Teachers: How Do I Teach This Math Concept?

My oldest grandson is in 6th grade and is having trouble with Math/Arithmetic. He got a ‘D’ on his first report card, so his Mom and I have started him on practicing math after school at a website called IXL.com. This is a site that is recommended by our county school system, and we have been using it for weeks now for our youngest grandson in 1st grade.

When we realized the the oldest grandson was struggling with math, I set up a new account and started him at the 4th grade level just to see at what level he really needs to be.

His first set of problems were called “Number sense: Convert between place values” and included problems like:

*1. Solve: _________ten millions = 700,000 hundreds

  1. Solve: _________hundred thousands = 70 ten thousands

  2. Solve: _________hundred millions = 40,000,000 tens

  3. Solve: 5 hundred millions = _________ thousands*

It seems that he was not taught this concept when he was in 4th grade, and my grandson doesn’t have a clue about how to solve a lot of these. I can’t figure out how to teach the concept to him, and to be fair, I can’t get a lot of these right without a calculator.

Are there any shortcuts to solving problems like these, or is there a way to think about problems like these that I can pass along to him?

If I was solving this, I would just add in the zeros.

For example, (wait, I’m not doing your homework for you, am I?) :

700,000 hundreds = 700 000 00 (because the hundreds have 2 zeros) = 70,000,000 = 7 ten millions (ten million has 7 zeros)

So you have to know how many digits “hundred millions” and “thousands” have.

I’m not a math teacher, but I love math.

If I’m interpreting the math problem correctly it’s a “shifting the decimal” place problem.

I imagine your grandson knows about money. 1 dollar = 100 cents. The name of the unit shifts the decimal place. You can do it visually with distances too. 1 meter = 100 cm = 1000 mm. And of course the other way. 10 mm = 1 cm = 0.01 meters. Get a ruler. Draw it. Move the decimal place. I’d bet he can solve that pretty easily.

I find the problem, as written, rather confusing myself.

Rant: I may be a terminology thing. I was always very good at math (and majored in physics) and currently work computer science stuff (writing code). I continue to have problems with terminology, particularly in math and programming. The phrase “Convert between place values” makes little sense to me. Once you show me what you want, I can do it easily. I just don’t call it that :slight_smile: It’s my little math/science pet peeve. I bet it turns off lots of folks who would otherwise find math quite easy.

I have to add, this isn’t so much a math problem as it is an english problem. In order to solve the problems, one must know what the english terms hundred, thousand, million, billion, etc mean and what they look like when written out in numbers. Wouldn’t hurt for congress to take a refresher course on this material.

Yup. Me too. I think the actual concept is pretty clear and straightforward, but the terminology seems to make the problems needlessly complicated (they’ve gotten my head twisted around) and I am having a problem with trying to explain this to my grandson.

I am also assuming that this particular concept, and the way that they are worded, is a State requirement, so I am reluctant to disregard the entire set of problems at this time.

Still, my grandson is now in 6th grade, and these problems are shown to be at the 4th grade level.

Heh. No, It’s been a very long time since I needed to do homework like this.

I’d just add on the zeros (write them out as numbers), then make them balance by canceling the matching zeros (or, conversely, making sure they have the same number of zeros when you fill in the blank).

The first would be:

_________ten millions = 700,000 hundreds

_________ 0,000,000 = 700,000 00

To make them match you need a 7 in the front of the left one.

So for the second one:

_________hundred thousands = 70 ten thousands

_________ 00,000 = 70 0,000

_______ = 7

And the third:

_________hundred millions = 40,000,000 tens

_________ 00,000,000 = 40,000,000 0

_________ = 4

And the last:

5 hundred millions = _________ thousands

500,000,000 = ________ 000

500,000 = ______

I’m a “math person” with lots of tutoring and teaching experience, and I also find these problems confusing. One thing that makes them tough is that they dive right in to millions, hundred thousands, etc. Try these:

6 tens = _____ ones

2 hundreds = _____ tens

4 thousands = ______ hundreds = _____ tens

If those are tough, break it down further:

1 ten = _____ ones

1 hundred = _____ tens

1 thousand = _____ hundreds = _____ tens

If he can get that, say, 1 hundred = 10 tens, then go back to, “How many tens in 2 hundreds?” If he struggles with that, reinforce with something like, “If there are **ten **tens in one hundred, how many tens in **two **hundred?”

