> Looking for creative ways to teach fractions to first grade.
> new to first, 1/3/01

My kids loved the Hershey's Milk Chocolate Fractions Book by Jerry Palotta [see link above]. You use chocolate bars to make different combinations up to 12ths.

Cindy, 1/03/01 on teachers.net primary board

- - - - -

I have my students make a Pumpkin Fraction Pie. You need two paper plates and an orange construction paper circle with six wedges drawn on it and a huge dot in the middle. Glue the orange circle in the center of one of the paper plates. Cut a slit to the center of both plates. Slit the two slots together, then tell the students a story about someone making a pie, that the white part represents the pie dish, and a story about the setbacks the pie maker had with a dog, etc. eating up the pie. I like to dude it up with silly stuff. During the course of the story, you write down what fraction of pie is still there and what fraction is now missing.

kathy/2/wi, 1/03/01 on teachers.net primary board

- - - - -

Our Saxon math series introduces fractions using vegetables. The lesson stretches over a couple of days and integrates a graph of which veggies they liked and those that they didn't. It's lots of fun, and the kids usually taste veggies that they haven't eaten before. I don't have the lesson with me right now, so I'm going on memory from last year's results (lesson usually falls in the spring).

1/2 - cherry tomatoes
1/4 - mushrooms
1/3 - green beans (yes, raw. They're actually quiet good.)
1/6 - carrots
1/5 - cucumbers
1/8 - celery

Becki 1st, 1/03/01 on teachers.net primary board

- - - - -

On my site I have a listing of some excellent books to use when introducing fractions to first graders.
Listing of Fraction Books

Many deal with pizza... a popular item among first graders! We use playdough to make pizza and cut it into halves, thirds and quarters using plastic, dull knives. I also have a blackline master of pizzas divided into halves, thirds and quarters and another of mushrooms, pepperoni and meatballs. They color and cut out, then I direct them to "make" a pizza with l/2 mushrooms and l/2 pepperoni, etc.

After reading Gator Pie [by Louise Mathews, Sundance Publishing, 1995, currently out of print], I give them a pie-shaped piece of paper and they decide how many animals (2, 3, 4 or 8) they want to feed this pie to. They draw the lines, cut it out and then we make a book following the pattern of Gator Pie.

Melissa, NJ, 1/03/01 on teachers.net primary board

- - - - -

"Fractions Are As Easy As Pie" is a game that has been around forever and is still available. If I remember correctly, the cherry pies are divided into halves, quarters, and eighths and the lemon pies are divided into thirds and sixths.

Another idea to use is to write the fraction in a totally vertical orientation as:

1 out of
2 equal parts

It helps children to understand the how and why of written fractions.

Grace/IL, Spel-Lang Tree, 1/03/01 on teachers.net primary board
top

> I am in need of a creative lesson on helping the students
> understand equivalent fractions and parts of a whole.
sugars/tx, 10/13/00

Paper Folding

I start each student with a piece of blank paper. They fold it in half, along either direction, and we quickly color one half of it. Then we continue folding and counting the colored sections: 2/4 4/8 8/16 ... but hasn't the amount of the paper we colored stayed the same? Then try thirds, sixths ...

After that we start talking about pizza pies, or birthday cakes, to see that eating 1/4 of the cake might mean eating 1 large piece of a cake that was cut into 4 pieces, or 3 slices of a pie that was cut into twelve smaller pieces. The smaller the pieces (the more of them there are, the larger the bottom number), the more you have to eat (the top number tells you how many you ate, the bottom number tells what kind of pieces they are -- the total number you cut the pie into and the relative size of each piece).

I don't think this is particularly clever or interesting, but it does seem to get the point across. Then when you have the fractions 1/2, 2/4, 4/8, 8/16, 16/32 written across the board as you fold the paper, you can look for a numeric "rule" -- because you can't always count on having a piece of paper handy to fold.

DSF/NJ (Donna), 10/14/00 on teachers.net math board

- - - - -

Fractions are as easy as pigs

One way to help students to understand the basics of adding and subtracting fractions (denominators must be the same; add/subtract the numerators; DO NOT add/subtract the denominators) is to teach the students what the parts of a fraction really are: numbers and names. This also helps combat the frequently-taught but incorrect idea that a fraction and a ratio are the same. A ratio may look like a fraction, but it is not a fraction.

FRACTIONS ARE AS EASY AS PIGS

What is 2 pigs plus 3 pigs? 5 pigs
(Write as a fraction: 2/pigs + 3/pigs = 5/pigs)
Notice, we do not end up saying the answer is 5 horses.

