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Place Value
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* place value up to 99
* base ten blocks and site
* place value and calendar math
* place value games for upper elementary
* place value activities for upper elementary
* place value process without numbers
* place value with decimals

* Place value up to 99

> I am currently teaching place value up to 99 to my class of
> 2nd graders. They can fill out a worksheet but I am not so
> sure that they gain the concept that 10 ones equal one ten
> and so on. Does anyone have a great hands on activity that
> they could share? Also, if you know of a great math internet
> site with hands on lesson plans and/or titles of books please
> send that along as well. Thanks in advance!!
> Candie, 10/28/00

craft stick bundless and milk cartons

We count the days of school we attend. I have taken milk cartons from the lunch room and covered them with construction paper. I have three cartons. They are labeled ones, tens, and hundreds. Everyday we put a craft stick in the ones carton. When we have ten we bundle them with a rubber band and put them in the tens carton. Every time we count up to ten we bundle and it goes to the tens carton. When we have ten tens we bundle them and put them in the hundreds carton. I have found this to be beneficial in helping them understand place value.

suzie-q, 10/28/00 on primary elementary board

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pennies and dimes on a piggy bank bulletin board

I also count the first 100 days of school. On a bulletin board I have a pig pink piggy bank cut out. Everyday we put up a penny (velcro spots on the bulletin board and on back of large paper coins). When we get 10 pennies, I take them down, change to a dime and stick it in the bank. Everyday we count the money orally. I teach first grade, and this really seemed to help last year.

vicki dugan, 10/29/00 on primary elementary board

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pinto beans, cups, and envelopes

I give each child pinto beans and small paper cups (the size for candy or medicine). Together we count our "cherries" and when we have 10 we put them in a "bucket." When we have filled 10 buckets, we fill a "truck" (business envelope). This is done on a mat that is divided into tens and ones. Each child must also write the number as we do it. This goes pretty slow because I keep them together but it is very effective and the kids seem to like it. We usually go to about 150. Most of the kids are ready to go on counting after this without the "cherries" but a few continue to need them and I let them use them. Eventually the class writes to 1000 (on their own after 150). This is a 2nd grade class.

Posted by Colleen on 10/28/00

* Base Ten Blocks and Web site for place value

> I am currently teaching place value up to 99 ... Does
> anyone have a great hands on activity that
> they could share? Also, if you know of a great math
> internet site with hands on lesson plans and/or titles of
> books please send that along as well.

I like all the hands-on activities already shared; the more hands-on work the better! And most of the materials mentioned are free. If you can afford them, I highly recommend the Base Ten Blocks (also known as Powers of Ten Blocks), which visually show the children that a 10 stick really is worth ten ones, because it is exactly the same as ten unit-blocks placed end to end. And the hundreds are exactly the same as ten ten-rods placed side by side. Some sets include a few thousands, which are exactly the same as ten hundreds stacked on top of each other.

The Powers of Ten blocks work best if you also have "trading mats" which you could also make yourself out of large paper (legal size or larger). Turn the sheet horizontally and divide it into thirds; draw a symbol for the ones at the top of the right section, a ten-rod at the top of the middle section, and a hundred block at the top of the left section. Then if children are doing two-digit addition or subtraction, they can illustrate the problems on the trading mat and show the trades needed. Example:

28 + 34

Set out 2 tens and 8 ones.
Below them set out 3 tens and 4 ones.
Now apply the rule mentioned in the other posts, that if you have 10 or more ones you need to trade for a ten.
So the child picks up 10 ones, trades them for one more 10, and now puts the upper and lower sets together, making 6 tens and 2 ones.

To subtract:

31 - 14

Set out 3 tens and one one.
You cannot take away 4 ones yet.
Trade one ten for 10 ones; now you have 2 tens and 11 ones.
Now you can subtract one ten and 4 ones, leaving 1 ten and 7 ones, 17.

So you are physically going through every step of the process.

There is a great Web site which makes this much, much easier!!! (Although sometimes it is helpful to have the slow step-by-step hands-on process, especially in second grade!) The site is

base ten blocks

(but do not try it with AOL; it freezes up. If you have AOL, you also need to open Internet Explorer and then copy and paste the URL.)

The site is a java applet which makes it easier to do the steps above, because to "trade" a ten for ten ones, all you have to do is click on the hammer tool and then "hammer" a ten, and it instantly becomes ten ones. To make ten ones into a ten rod, you just need to line up ten ones and then hit them with the "glue." Instructions can be accessed from the bottom of the page. You can use different background mats so that the objects can illustrate decimals... you can even use them for algebra!