The important recognition here is that the decimal place value system is based on powers of 10, and there are 10 of each “thing” inside each “next bigger thing,” i.e., ten hundreds in a thousand, ten “ten millions” inside each “hundred millions” and so on.

Another important and relevant skill that make this tough for some students is the inability to quickly multiply or divide by powers of 10 by moving the decimal point and/or adding/subtracting zeroes.

Can your grandson do 53 x 10 quickly? How about 6,300 divided by 10?

Basically, the problems you posted need to be scaled back and built up to.

I hope that helps!

Okay Jas09, shiftless, MobiusStripes and yearofglad. This is starting to penetrate my thick skull. I’m seeing a way to think about these problems in a way that I can teach my grandson.

I do appreciate your help.

I’m pretty sure that he manages this okay, but I’m going to find out later today.

And I am glad to hear that a pro thinks that these sorts of problems are confusing. Maybe I’m not a total bonehead.

The first thing to understand is how we count. We count by singles, until we have completed a group of 10. So, 10 is written with that lovely zero to show that we have 1 group of 10, with 0 singles. We continue counting, up to 20. And, what is 20? It is 2 groups of 10, with 0 singles. Let’s take it all the way to 100. We have now reached 10 groups of 10, with 0 singles. Another way to say that is that we have 1 group of 100, 0 tens, and 0 singles. How about counting to 1000? Now, we have 100 groups of ten. Or, 10 groups of 100. Next is 10,000. Which is–10 groups of 1000 or 100 groups of 100, or 1000 groups of 10.

Notice that as you complete a multiple of 10, you add another 0. 1 is 1. 10 is ten 1s. 100 is ten times 10 1s. 1000 is (ten times 10 1s) times 10.

Once the basic concept is clear, carry it through to higher numbers.

The concept of ones, tens, hundreds is taught as early as Grade 1, and thousands in Grade 2, based on my past 15 years of watching and helping my mother prepare her classroom for those grades (in Québec, but I’m sure it’s very similar in other places!). By grade 4, it is reasonable to assume that the terms “millions” has been introduced, because it’s just more of the same. Your grandson might not specifically remember these types of problems, but the conceptual level is definitely something he would have been expected to reach.

I think your grandson could be helped by looking at a number, say 2345 and figuring out how many ones, tens, hundreds and thousands there are. Then re-introduce the concept of “ten thousand” and decompose a series of numbers in that range, then “hundred thousand” and then “million”.

If he can tell you how many of each grouping there are in 7 639 032 and similar numbers consistently, then you can start mixing it up with the written words as well (for some students, they can learn the words and/or learn the numbers but struggle with things like “2 thousand”; it’s just the way their brain is wired). By this point, he should be able to tackle the problem as presented in the OP. It’s a really weird question, especially because it’s using terms that we don’t use in normal speech “seven ten million” but in the end, that’s all this is.

I think by grade 6 your grandson is going to be or has been introduced to fractions and decimal values. Getting him really comfortable with “ones, tens, hundreds” will help him understand “tenths, thousands, hundredths”.

Good luck! I think it’s great that you’re helping out your grandson!

My niece and nephew (age 16 and 15, believe it or not) look at me like I’m growing another head when I ask them to do this sort of thing, or any kind of “real world” math at all. It came up specifically when I was quizzing them on tipping and explained how easy it is to tip around 20% - you just move the decimal place and double. Huh? And they gave me the most crackpot insane answers when I made them do it at a restaurant - they have no concept of “hey, does this make sense?”

Same thing when I had them add up what we bought at the grocery store for dinner and divide to find how much we spent per person. “Honey, does three cents a person make sense with these numbers?” “Huh?”

I think you’re right. I also think that putting the “fill in the blank” part on the right side of the equation, as you’ve done, makes it slightly clearer how to approach the problem.

The way I’d think of problems like the OP’s is as a two-step process:

“Solve: _________ten millions = 700,000 hundreds”

Step 1: What is 700,000 hundreds?
Step 2: Now, how many ten millions is that?

I cannot recommend this site enough, short to the point videos that he can watch and rewatch as much as he wants.

Ask him if he remembers putting numbers into expanded form. That’s when you convert 8,042 into “8x1000+4x10+2”. Perhaps he never quite understood that concept. Or perhaps he just doesn’t understand what “6 tens” means. I bet it’s the second, actually.