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* How do you teach addition and subtraction in first grade?
* Do you know some good games and activities for teaching and practicing basic facts?
* How can I help my students to internalize subtraction concepts?
* What can I do about 3rd and 4thgraders who still don't know their subtraction facts?
* What are some handson and mental math alternatives to worksheets?
* Do you know some addition rhymes?
* What activities help develop the concept of "fact families"?
* Can you suggest some good web sites for practicing basic math facts?
* What do you think about "Touch Math"?
* teaching addition and subtraction in first grade
> My children usually use their fingers to find the sum, but counting up and counting back For the addition facts, I tell the kids to "think the biggest number first and add up." Think "9" and count on 7 more for 7 + 9. For the subtraction facts, if there is a big number on the bottom, ex. 11  8, think 8 and count up to 11. Little number on the bottom, ex. 11  3, think 11 and count back 3. It works for us. Hope this helps. 2nd grade on 11/02/00 on teachers.net primary elementary board      North Carolina Math Site Strategies for Instruction in Mathematics K5 This is a superb site with very readable, doable math lessons and gamesa lot that will help you with the drill and repetition that they will need, in a fun way. Scroll down to the First Grade and the year is divided into 4 quarters plus a section of blackline masters. In our school, to do these harder addition problems, we tell the students to "put the big number in your brain" and "count on" from that number using their fingers for the second addend. (eg) For 8 + 6, they would touch their head and say, "8 in my brain... (and putting up six fingers) 9, 10, 11, 12, 13, 14." This works well for my first grade. Darcy, 11/02/00 on teachers.net primary elementary board      If you have trouble getting to that great N.C. math instruction site, just type in
Click on instructional resources. Good luck! It is worth the trouble to get there! Cindy, 7/21/00 on teachers.net primary elementary board      Saxon Math I really like the way Saxon math teaches the facts. They teach "strategies" instead of using fingers/manipulatives (although manipulatives are used in intros. and as needed). There are doubles, which the children simply memorize easily. There are "plus one" facts (like counting to the next number), "plus zero" facts, which, again, are easy to see after using manipulatives for a little bit). There are "doubles plus one" facts, "adding two" facts, etc. You teach a STRATEGY for remembering and then the kids practice DAILY in a variety of wayspaper practice, raps, string "wrapups", etc., etc. It's the best way I've seen so far, as opposed to the old methods we used to teach!
Diana/1/OH, 11/02/00 on teachers.net primary elementary board

more activities for addition and subtraction in first grade
> Does anyone have ideas on how to teach beginning addition pushing together sets of teddy bear counters I've found it really helpful to have my students use teddy bears to form two sets and then slide them together to find the sum. I start the lesson by telling them the number of bears they should put in each set. I make sure they place the first set on the left side of their desk and the second set on the right side. I then say the numbers for example " 5 plus 2 equals" When I say "equals" the students slide the sets together and then count to find the sum. I do this several times before writing a math sentence on the board. I stress the words "sets" and "sums". After we do this for a couple of days, then I allow my students to use their math workbook pages. I feel strongly that they children should "feel" the sets going together. I've found it to be very successful over the years. Glenda, 10/28/00 on teachers.net primary elementary board      Shake the Beans I do an activity with my 1st graders called "Shake the Beans". You need the following:
12 bag(s) of large lima beans Spray the beans with green on one side and orange on the other side. After they are dry, put about 2030 beans in each ziploc bag. Make enough bags so each student has his/her own bag. Activity: 1. Each student takes out a set number of beans that you are working on. For example, if you are wanting to find all the number combinations for 7, they would take 7 beans (only) out of their bag. Then zip the bag up and put in their desks or just somewhere away from where they are working. 2. Students will shake the beans gently in their hands and then gently let them out on their desk. 3. They put the green together on one side of their desk and the orange together on the other side of their desk.
4. Next, they are to record their results. There are several
ways they can do this. They can make a table to record their
info.
etc. I also have a worksheet that has beans drawn on them. They continue shaking the beans to find all the number combinations for the sum they are working on.
Another great resource is the math series called
Tweety/ 1st grade, 10/30/00 on teachers.net primary elementary board 
* floor games for addition and subtraction
> Help!! I'm a Grad Student in NY and I need to devise a floor Subtraction Bowling
How about subtraction bowling? or you could reverse the system and have them add to find the total pins toppled in two tries. Giant Cards and Dice
Make giant cards 1  12
The first student plays until they turn over all the large
cards. The turn ends if they can not turn over cards to equal
the rolled amount.