Wendy P of Math Cats, 10/28/00 on primary board

* Calendar Math for Place Value and Trading

> I am looking for a good resource with math calendar activities
> for 2nd grade.

Tammie, here are most of the activities thatI do for calendar math:

My bulletin board consists of.......
* a 100 chart (laminated so I can cross off the days to 100 with an overhead pen)
* a sheet of chart paper (for tally marks)
* an index card with odd/even written on it
* a pop lid box divided into 3 sections... 100's, 10's and ones with 10 push pins in the ones section so I can hang a unifix cube as we count the days, and a library card stapled under each section so I can put an index card with the # written on it in the appropriate one
* 4 zip loc bags (for quarters, dimes, nickels, pennies
* a clock with movable hands
* a place for me to put up the shape of the day
* I also made up a way to display cups, pints, and quarts

How I use my board:

Let's say that it is the first day of school. I begin by crossing off the number 1 on the 100's board.

I then put up one tally mark on my chart paper that is posted under it.

I then add 1 unifix cube to the one's section of the "box" and I put an index card with the #1 on it under the ones section to show the # I have made.

I then ask if the # is odd/even and explain why.

I then add 1 penny to the zip loc bag and write 1 cent on a post-it note and display that.

I then make my clock say 1 minute after 9 and write the time on a post-it note and display it under the clock.

I then add a card labeled "1 cup" to a special place on the board as well.

I then display a shape of the day on the board and we discuss the properties of it.

As you can see, after the 9th day of school for example, you add 1 more cube and then you can change your ones in for a ten, your nickel and 5 pennies for a dime, etc.

I have also added measurement.... Day 1 is 1 inch, and so on.

I also have them make as many equations as they can that will equal the # of the day. I write some of their ides an a chart. I then announce "teacher's turn" and I model some "incredible equations." Like if it's the 50th day of school, I will write
25 + 10 + 10 + 5 = 50
or (65 + 5) - 20 = 50, etc.

I hope this makes sense. I probably went into alot more detail than you needed but I LOVE doing the calendar.

Kaye, 6/26/00 on math board

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> Looking for Kaye
> I love the calendar activities you posted 6/26 and am
> gathering the things necessary to implement them... but I
> have a couple questions. Do you use the unifix cubes only
> for the ones? Is there anything to keep track of the tens?
> Thanks for your great ideas! 9/04/00

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You Found Me!
I take the 10 ones that I made from the cubes and link them together into a "ten." I then move this over to the "tens" section and tape the "ten stick" to that area. I continue to do this until we reach 100, in which case I remove all of the tens and trade for a hundred (the hundreds that came with my math kit. They are made out of wood.) I continue on until the last day of school.

I have seen people use straws, and I think that will work fine too. I just want to use the unifix cubes because that is what they see in their math books and on our end-of-grade tests and I want to be consistent with that. (They even make a special pocket chart for the straws now.)

Underneath my hundreds, tens, and ones section I have a copy of a blank hundreds board that I ran off. As we add a one each day I color in one cube on the chart to show how to graph what I have modeled with the cubes. This helps move them from the concrete to the picture level.

Did I mention that I added cups, pints, quarts, 1/2 gallon, gallon? I drew off blocks to represent this and I cut out squares from construction paper and laminated them to fit in the blocks and labeled them. On the 1st day I put up one square. That was 1 cup. Next day I added another square and that was 2 cups. I moved them both to the pint section to show 2 cups makes a pint, etc. We go on til we get to a gallon. I have even used real water and added a cup a day til we got to a gallon and demonstrated all the conversions along the way.

I hope you can make sense out of this! Sorry this so long but I think the calendar is a great tool. I can't seem to get my kids to learn how to tell time, count, etc. by just doing a "unit." It takes REPETITION over a long period of time for most of them.

Kaye, 9/04/00 on math board

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I bet you're sorry you found me by now. Is this too much information or what? But I would like to tell you that I have made what I think is a big improvement to the board. Instead of using the ziploc bags for the money section, I bought the big money bulletin board set and laminated the pieces. I laminated a piece of chart paper and divided it into penny, nickel, dime, and quarter sections. I attached velcro to the backs of the money pieces and to the chart. The kids can SEE this much better (and I try to show the real money too). I have used play money that they have stored in film canisters and they model the money amounts as we go along, making the trades etc. I usually only do this part when I know it is on a day when we can make a "trade" like on the 5, 10, 15 etc. day of school.

