MUS people-problems, help!

[happyWImom]

We have used MUS Alpha, Beta, and are on Gamma.  Up until now, all has been great.  But, we are now entering the double-digit multiplication, and both my dd & I are having a hard time with the way he does it! :eek:   Part of it was the way I learned, but when he breaks it down into the form that is supposed to "help" you when you get to algebra-that's what we can't get!  For example 21

                                                                                                                                                                                  x 14 

                                                                                                                                                                                     84

                                                                                                                                                                                   210

                                                                                                                                                                                   294

                                                                                                                                                I know how to do it this way, and dd gets it, also.  But, he also wants it done this way:  20 + 1

                                                                  x10 + 4

                                                                    80 + 4

                                                                 200  + 10

                                                                 200 +90 + 4    Hopefully you see what I'm trying to say, here!  Now, my fear is that we won't "get" MUS when we get to algebra!!!  What should I do, then?  I am/was planning on using MUS for the next few levels, at least.  Will that be okay, and then should we switch to something else (what????) when we get to algebra?  Help-please advise!!

[mom2bee]

I don't use MUS but the way he separates the tens from the ones makes perfect sense to me. I would encourage you to give it a try for a little while longer before you switch since MUS--overall, works for your guys. Maybe work a little ways ahead of your daughter using base-ten blocks and one units so that you can get used to what is being done?

 

Just focus on the base ten concept. Base ten, the way that Mr. Demme seems to be doing it, can help you to see the logic behind adding/subtracting like terms later on when you start adding things like (4x + 11) and (7x + 2).

 

You would add the X terms (4x + 7x) and add the constants (11 + 2) and get 11x + 13.

[happyWImom]

I don't use MUS but the way he separates the tens from the ones makes perfect sense to me. I would encourage you to give it a try for a little while longer before you switch since MUS--overall, works for your guys. Maybe work a little ways ahead of your daughter using base-ten blocks and one units so that you can get used to what is being done?

 

Just focus on the base ten concept. Base ten, the way that Mr. Demme seems to be doing it, can help you to see the logic behind adding/subtracting like terms later on when you start adding things like (4x + 11) and (7x + 2).

 

You would add the X terms (4x + 7x) and add the constants (11 + 2) and get 11x + 13.

Can you tell that I got a D in algebra?  We have also started LOF from the beginning, which does have algebraic concepts (using them how you describe) and they seem to be easier for us.  Maybe since they're so much more basic.

 

Honestly, it is terrible when your brain just doesn't seem to "get it"!  My ds, however has a more mathematical way of thinking, and I am betting he will understand this.  Too bad he's not at the same lesson, or he could explain it to us!

[letsplaymath]

Are you actually getting out the MUS blocks and building the problem, or are you trying to do it as an abstract set of steps to follow? If you are using the blocks, you should be able to SEE each step and why it makes sense.

 

Multiplication with blocks means making a rectangle (thus there's an obvious connection with the concept of area). The LENGTH of the rectangle is the number of blocks in each row (in your case, 21 blocks in each row). The WIDTH of the rectangle is the number of rows (in your case, 14 of them). Then the AREA of your rectangle will be the total number of blocks: 14 rows of 21 blocks per row.

 

But the whole, big area can also be seen as four smaller sections, splitting the length and width along place value lines. That is, the length is split into the 20-block (2 tens) section and the additional 1-block section. And the width is split into the 10-block section and the additional 4-block section. So that means the big rectangular area splits into four smaller rectangles: 20x10 and 1x10 and 20x4 and 1x4.

 

Basically, the blocks are showing a physical demonstration of what the steps of the standard multiplication method did. If you watch yourself go through the standard method, you should see each of these four smaller multiplications. But for many people, we learned to do the steps of the standard method without understanding what they meant. The block method, by breaking out the place value steps and showing how they each work individually, is supposed to build a firmer understanding.

 

And this same block or box method (it's called the "box method" when you just draw the boxes on paper, rather than building the rectangle with blocks) will be super-useful in algebra, for multiplying polynomials and for factoring them, and even for learning to understand the quadratic formula. So it really is worth pulling out the blocks and figuring out what's going on.

[happyWImom]

Are you actually getting out the MUS blocks and building the problem, or are you trying to do it as an abstract set of steps to follow? If you are using the blocks, you should be able to SEE each step and why it makes sense.

 

Multiplication with blocks means making a rectangle (thus there's an obvious connection with the concept of area). The LENGTH of the rectangle is the number of blocks in each row (in your case, 21 blocks in each row). The WIDTH of the rectangle is the number of rows (in your case, 14 of them). Then the AREA of your rectangle will be the total number of blocks: 14 rows of 21 blocks per row.

 

But the whole, big area can also be seen as four smaller sections, splitting the length and width along place value lines. That is, the length is split into the 20-block (2 tens) section and the additional 1-block section. And the width is split into the 10-block section and the additional 4-block section. So that means the big rectangular area splits into four smaller rectangles: 20x10 and 1x10 and 20x4 and 1x4.

 

Basically, the blocks are showing a physical demonstration of what the steps of the standard multiplication method did. If you watch yourself go through the standard method, you should see each of these four smaller multiplications. But for many people, we learned to do the steps of the standard method without understanding what they meant. The block method, by breaking out the place value steps and showing how they each work individually, is supposed to build a firmer understanding.

 

And this same block or box method (it's called the "box method" when you just draw the boxes on paper, rather than building the rectangle with blocks) will be super-useful in algebra, for multiplying polynomials and for factoring them, and even for learning to understand the quadratic formula. So it really is worth pulling out the blocks and figuring out what's going on.