S.J., 10/03/00 on teachers.net math board 
Addition & Subtraction Chart Print this child friendly chart. Buy a box of Cheeriosized cereal for math class and then have a blast. http://www.kidsrunning.com/school/krschool1027addsubchart.html I use this blank with a page of problems. The kids use the top row to do addition and the bottom to do subtraction, and the fun part is when they do the take away part on the bottom they get to eat the cereal. Please try this. I just made it. Also check out the whole Run the Seasons program. You can find it at www.carolgoodrow.com It's going to be full of handson first grade academics.
Carol, 10/27/00 on teachers.net primary elementary board

3rd grade Addition Lesson  Sports
> I'm looking for a lesson for third grade that involves This is a game the kids beg for. Draw a field on the board. Just a line with 10 yards marked off down from the 50 towards both goals in the center and goals on each end. I have a magnetic whiteboard and made a football with a magnet on the back. It starts at the 50 yard line. The class is in two teams. The first two come up. I use flashcards but you could give problems etc. The first correct answer advances their ball 10 yards toward their goal. The ball will move back and forth. When a team gets to their goal, they get a touchdown. I have added some rules, such as: As the ref, I can give penalties for Unneccessary Roughness (pushing in lines), Interference (giving an answer when not your turn), Unsportsmanlike Conduct (rude to a teammate for not getting answer), Excessive Celebrating (that is not what it is called but when the player brags and showboats about beating someone)... Adapt for you but it is fun.
Gail, 11/16/00 on teachers.net primary elementary board 
* At my wit's end with 1st grade subtraction!
> Please help...Have tried everything I know..,but still have keep it simple and have it match their world: stories and manipulatives Lucy, I always start with stories that I make out loud. They can understand these because they match their real world. For example: Susie has 3 cute dollies that she keeps on her bed. Her little sister likes them too.One day her little sister just "borrows" one. When Susie comes home from school, how many are still on her bed? Or Tommy took 5 cookies to school for a snack, but he dropped one on the way to get on the bus. How many cookies does he have for snack now? Please try this. It works. EVERY kid, no matter how poor in math, will be able to answer these. I do this every year. Next, I start to get a little abstract. I let them use manipulatives to act these type of problems out. You can do this whole class. Another level will be writing the number sentence on the board, etc. They need to learn that the first number is the number you start with and the second is the number you take away.
THEN you have to start getting a bit abstract. Carol, KidsRunning.Com, 11/09/00 on teachers.net primary elementary board      Shell Game Try the shell game. ex. I have a child count 5 manipulatives. Then I put three under a bowl (shell) and ask them how many I should put under the second bowl to make 5. They can see the remaining shells so that they should know the answer. I always give them the number sentence right after (5  3 = 2). I work from there until they can get the answer without having to see the remaining objects first. They love it when I lift the second bowl and they are right. The rest of the class can play this game with partners while you work with a small group. If they grasp the concept then you can proceed to abstract. Eileen G, 11/11/00 on teachers.net primary elementary board      Missing Addends, Cuisenaire Rods, "trash can"
Wow. You have tried all the things that *should* work! I am
assuming since you are not at your wit's end about addition
that these children have absorbed the concept of addition
successfully. So maybe you can turn that to their
advantage. I have noticed that many children who can
instantly tell me that 6 + 1 = 7 are thrown for a loop when I
ask them "What is 7  6?" or even "What is 7  1?" When I
turn it into an addition problem with a missing addend,
sometimes that helps. For instance, "I'm holding up six
fingers. How many more do I need to make 7?" They can
usually tell me that I just need one more. Then I model for
them a way that could be represented:
Now, working backwards with the same problem: It is harder for kids to subtract larger quantities, like 7  6. So it is very important to get them comfortable with the idea of fact families, and also with missing number problems. For 7  6, it is easier to "count up," and say, "Start with 6; how many more to make 7?" Turn that subtraction problem into an addition problem. The number line is great to use, but it is definitely trickier to subtract on a number line than to add with one. Sometimes kids have a hard time knowing where to begin counting backwards when subtracting on a number line. Do you ever use Cuisenaire rods with a centimeter ruler? That way the students can see and feel the "worth" of a number. You can explore the four facts in a fact family easily that way. They can also add and subtract with Cuisenaire rods without using a ruler/number line. Using the same problem as above, you could set out a black (seven) rod, and right above it you could set out a dark green (six) rod. Ask the student what rod is needed next to the green rod so that the two together will equal the length of the black rod. The student should have no trouble determining that it is a white (one) rod. Now while those rods are set up, you can look at the four facts: 6 + 1 = 7. If you reverse them: 1 + 6 = 7. If you take away the white: 7  1 = 6. Take away the green instead: 7  6 = 1. One confusing thing about subtraction in word problems is that sometimes we are "taking away," but sometimes we are comparing to see which group is larger. So while you are continuing to do lots of manipulative activities to build these concepts, you should keep in mind that you need to model both types of subtraction. With the Cuisenaire rods example above, you could model it both ways. When you remove the white (one) rod, you are taking one away. But you are also comparing the remaining two rods and seeing that the black (seven) rod is one unit larger than the green (six) rod. It's good that you've been doing a lot of work with manipulatives, and I'm sure you'll keep doing a lot more. In the early grades, the more work with manipulatives the better, even for children who "get it." I have observed some young children having a difficult time solving simple problems with manipulatives such as small blocks. I think in some cases they are still developing their fine motor skills, and it is taking most of their concentration just to pick up and grasp the objects in their hand while they are "taking away," so they aren't really focusing on the specific math problem at hand. Maybe you could use the lid of an egg carton for setting up the initial problem (7 objects), and then use another container like a paper cup for holding the objects being removed. That way if a child is solving 7  6, he/she can pick up one at a time from the 7 in the egg carton lid, and place one object at a time in the cup while counting out six of them, until one is left in the lid. (When they are in the cup they are harder to see and seem to be more "removed" than if they are just pushed aside.) You could call the cup the "trash can" or something so it seems more as if these objects are being discarded from the problem.
Wendy P of Math Cats, 11/9/00 on teachers.net math board

* My 3/4 graders just can't get subtraction facts!!
> My third and fourth grade students are having so much Mad Minute Use a Mad Minute test everyday. I teach the second grade and have given a Mad Minute test everday this year. Every single one of my second graders knows those facts and can rapidly recall them! Molly, 11/15/00 on teachers.net primary elementary board      Make a Ladder Let's see if I can remember this great strategy that I used to teach 3rd graders.
Okay, if the problem was 15  8:
One more: 12  7 The key was building off of the steps from 10 which they knew. It really worked and easily transferred to a mental strategy. Good luck,
Carol of kidsrunning.com, 11/16/00 on teachers.net primary elementary board 
* May I suggest some handson and mental math alternatives?
> Anyone know of a site where I can find some printable math I agree that daily quick practice and learning the facts cold is important. When I used to teach second grade math, it took some of my students months to be solid with the basic addition and subtraction facts up to 9 + 9. But we don't need drill worksheets to accomplish factlearning. At second grade level, a child who does not know the facts cold can still benefit from lots of handson work with manipulatives. I used to find it very helpful to use Cuisenaire rods with number tracks or centimeter rulers. (Number tracks hold the rods in a "train." For the problem 8 + 6, for instance, a child would place a rod of the value 8 (8 cm long) in the track or alongside the centimeter ruler. Then the child would place a six rod endtoend with it and see that the combined length was 14 cm. I