Kaye, 9/04/00 on math board

* Place Value Games for Upper Elementary

> I was wondering if any of you have a FUN place value game
> to play with my 4th graders. My students are currently learning
> how to express numbers in different ways (word, standard,
> expanded), and are also practicing saying numbers correctly
> to the millions. Can you please share any activities or games??!!
> Marci/4th, 10/27/00

game with one die or deck of cards

You can play this game with 1 die or a deck of cards with the jokers, 10's, kings, queens, & jacks removed. Kids make a place value chart as high as what you've taught. They take turns rolling die or drawing a card & put that # in any position they want. The object of the game is to create the highest or the lowest #. If using a die, they must use each # rolled. If using cards, they don't have to use a card, but their turn is over after 1 card. If the deck is finished before you fill in your spaces, all empty spaces become 0's. Hope this helps! :)

jody, 10/27/00 upper elementary board

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homemade board game

I have place value games my Year 4s love, using a pile of cards with a number on each one, and game boards I made up. Each child chooses a number (of whatever level of difficulty you have taught). This is their number for one full circuit around the board. They roll a die and move a counter around when it's their turn.

On the board are squares with instructions like "Read your number aloud," or "Say how many hundreds are in your number," or "What is 1 more than your number?" or "Make your number using blocks," or whatever skills you wish them to practice.

After they go around the board once, they choose a different number for the next round. They can score a point for each correct answer, or have to move their counter back to the space they just came from for incorrect answers.

Kris, 10/28/00 on upper elementary board

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Game with two teams and large number cards

I played a game with my third grade class who was learning place value to the hundred thousands place. We broke my class of twenty into two teams of 10. Each student was given a large number card 0 - 9. I would read a number such as "12,543" and the students would arrange themselves in the proper order. The students seemed to have a lot of fun and it really reinforced the concept that I was teaching.

Debbie, 10/28/00 on upper elementary board

* Place Value Activities, Upper Elementary

I have found the best way to teach place value into the millions is with my number tiles. I just wanted to share this with you all. The children are learning expanded form, word form, and standard form from using the tiles. I may put something on the overhead such as 20,000 + 6,000 + 80 + 5 and they know that they need to use five tiles because the largest number has five digits even though there are no hundreds. They are learning to place a zero in place, utilizing manipulatives and using the book as a reference.

Cleo, NBCT, 9/25/00 on upper elementary board

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Thanks for a great idea. I play a "Digit" place game with 4th graders that they really enjoy. I pick a number (then I let someone else pick one) either with two or three digits right now--later in the year they get bigger. I give them the range of "x" and they make guesses with me recording if any of the numbers within their guess is correct and then if the correct digits are in the correct place. I use a chart to do this something like below: (digits must all be different)

X > 20 and X < 99 (i.e.,say the number is 75)

Guess Digit Place

79: 1 digit correct, 1 in the right place
95: 1 digit correct, 1 in the right place
75: 2 digits correct, 2 in the right place

I can't wait to try your tile game though, I think it will be especially useful for those larger numbers!

Ellie, 9/25/00 on upper elementary board

* the "infamous place value post" on the process

I posted this before for someone with the same question. It really solves the place value problem. Hope it helps!


Monday, July 31, 2000 5:44:48 PM

The critical learning in place value is understanding the period [units, thousands, millions, etc.] and the name of the place in each period. Dr. Madeline Hunter described a way for teaching this so kids can generalize the principle, rather than just have examples. You start with just lines:


(This would stand for 100,100,100 or a similar #)

Then you teach them the name of each period and an explanation so they see that the period on the right is the units, etc. Give them lots of practice just learning these names. With math, often taking the numbers out is what is necessary for them to see the process. I always put this on a big chart and we'd practice several times a day saying the periods. I'd point, they would name.

Next step is to teach them the place within each. They see a definite pattern quickly--every period had 3 places and the names are the same: ones, tens, hundreds. I would write those on the chart itself (perpendicular to the lines. Then you practice with these. Point to a line, they will say "that is 10 thousand." Point to another and they will say "100 units" or "1 million." Lots of oral practice on places without numbers is the key for them to see the pattern and thus remember it. Numbers in math totally throw the process! Strange, huh?

Once they have this, you put a number in one of the spaces and zeroes in the others. They will say, depending where the number is, "that's 10 million" or "that's 20 thousand" or "that's 10."

Once they have this, you show them how you do not have to put the zeroes in to the left of the number---not 010,000, but 10,000.