The top of a fraction is a NUMBER: 1, 2, 3, etc.
The bottom of a fraction is a NAME: half, third, fourth, etc.
We can add and subtract numbers. We cannot add and subtract names.

Denominate means: to name
Political parties nominate (name) their candidates.
Religious denominations are identified by their names.
The denominations of money are the names of the coins and bills.

Ask each student their "denominator." Don't give it away. Ask each one until one finally says their name. Continue through the room... Their name is their denominator.

When you practice adding and subtracting fractions with like denominators, actually say "pigs" instead the fraction name. Then say, "Instead of pigs, we are using ..." and let them answer with the appropriate denominator.

It is fun when doing subtraction to say, "If we have 5 pigs and eat 3 pigs, besides a stomachache, what is left?"

The transition to unlike denominators is automatic. If the names are not the same, you can't add the fractions.
2/pigs + 3 horses is still 2/pigs and 3/horses (unless we discover a "common denominator" -- a common name: farm animals).

Once the students know they must have a common name (denominator) in order to add or subtract, they have a reason to learn about common denominators.

By the way, I always begin common denominators without worrying about the Least Common Denominator (LCD). Once they can find a common denominator (multiply the denominators), add or subtract, and then reduce, they can be led to finding "easier" denominators to work with. Students who have too much difficulty with LCD can still get the correct answer; they just have more reducing to do. Those who can find a lower common denominator have less reducing.

This is a very basic rendering of "Fractions are as easy as pigs."

AWP, 10/12/00 on teachers.net math board

- - - - -

Candy Fractions

To make sure that children really understand fractions, I get their attention by bringing out Hershey Bars. First we look at it and determine how many sections it is divided into. We talk about how each section is 1/12 of the whole bar. Then I pass out rectangles of brown construction paper. They divide the paper as the candy is divided and mark each section as 1/12.

Then I break the candy bar in half. We talk about all the different ways that we could divide the candy bar in halves. The children cut their paper candy bars in two. Then we talk about what is in each half. We cut one of the halves in half and I write on the board all the statements that the children can make about their "candy bars" i.e.: "There are six twelfths in each half," "there are two halves in a whole," "there are three twelfths in a fourth," etc.

After the children are familiar with the basics of Hershey Bar fractions, I introduce M & M fractions. I get a regular size bag of peanut M & M's. I open them and we try to divide them evenly. (If I am lucky, and there are an odd number of candies in the bag, I correct the problem by eating one.) Then I give the children a sheet of paper with a bag drawn on it. They draw the correct number of M & M's in the bag with colored crayons. We divide the M&M's into two piles. They cut their picture of the M&M's in two. Then we follow the same procedure that we did with the Hershey Bar fractions.

Of course, if you have a small class or are home-schooling, you can use the actual candy bars and M & M bags instead of the paper counterparts. In any case, after the children have learned the concepts, I usually break up the candy bars (I keep a few extras so that everyone will get a piece) and give everyone a taste.

Hannah Means, letter to Math Cats, 11/25/00
Visit me at http://hannahmeans.bizland.com (A New Teacher's Survival Guide)
top

> A fellow teacher and I will be teaching a Summer Academy
> for Pre-AP 6th graders going into 7th grade Pre-Algebra.
> We are wanting Games that will reinforce operations with
> Fractions and Decimals. No worksheets etc.... just games...
> the title of our academy is "Math -- It's All Fun and Games!"
> Melissa, 5/31/00

Fraction Blackjack

One game that my students enjoy the challenge of is Blackjack 1. You need a set of fraction cards per student (or you can make them from index cards.) The same rules as Blackjack apply. Instead of trying to get to 21, they want to try and get close to 1 without going over. With this game they practice addition and comparing -- it's great. You can also make it more challenging or bring in mixed numbers with Blackjack 2 or Blackjack 3. (Blackjack 2 means to try to get as close to 2 as possible without going over.)

I am not sure where to buy fraction cards. I have one set that I received when I took over a classroom. However, I have always had the students create their own sets and we used them for several games. I gave each students a set of index cards (3 1/2 X 5) and they wrote the fractions in pencil so they couldn't be seen through the cards. These are the fractions we included: all fractions with a denominator of 2, 3, 4, 5, 6, 8, 10, and 12. (To challenge the students you may want to use the 7, 9, and 11 denominators as well.) I also had the students include 2 0's such as 0/3 and 0/4 and two 1's such as 3/3 and 4/4. Each game required two sets of cards, so I had the students write their initials in the corner of their set so they would get a complete set back after the game.