would have the child take it one step further: above the 6 cm rod, the child would place two rods: one to reach 10 (the 2) and one for the remainder (4). Now the child had a visual picture that 8 + 6 = 8 + 2 + 4. Why? Because at the same time, the students were developing the concept of using 10 as an "anchor" in solving mental math problems and were also learning to visualize a mental number line. When they became adept at this, it was much easier for them to add twodigit numbers in their heads, later on. For instance: 28 + 36 Along with the usual pencil and paper method involving regrouping, I would also teach them to mentally add the 20 + the 30 to reach 50 and then to add on the 8, to reach 58, and then the 6, to reach 64. This final step was easy if they had had lots of handson experience with the sort of problem I described above, breaking the problem into pieces to reach a "10." And this same skill made it much easier for them to begin learning multiplication tables near the end of second grade, or for my thirdgrade students in other years. For instance, skipcounting by 6's, we'd first do it on a number line (pausing at each 10 along the way): 6 + (4 + 2) + 6 + (2 + 4) + 6 = 6....(10)..12...18...(20)..24...30 and then we would see that the same pattern repeated again for the sixes from 30 to 60. As a parent, when my oldest child was in first grade and was expected to memorize the addition and subtraction facts, his most meaningful work was done in the bathtub! I used the same strategy with my second and third grade students to help them learn and UNDERSTAND the facts, but of course without the bathtub setting. But if any parents are reading this, I still think nothing beats bathtub math! It worked like this: As I sat beside the tub while my son was soaking and playing, which was a nice, relaxing time (either before or after the gettingclean part), I would ask him fact problems. As soon as I'd say the question, I would start lightly slapping my leg, about one slap per second. He would try to answer within ten slaps. If he couldn't, then he could take as much time as he needed (I'd stop slapping my leg of course), but along with the answer he would need to verbalize an explanation of how he arrived at the answer. No fingers allowed. There were three basic strategies which we found useful:
1) using 10 as an anchor, as I've described above
For strategy #2: if I said "7 + 8," his answer might be,
"Well, I knew that 7 + 7 is 14 (because the doubles are easy
to learn), so I added one more, because 8 is one more than
7. So it is 15." For strategy #3: if I said "9 + 8," he might say, "10 + 8 would be 18, so 9 + 8 is one less, 17." Gradually we would shorten the number of slaps, working our way down to 3 seconds, as more and more facts became familiar friends. After we did this each evening for a week, he could answer any fact within three seconds. Either he had simply learned them from the repetition, or he had become so adept at the mental strategies that he could implement them within moments. And these same strategies served him (and my students) well in a variety of ways throughout the years. As a teacher, I sent home information sheets to the parents describing some of these strategies for learning the facts and asked them to reinforce them at home. (I may have even recommended the bathtub!) In the classroom, for your quick fact drill every day (after plenty of handson work), you could simply pair students and have them take turns asking each other math facts and answering within an agreedupon seconds (or verbalizing a strategy). You could give each pair of students one fact sheet and have them take turns asking random facts from the sheet. You could use these same sheets all year, because they never need to be written on. But they really don't even need that.
Wendy P of Math Cats, 10/25/00 on teachers.net primary elementary board

* Addition Rhymes, do you know more? I am teaching an undergraduate course, and several of the participants want those addition (and multiplication) rhymes to help their students remember those troublesome facts. I have the following, but would be interested in hearing others. Doubles Addition Rhymes
1 Snickers bar
2 socks
3 little pigs
4 dinner
5 on the left
6 for myself
7 little cups
I 8 and I
9 good guys
10t (tent)
KathyB/1st/IA, 9/08/00 on teachers.net math board Doubles Rhymes Invented by Ian, grade 2
1 + 1 = 2
2 + 2 = 4
3 + 3 = 6
4 + 4 = 8
5 + 5 = 10
6 + 6 = 12
7 + 7 = 14
8 + 8 = 16
9 + 9 = 18
10 + 10 = 20 We made this into a book and the kids memorized the poems. It worked! The kids know their doubles by heart.
