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Thousandth   

by Gail Englert

A response to the question:

How do I introduce the concept of thousandth, based on their prior knowledge of tenths and hundredths?

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How do I introduce the concept of thousandth to Grade 5, based on their prior knowledge of tenths and hundredths? Can you recommend activities for teaching the concept?

Emily

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Dear Emily,

What sorts of models did you use to work with tenths and hundredths? In my fifth grade classroom we use unit blocks (Dienes blocks), and we change the unit that names one whole often, so my students get used to using wholes of different sizes. One day a flat might be the whole, and the next day, it might be a long.

That makes it easier for me to help my students understand that each place value is ten times larger (or smaller) than the one next to it.

Once students see that relationship, it is not difficult for them to understand that thousandths are hundredths cut into ten pieces...

A fun activity that helps to illustrate this in a rather silly way is to talk about gas station price signs. Often these stations have 9 elevated numbers after the price number. It annoys me that they do that, since it sort of resembles an exponent. I refer to that number, and have students make observations on their way home to confirm it. Then, we draw a model of a "giant" penny (about the size of a paper plate) and cut it out. We use a protractor to divide it into ten equal parts, then cut it into tenths. I remind my students that a penny is a hundredth of a dollar. From that, we decide that each of the tiny pieces of penny must be a thousandth.

Hope this gives you a starting point.

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Dear Gail,

Do we tell the students how to write the symbol ie. 0.001 in the first place? When should we introduce that and how? What other models can we use besides the base 10 models? Are there any other "hands-materials" that we can use to teach the thousandths concept?

I need to create a worksheet and it has to be interesting and meaningful. Can you help me to think of some activities?

Emily

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Dear Emily,

I am guessing that your students already know how to write decimals in the tenths and hundredths places. If they have, then this is just another step in the development of their place value understanding. You should relate the decimal to the fraction, though. I am assuming they have an understanding of what the numerator and denominator mean. Relating 1/100 or 1/1000 would be a step in helping them visualize the relative magnitudes of the decimal amounts.

Have you played any counting games with the calculator? When you use the constant function on a calculator, and have it add 0.01, the students can see what happens as the number grows larger. If you do not have the number of decimal places fixed, when it gets to 10/100, the display will not read 0.10 because the calculator automatically leaves off trailing zeroes (at least, my Explorers do.) So, trying that same sort of activity with a + 0.001 constant could help students make the connection between tenths and hundredths and thousandths.

Surely they already write money amounts. This would be a good time to help them relate the place values they see on one side of the decimal with those they see on the other side. I do not know how advanced your students are, but they might be interested in what happens to the exponents as we move back and forth across the place value line. One side of the decimal point has positive exponents, and the other side has negative exponents.

As for other hands on materials, you can take 1 cm graph paper and cut some "wholes" from it, (10 X 10 squares), then some tenths (1X10 rectangles), and some hundredths (1X1 squares). Then, ask your students to cut one of the hundredths into ten pieces. (They could use the mm markings on their rulers...)

There are some really cute materials put out by Creative Publications. The ones that come quickly to mind are the decimal dog (which is a hotdog cut into tenths and hundredths, or hundredths and thousandths, depending on how you value the whole hotdog), and fries. My fourth graders loved playing with them last year.

Talking about an interesting and meaningful worksheet, I favor some sort of comparing acitivity, where they have to color/shade the two decimals and make discoveries about the relative sizes. I would love to hear about what you come up with.

-Gail, for the T2T service

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