, but when she is ready she moves to the next level, I just have to hold myself back from pushing.
Another thing, when we had division troubles, I generated sample problems or bought a workbook from the grocery store tha t had the kinds of problems I needed and worked on them until she could do the problems, AND, explain to my why she was doing what she was doing.
I just took a few day break from the MUS book until we were ready to move on.
Best wishes,
Viv
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Viv
Wife to Rick (7/83), Mom to dd#1(6/87), dd#2(1/90), and dd#3(6/94) in central PA.
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ALmom
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| Posted: Jan 18 2007 at 5:50pm | IP Logged
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I have shown it without the manipulatives but showing the steps on paper.
Ie 126
X 23
__________
18 units
12 tens
4 tens
etc. and adding at the end. Having lined paper so all the columns match up does help. My boys hated manipulatives so while I could use the explanation and it helped them understand why better, they shut me off if manipulatives came out.
I also have shown the connection between the shortcut and the other way - both legitimate ways of keeping track of units, tens, hundreds... etc.
We are in the same place with our 4th grader and I just did this with him and light bulbs went off.
Janet
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mom3aut1not
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| Posted: Jan 18 2007 at 7:44pm | IP Logged
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Kim,
The way I did this in the past was to go very much step-by-step and to stress patterns and properties of mathematics. This took as long as needed. I did this with two bright autistic kids, (autistic kids are notorious for having trouble with generalization. This was particularily true of my younger dd) and it worked well. No text did it exactly this way so I just sat down with paper and pencil. (My kids had worked a great deal already with cuisenaire rods and base ten materials and could visualize the initial problems I made up.)
1. First talk about 2x10, 3x10, and so on. Try to get the student to see the pattern. Also try to use a problem they can easily see or already know; I find that 2x10 is a good one to start off with.
2. Remind the student about the communtativity of multiplication (teach it if you haven't*) and go over 10x2, 10x3, etc.
4. Then talk about 2x20, 2x30, ...., 3x20, 3x30,.... and again attend to the pattern.
5. Again use commutativity to cover 20x2, and so on.
6. Then try something like 3x25 (single digit by double digit). Separate the problem into two parts 3x25 = 3x20 +3x5 (refer to the distributive law. Again teach it if necessary*). Then add the answers.
7. Try a number of such problems until the procedure is clear.
8. Then try 20x10. Refer to the pattern we saw in #4. Gently guide the student if necessary to see that 20x10 is 200 and follows the same pattern. Do a few more similar problems and lead the student to the pattern in general.
9. Now to 34x45 or a similar problem of your choice. Break it into four subproblems: 34x45 = 30x40 + 30x5 + 4x40 + 4x5. Solve the subproblems and add the result. Write the problem in the following way:
45
x34
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1200
150
160
20
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1530
10. After the student is comfortable with this, show the standard notation and how it connects to this notation. Do this for a while.
11. If your student is really comfortable with this, extending it to three or more digits is much less time consuming-- they "get it" pretty easily.
*Teach these properties before you start this if at all possible. Personally, I would delay mult-digit multiplication to teach these two properties. Use manipulatives and math stories to make these properties concretely real to the student.
HTH.
In Christ,
Deborah
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Kim F
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| Posted: Jan 19 2007 at 6:15pm | IP Logged
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Thanks - will give it another try on Monday!
Kim
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Leonie
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| Posted: Jan 20 2007 at 10:08pm | IP Logged
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We've aproached pretty much like Deborah and Janet - and with experience they seem to get it. Let us know how it goes Kim and if we can find any more info to help....
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Leonie in Sydney
Living Without School
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4Real Forums : Living and Loving Numbers
Topic: Multi-digit multiplication