Carol Goodrow, message to Math Cats 11/7/01 
* Fun and Interesting Lesson for Fact Families
> I am being observed on Wednesday and would like to know if Fact Family House
(I think I might have got this from this board last
year...) LL/NYC, 9/16/00 on teachers.net primary elementary board      Fact Family Album and Card Game I just did fact families and this is a fun language connection. My students made a fact family album. I gave each student a pair of numbers. They found the third member of their fact family by adding the two together. I then gave the class this cloze passage:
We are a fact family. There are three members in our family. Their names are 5, 4,
and 9. We can do four things together  They then illustrated their fact family. I did this on the writing paper that has the space at the top for illustrating. I am going to make a class book out of it. Another idea is to use a deck of cards, taking out the face cards. Give each student 2 cards. They figure out what the third member of their fact family is and then pass the cards or lay them down. You can make it competitive by having them keep track of how many fact families they complete. Jessica/3/MO, 9/16/00 on teachers.net primary elementary board      Spinners Our math book has one lesson on "fact families" but I think it's very important to spend more time on this concept. We do fact families for a few minutes each day for about two weeks. The students write them daily in their math notebooks and then we do activities. We have made the houses above and sometimes use spinners. Each student has a spinner and spins two times. He adds the two numbers together for the family and writes the other three sentences. Ex: Spin 3 and 4. Write: 3+4=7 4+3=7 73=4 74=3 If they get the same two numbers then one of the numbers has to be written in colored pencil so they understand it is a different number. They love spinners!      Kids hold math symbol sheets and arrange themselves We just did a lesson last week where we thought of 3 or 4 fact families. Then we put each one on 9 by 12 construction paper, one number on each piece. We used a different color for each problem. We also had a paper with a plus sign, equal sign, and subtraction sign. I'd say a problemex. 9 + 4. The kids with the right numbers had to come up front and arrange themselves in the right order to make the fact familyswitching their order each time and also switching to the subtraction sign when necessary. They loved it and it really helped. Good luck. anonymous, 9/16/00 on teachers.net primary elementary board     
> HELP  I need some NEW and INTERESTING ideas for teaching fact families. Dominoes Have you tried giving each child a couple of dominoes and have them write the fact families they depict? They can turn the dominoes around to see how the addends shift places. Grace/IL, 11/09/00 teachers.net primary elementary board      Upstairs and Downstairs Windows I have the kids cut out a house shape (construction paper) and they write the two addition facts in upstairs windows, two subtraction facts in the bottom windows.
Shari, 11/10/00 on teachers.net primary elementary board

* sites to practice basic math facts Try www.schoolexpress.com/fws/default.asp (formerly www.freeworksheets.com) Also www.mathstories.com [Note: mathstories.com now requires a paid subscription.] These are helpful. Good luck! Kim S, 11/27/00 on teachers.net primary elementary board      aaamath.com is a good site for elementary children. You can have levels from K to upper elementary. They have many different skills to practice. Hope this helps!! Erin, 11/28/00 on teachers.net primary elementary board
[Also be sure to check out the other web sites recommended elsewhere on this page, such as the North Carolina site.]

* Touch Math
> Has anyone had experience using Touch Math with first I have used it for years and really like it. I also do other things (fact memorization, etc. because of district requirements) but I started using touch math years ago when I relocated to another state and stumbled on a teacher's edition in my new classroom. The subtraction can get a little tricky at first, but they usually catch on fairly quickly. I also use a lot of manipulatives in math, but this program helps fill in the gaps for students who have difficulty memorizing and for those who need something more concrete. By the way...teach both forms of the number 4 (closed top as here and open top) so they will be able to use the points with any form of typing/writing. Do the same with the 9/6. They need to be able to visualize the points on various types of number formation/writing. ww, 11/05/00 on teachers.net math board      Touch Math Hurts Students' Future Chances in Math I teach upper level math in school ( 7  12 math) and I have come to realize that touch math seriously hurts the students' future ability in mathematics. Students must memorize basic math facts to the point of automaticity. I discovered that the elemantary teachers were using this method because memorization has fallen out of favor in trendy educational circles. anonymous, 11/7/00 on teachers.net math board      Re: Touch Math Hurts Students...  