New question since my last math post

[Tiramisu]

With the help of kind souls, I started having DD10 do math on PDF printed graph paper at a 2 squares per inch setting. I copied problems from the intensive practice workbook and she got the right! No frustration!

 

However...

 

Even though I had put a zero in the partial product of the first couple of the problems as a reminder that she was multiplying tens, she disregarded that. What she did to get the correct answer is to add the partial products on an angle. By doing so she showed she was aware of the place value and respected it to get the correct answer even though it wasn't apparent if you just looked at the partial products.

 

I don't know if what she did would make sense to anyone based on my description. ??

 

Basically what looked like she was messing up by not lining up right was a little more complicated. Now with the grid, things line up neatly, but she's created her own method.

[regentrude]

can you post a pic? I have no clue what you are saying

[Monica_in_Switzerland]

I see what you are saying.  

 

My advice would be, if she clearly, CLEARLY understands why her method works... why not?  The difficulty would be if she ever needs her work graded for some outside class or test in the future.  However, by the time she gets to that sort of class or test, in all likelihood she would solve a multi-digit multiplication with a calculator.  

[Tiramisu]

can you post a pic? I have no clue what you are saying

I haven't been able to upload pics to the forum on my phone. And I'm sorry I can't describe it better.

 

Imagine she is multplying 123 by 45. She multiples the 123 by 5 first and writes down the partial product 615. Then she multiples 123 by 4 (which is really forty) and writes 492 directly under the 615 (so that the place value positions are not correctly lined up vertically). There is a zero after the 2, on the end, so 4920 ( the correct partial product) is written down but moved one position to the right. Finally, she adds the 615 and the 4920 on a diagonal so the place value matches and she gets a correct answer.

Edited October 18, 2016 by Tiramisu

[mtomom]

It sounds like it works for her, and that she does understand she's got to think of place value in that she's doing the diagonal adding.

 

However, it would bug me that she's writing them in a way that doesn't show place value. I guess she wouldn't forget if she always does it the same way, but given she's just starting with this (?) I think I'd ask her to practice lining them by place instead.

[Tiramisu]

It sounds like it works for her, and that she does understand she's got to think of place value in that she's doing the diagonal adding.

 

However, it would bug me that she's writing them in a way that doesn't show place value. I guess she wouldn't forget if she always does it the same way, but given she's just starting with this (?) I think I'd ask her to practice lining them by place instead.

 

I think I'm going to do this. I may draw a black box around the problem, only leaving room for the spaces that she needs to use, and no extra spaces to the right beyond where the ones place value column would be.

Edited October 18, 2016 by Tiramisu

[wendyroo]

Yeah, I would try to nip that in the bud.

 

I always tell my kids that getting the right answer is actually one of the less interesting goals of math.  On a deeper level, the true goal of math is to communicate and share ideas.  Math is a language, with commonly accepted definitions and syntax and grammar.  When "writing" in math language, it is important to consider if others would be able to understand the ideas you are expressing.  Would someone be able to look at your work and clearly pinpoint where you made an error?  Would someone be able to learn from your work and seamlessly expand on it?  If you died mid-equation, would someone be able to step in and finish your mathematical magnum opus?

 

Strive for clarity...line up your place values.

 

Wendy

[Tiramisu]

Yeah, I would try to nip that in the bud.

 

I always tell my kids that getting the right answer is actually one of the less interesting goals of math. On a deeper level, the true goal of math is to communicate and share ideas. Math is a language, with commonly accepted definitions and syntax and grammar. When "writing" in math language, it is important to consider if others would be able to understand the ideas you are expressing. Would someone be able to look at your work and clearly pinpoint where you made an error? Would someone be able to learn from your work and seamlessly expand on it? If you died mid-equation, would someone be able to step in and finish your mathematical magnum opus?

 

Strive for clarity...line up your place values.

 

Wendy

I like this!

 

I have the borders for tomorrow's work pencilled in. I hope that by doing it this way for a bit, it will sink in. But I imagine I may have to do at least one of those types of problems each day for the rest of the year if I want her to really remember it. She is very slow to develop automaticity.

[letsplaymath]

There are MANY "right" ways to do multiplication, and it sounds like your daughter has invented a version of the lattice method. There's no reason why she shouldn't continue to use her method. The fact that she knows to add on the slant shows an understanding of place value.

 

One of the freedoms of homeschooling is to let kids do things in ways that make sense to them, without forcing each unique peg into the standard schoolish hole.

 

We each have to choose our battles. There are some things we must insist our children do the standard way, and others where we can give them freedom. If her method bothers you enough that you want to fight a Do-It-My-Way battle, that's for you to decide. But her method is sound, as long as she keeps place value in mind.