Shoot!  We did get the blocks out for the first few that he did, and sort of got it, but then when she started doing the other prac. probs, she didn't, and that's where we had trouble.  I know she is going to totally fight me on it, because it will take a lot more time, and she was understanding & whipping through the problems the "regular" way.  Bummer! :banghead:   

 

Thanks for taking the time to spell it out for me though, what you've said makes sense, and I do want her to know the reason behind it so that she will understand algebra & not take after me.

[MerryAtHope]

We have used MUS Alpha, Beta, and are on Gamma.  Up until now, all has been great.  But, we are now entering the double-digit multiplication, and both my dd & I are having a hard time with the way he does it! :eek:   Part of it was the way I learned, but when he breaks it down into the form that is supposed to "help" you when you get to algebra-that's what we can't get!  For example 21

                                                                                                                                                                                  x 14 

                                                                                                                                                                                     84

                                                                                                                                                                                   210

                                                                                                                                                                                   294

                                                                                                                                                I know how to do it this way, and dd gets it, also.  But, he also wants it done this way:  20 + 1

                                                                  x10 + 4

                                                                    80 + 4

                                                                 200  + 10

                                                                 200 +90 + 4    Hopefully you see what I'm trying to say, here!  Now, my fear is that we won't "get" MUS when we get to algebra!!!  What should I do, then?  I am/was planning on using MUS for the next few levels, at least.  Will that be okay, and then should we switch to something else (what????) when we get to algebra?  Help-please advise!!

 

I wouldn't switch just because you've hit a glitch here, especially since it has worked well all along.  He's wanting to make sure that you understand place value and how to multiply things out--when you hit algebra, you'll have to multiply equations that way. You're really not doing anything different than what he's saying to do--when you get "84" as the first answer, you multiplied the 4 times the 1, and the 4 times the 2 tens (or 20). With the 2nd line, you multiplied 10 (1 ten) times 1 and 10 times 20 (2 tens) to get "210." He's making that very clear by writing out what the numbers actually are--21 is 20 + 1. 210 is 200 + 10. When numbers in equations are replaced by X's and Y's, you'll multiply them out in a similar fashion (we can't add x+1 and get a number like x1 the we can add 20 + 1 and get 21--so he's showing with simple numbers that we're really multiplying equations already without really thinking about it).

 

Then, when you add your products together to get the final product, you add like things--hundreds to hundereds, tens to tens, ones to ones.  That's how he gets 200 + 90 (80 + 10) + 4.  In Algebra, you would add X squareds to X squareds, X's to X's, numbers to numbers--like things get added up together after you multiply. 

 

Does that help any?

 

Merry :-)

 

 

[happyWImom]

I wouldn't switch just because you've hit a glitch here, especially since it has worked well all along.  He's wanting to make sure that you understand place value and how to multiply things out--when you hit algebra, you'll have to multiply equations that way. You're really not doing anything different than what he's saying to do--when you get "84" as the first answer, you multiplied the 4 times the 1, and the 4 times the 2 tens (or 20). With the 2nd line, you multiplied 10 (1 ten) times 1 and 10 times 20 (2 tens) to get "210." He's making that very clear by writing out what the numbers actually are--21 is 20 + 1. 210 is 200 + 10. When numbers in equations are replaced by X's and Y's, you'll multiply them out in a similar fashion (we can't add x+1 and get a number like x1 the we can add 20 + 1 and get 21--so he's showing with simple numbers that we're really multiplying equations already without really thinking about it).

 

Then, when you add your products together to get the final product, you add like things--hundreds to hundereds, tens to tens, ones to ones.  That's how he gets 200 + 90 (80 + 10) + 4.  In Algebra, you would add X squareds to X squareds, X's to X's, numbers to numbers--like things get added up together after you multiply. 

 

Does that help any?

 

Merry :-)

Merry:

Yes, thank you!  I feel so dumb-but honestly, I need it really spelled out.  I do think I will need to do them myself, ahead of dd, so that I will have it down & be able to help her more.  Darn, I thought I was done with all of this!  Math was my worst subject-dread it!

[tomandlorih]

We have used MUS Alpha, Beta, and are on Gamma.  Up until now, all has been great.  But, we are now entering the double-digit multiplication, and both my dd & I are having a hard time with the way he does it! :eek:   Part of it was the way I learned, but when he breaks it down into the form that is supposed to "help" you when you get to algebra-that's what we can't get!  For example 21

                                                                                                                                                                                  x 14 

                                                                                                                                                                                     84

                                                                                                                                                                                   210

                                                                                                                                                                                   294

                                                                                                                                                I know how to do it this way, and dd gets it, also.  But, he also wants it done this way:  20 + 1

                                                                  x10 + 4

                                                                    80 + 4

                                                                 200  + 10

                                                                 200 +90 + 4    Hopefully you see what I'm trying to say, here!  Now, my fear is that we won't "get" MUS when we get to algebra!!!  What should I do, then?  I am/was planning on using MUS for the next few levels, at least.  Will that be okay, and then should we switch to something else (what????) when we get to algebra?  Help-please advise!!

We have used MUS from the beginning and are in Epsilon this year.  When we got to those couple of lessons .. I just taught dd the first way you listed because she "got it" that way.  I hope this doesn't mess us up for Algebra but she gets base ten/place value fine..  But this was just odd so we skipped it.  It's just a couple of lessons though and then he moves on.  

[Guest]

Mr. Demme often shows several ways to work a problem to meet different kids learning styles.  For example, in todays lesson, he showed three different ways to do a problem.  He said on the dvd that he showed all the different ways so the teacher could use what works best for her kids learning style.  If your child understands it the first way I would move on, and not worry about it.