Last step is to let them write numbers on the lines after you dictate them. You say 10,000 and they write the numbers on the lines. They think this is a great game--and by this time they really understand the concept. Do two or three of these several times a day rather than 20 one time. This really helps learning and remembering.

Soon, you take away the lines and just dictate the number--they write. Again do a couple several times a day. They will learn to read the numbers much better after they can write them. Kids don't really have a concept under executive control until they can GENERATE examples.

Also you put a numeral on the board and let them think how they would read it and then read it to a partner. This gives everyone practice and they can check their response with the partner.

Taking the numbers out helps kids to see the PROCESS. It is powerful. When I took the numbers out of math until the kids saw the process, they actually could do it. There is a reason for this: in math, the mindset to compute is powerful. Give them numbers and they want to compute the answer. However, in math, the process is what matters. Take out the numbers, they CAN'T compute, and they will look at process. Obviously, once they have the process you put the numbers back in. But, now, they understand what they are doing.

I'll bet this is as clear as mud! Hard to explain in writing... Good luck.

Jan, 9/28/00 on upper elementary board

* game for place value with decimals

> I would like to get some "hands-on" activities for decimals.
> I teach 6th grade math and they have already had an
> introduction to decimals in 5th grade. I want to make it fun!

> Paige, 10/02/00

The only game I know is to have a competition as to who can produce the largest decimal number: each child has a "game board" that is really the columns hundreds, tens, ones, tenths, hundredths, thousandths... You can include any columns you want to "test" on. Then have a set of large index cards with one digit 0 - 9 on each. Or, use a standard deck of cards for the overhead, or go to the dollar store and purchase a jumbo size deck of cards (for people with arthritis and poor eyesight). Then just remove the pictures and 10's. You could also use a die (but then you only get 1 - 6) or make your own decagon die.

Anyway... Shuffle the cards, turn over the top one and read off the value. They have 10 seconds to place that number in a column on the game board. They cannot change their minds once it is in place. Continue until all of the columns are filled. Then see who produced the largest value number.

After a few games the kids catch on to the concept. That's when you change the rules. Now try to produce the smallest value.

DSF/NJ (Donna), 10/06/00 on math board

decimal place value concepts

> I teach 7th graders, and noticed that they don't understand
> how to read numbers containing decimals (through ten-
> thousandths)... example: 15.7432
> Lauri/ms math

Hundreds board activity for decimals I teach 5th graders so I don't go that far into decimals, but it sounds like you should go back to the beginning of decimal place value. Work your way over one spot at a time. For example, one day, introduce the tenths spot and work on that for a bit. Then, go to the hundredths spot--but stop there for the day. I don't have any creative ideas, because as far as reading decimals, we just do a lot of oral practice. Maybe make some type of matching worksheet that you could make yourself. Or use a "hundreds" board activity--but you make it yourself--without the 1-100 on it. Write a bunch of decimals on it and then have questions such as color all the decimals blue that have the 4 in the hundredths spot...

Jody, 9/07/00 on math board

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Method for saying decimal numbers

How does one method that works for all decimal place values sound?

1) Place a 1 under the decimal point.
2) Place zeroes to the right under each digit until you reach the end.
3) Read that number with 'th' or "ths" at the end.

When students find out they can read "big" (actually small) numbers this way, the tenths, hundredths, and thousandths are easy.

EXAMPLE: 53.02486891

Put a 1 under the decimal point and then fill out with 00000000
It looks like: 100000000 (one hundred million)
It is read as "Fifty-three and two million four hundred eighty-six thousand, eight hundred ninety-one hundred millionths."

EXAMPLE: 2.408

Put a 1 under the decimal and then fill out with 000
It looks like: 1000 (one thousand)
It is read as "Two and four hundred eight thousandths."

I am sorry, but part of your problem are those who allow students to say "and" while reading a number without it meaning the decimal point.

AWP, 10/01/00 on math board

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digit and decimal tiles

Thanks to AWP - that was a great idea that I had never heard of.

I also have manipulative digit tiles and a decimal tile and we practice making decimal numbers.

karen/tx, 10/04/00 on math board

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same method works with regular place value

This is from AWP. I shared how I teach decimal place value with my students (4th grade). The same basic method is used for regular place value -- actually the decimal version is a modification of my method for determining place value and reading numbers.

For a person to determine the place value of a non-decimal number:
Place a 1 under the digit you are working with.
Place a zero under each digit to its right.
Read the number. 10 = tens; 100 = hundreds; 100,000 = hundred thousands.

The modification for the decimals is that the 1 can't go past the decimal point.

AWP, letter to Math Cats, 11/23/00

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