not if used properly If used properly, Touch Math is a supplemental program to be used along with traditional methods of teaching  not as a replacement. I found that my students DID learn the required facts as we used Touch Math. I now teach atrisk students. I have one child in third grade who has been struggling to learn math. She came to me a week ago with an attitude of hatred toward math. She simply didn't get it. And they were working on addition of two and three digit numbers. I spent a half hour showing her Touch Math. We worked some problems together that day and she completed a math worksheet on her own. She took it back to the teacher and made a 100 on it. She was ecstatic. She has come to me for 30 minutes each day. In four days she had done a complete turn around. She is now excited about math and actually looks forward to doing it. Today they began subtraction of two and three digit numbers. I showed her backward counting with Touch Math. Again the elation as she began to complete the assignment independently. Will she learn the basic math facts? Yes, because her teacher and I are both strong believers in memorization of math facts. I challenge the poster who is negative about Touch Math to prove that it is the Touch Math that is destroying students  or is it possibly that the teachers he/she is aware of are using it improperly? Sharyl, 11/10/00 on teachers.net math board      Touch Math hurts students' chances by not learning basic facts What is the goal? If the goal is to learn basic math facts to automaticity, then do that. Touch math only teaches them a process that will allow them to get the answer without memorizing the basic math facts to automaticity. We must teach what we want the students to learn. The first group of touch math kids are starting addition and subtraction of mixed numbers, division of decimals, and algebra this year. They are so slow and are so poorly prepared to deal with basic facts that they are NOT getting it. Those who know the basic facts effortlessly acquire the new concepts. The touch math kids are tip tip tipping their way into an endless spiral of frustration. l anonymous, 11/12/00 on teachers.net math board      I would check with your lower grade teachers then. When I utilized Touch Math as a SUPPLEMENTAL program in Oklahoma, our students also learned the basic facts. As they progressed upward on into junior high and high school, they had no problem with it. And I will go one step further, even though I can see that you have your mind already made up against Touch Math. When I was in 3rd/4th grade (a split class in Marland, Oklahoma) back in the late 1950's, our teacher, Mary Nell Lewis, taught us the exact same system as Touch Math. (Too bad she didn't patent it!) Yet isn't it amazing that even knowing a system like Touch Math, we were all able to still learn the basic math facts and be very successful in all areas of math, even as we progressed through school into higher level math. Do you have a problem with allowing students to count on their fingers until they learn the basic math facts? I do. I would prefer they utilize Touch Math rather than counting on fingers. As I stated earlier, Touch Math should be used as a SUPPLEMENTAL program. It doesn't and shouldn't replace learning basic math facts. My question to you is this  what do you propose students do until they learn the basic math facts? Perhaps you would prefer that they not attempt to work any math problems until they've learned the facts? Sharyl, 11/13/00 on teachers.net math board      Touch Math helped my daughter First I'd like to say that I'm not a teacher. My daughter in second grade was having a hard time adding on. She started using the number line and this helped. I soon realized that she was having a difficult time doing addition without this visual aid. I learned about touch points from a web site. In one week I couldn't believe the difference in her ability to add. What I like about touch points is you don't need any supplemental object to use it. The numbers are always on your paper. I would rather have my daughter use touch points than use her fingers. I've also found she is starting to memorize facts. She knows all of her double facts and the addition facts are coming. I've started using touch points with money. A nickel has 1 touch point. A dime has two touch points and a quarter 5 touch points. Each touch point the child counts by five, for those coins. A penny has one. She can count any amount of money now. She is starting to take two quarters and add from $.50. She is making progress. Why do teachers alway think there is only one way to teach? When a child learns to ride a bike we give them training wheels. Eventually, we take away the training wheels and they ride without them. A child with a broken leg needs a crutch. When the leg heals we remove the crutch. I believe the same is true with teaching math. If a child needs supportGIVE THEM SUPPORT TO HELP THEM BE SUCCESSFUL Val G. Just a mom, 11/15/00 on teachers.net math board      Thank you for your input. I agree wholeheartedly... I feel like THAT is the first step. If we can get them LIKING Math we can help them LEARN Math. As I said earlier, if Touch Math is used appropriately, it is a SUPPLEMENTAL method which supports traditional teaching. Those math facts should still be taught/learned, but in the mean time, Touch Math does away with counting on fingers. I, for one, despise the counting on fingers. Sharyl, 11/16/00 on teachers.net math board      About Touch Math I was rather dissapointed by the comment that touch math does nothing to help students learn and memorize their facts  It helped me tremendously when I had excessive difficulty with math as a young student and HAVE seen it work in other instances as well as a tutor myself!  Once the actual "touch" part is understood and mastered, students can simply visualize the points on the numbers and figure the answers with automaticity. While some students may struggle to get past counting the spots on the numbers by a certain stage, I have seen this strategy work not only for myself but with others as well. Jennifer P., 9/19/04, message to Math Cats      Touch Math hurts my daughter  she can't "undo" it I was "led" to this site looking for information on Touch Math  and how to "undo" it. My daughter learned math by Touch math in 2nd and 3rd (and 4th) grades and of course it helped her tremendously then. But now she is in 8th grade  and still needs to do her addition and subtraction this way. You cannot be very successful at 8th grade math using touch math as your basis. We are at a loss trying to figure out how to "undo" this Touch math and help her to move on. I see all of the postings regarding this subject are quite old... but thought someone might still tune in on the subject.
A Mom, 9/16/05, message to Math Cats


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