I remembered some other games:

Fraction War

Fraction War with the fraction cards: It is just like the card game of War, but with the fraction cards instead. This game helps students to compare fractions and encourages them to use number sense in comparison before using the algorithm of making equivalent fractions.

Memory

Memory with the fraction cards: It is just like the traditional "Memory" game, but any equivalent fractions are considered a match so 1/2 would be a match with 2/4. This game helps them to identify equivalent fractions. You can also play this game with fraction to decimal equivalence by making a set of decimal cards too.

Fraction/Decimal Bingo

Fraction/Decimal Bingo: The students have game boards with decimals on them. You call out fractions and if they have the decimal equivalence they can mark it on the board.

Kimberly, 5/31 and 6/1 on teachers.net math board
top

> I'm looking for hands-on, manipulative lessons for teaching
> and reinforcing fraction concepts... I hope to find some
> enrichment activities for adding and subtracting fractions
> with unlike denominators.

I went to google.com and typed in "fractions." A fair number of student-oriented sites came up on the first page of the listings. I visited most of the first-page links, and the bulk of the sites present lesson plans, or some ideas for hands-on activities (such as using measuring cups to show that 1/2 = 2/4 and so on). The few interactive Web pages were pretty simplistic, such as asking students to choose from a few multiple choice options when viewing a basic fraction illustration. You may find it useful to check out some of these sites, too.

I did not find exactly what you were looking for... a site which would enable students to add and subtract fractions with unlike denominators (meaningfully), so ... uh... I ended up staying up all night to create one myself! The only hitch is that it requires downloading a free MicroWorlds plug-in in order to use the project. But it is a very flexible project. The project page includes a link for downloading the free plug-in, and there is an accompanying project overview page for viewing a few screenshots to get an idea of how the project works, although of course the project overview is not interactive. If you download the plug-in, you'll be able to use hundreds of educational MicroWorlds projects at the MicroWorlds site (www.microworlds.com) as well as at all the sites on their links page.

These two pictures show two different ways of illustrating that 1/3 = 2/6 = 3/9 = 4/12. Basically, these are little screen shots from the project I developed. But on my project, the grid page includes a very large area for illustrating fractions. Students can illustrate many fractions at one time. If they want to add (using an example based on these animated gifs) 1/3 + 1/4, they could first make an illustration of 1/3 = 4/12, and next to it they could illustrate 1/4 = 3/12, and finally they could set up a representation of 7/12.

Now, I didn't think about including tools for writing problems, such as the + and - and = signs, but here's an idea. After the students illustrate their fractions, they can press the "PrtSc" (printscreen) key to save a screenshot of the computer's screen into the clipboard. Then they can open Paint (on a PC... Start -> Programs -> Accessories -> Paint) and press Edit -> Paste. They'll get a message that the clipboard image is larger than the paint area, and do they want to expand it? Choose yes. The screenshot is pasted. Now they can use the Paint tools to draw the signs for + or - or = ... or they can delete the unneeded portions of the picture and consolidate the needed portions; encircle the 4/12 and the 3/12; make a textbox stating the problem (1/3 + 1/4) or whatever. Then they can save their finished illustration of the problem, BUT be sure that they do not save using the Paint program's default (24-bit bitmap). They should click on file type and select GIF. (I saved an image both ways to compare, because I know how ridiculously huge the Paint files turn out. For the identical screenshot, the Paint (bitmap) image was 1.37 megabytes, and the GIF image was 33K. (When saving it as a GIF, they'll be cautioned that they may lose some picture quality; this is fine because it is just a few simple colors anyhow, so there will be no loss in quality.)

Now they can print out their little GIF image and start making a notebook or bulletin board of fraction problems with unlike denominators.

When all is said and done, it is probably easier just to do the same thing with colored pencils and graph paper! However, it is not so easy to illustrate pie slice problems by hand, and the other page of my project makes that easy (one pie at a time). To assemble an illustration of a pie problem with unlike denominators, they would need to save a couple of different screenshots and then copy and paste the relevant portions into another Paint file.

I really set up the project to be more of a fraction playground without worrying about saving pictures. This link takes you to the fractions project overview, and from there you can connect to the interactive project itself if you install the plug-in. (Sorry this was so long- winded... I'm tired!)

fractions project overview

Wendy P of Math Cats, 10/29/00 on teachers.net math board
top