Fractions

Here are some games I play with my kids after they each make a fraction kit.

How to Make a Fraction Kit
(adapted from Marilyn Burns About Teaching Mathematics)

Use 5 different colors (I use yellow, blue, green, red, and pink) of long construction paper (12 X 18). Cut each piece of long construction paper into 4 strips (3 X18). Each child will need one strip of each color.

Have the students take a particular color (I use yellow), fold it in half, and cut it into two pieces. Have them label each piece at ½. Then choose the second color (I use red) and have them fold it in half, and then half again. Have them cut and label each piece as ¼. Then have them cut the third strip (I use blue) and label as 1/8 and the fourth strip (I use green) as 1/16. Leave the last strip (pink) whole and label 1/1.


Things You Can Do with the Fraction Kit


Compare Fractions
Order Fractions
Equivalent Fractions
Games to Play with a Fraction Kit

First: You can make a fraction cube using a die and colored dots. Write ½ on a yellow dot, ¼ on a red dot, 1/8 on two blue dots, and 1/16 on two green dots. Stick the dots to the die to make your fraction die. You will need one die for each group. All games can be played with partners or small (4-5 students) groups.

Cover Up
This game can be played with two or more players. The object of the game is to be the first one to cover your entire whole (1/1) strip.
Rules:
1. Students start with the whole (1/1) strip in front of them.
2. Student rolls the fraction cube.
3. The fraction on the cube tells them what piece to place on their whole.
4. No overlapping pieces are allowed. If the fraction you roll won’t fit on your strip, you lose that turn.
5. You have to fill your strip exactly. If you only have 1/16 left, ½ won’t do.


Uncover
This game is a good game to introduce equivalent fractions.
Rules:
1. Students start with the whole (1/1) strip in front of them. They cover their whole strip with the two ½ pieces.
2. Student rolls the fraction cube.
3. A student has three options on each turn. They may remove a piece from the whole (only if they have the exact piece they rolled), they may exchange a piece (for example, they can take off a ½ and replace with one ¼ and two 1/8), or they may skip their turn.
4. If the student chooses to exchange on a turn, they cannot remove any pieces from the whole, they can only exchange equivalent pieces.

Put it in Order
Write 12 fractions on index cards, one fraction per card. Write them large enough for the whole class to see. Tell the students their job is to put the cards in order from least to greatest. Begin by placing an index card with the fraction ½ in the middle of your white board tray. Show the cards one at a time, each time asking the students where to place it. The students should use their fraction kit to make the fraction to find the order.

Here are sets of cards that work well with this activity. Avoid using equivalent fractions in this activity.

Set 1 – 1/16, 1/8, 3/16, ¼, 3/8, ½, 5/8, ¾, 15/16, 1/1, 9/8, 3/2

Set 2 – 1/8, 1/6, ¼, 1/3, ½, 2/3, 15/16, 8/8, 17/16, 7/6, 4/3

Set 3 – 1/16, 2/8, 3/8, ¼, 2/4, ¾, 7/8, 15/16, 4/4, 17/16, 9/8, 5/4

Hey there, LaTina! Thanks for your reply.

It just occurred to me if you're working on fractions right now, maybe you can use these 'Fraction' vocabulary cards that I made, as well. Each word and definition is a full page. (I had them on a large sized bulletin board.)

Also, I have a two paged document that I made when we worked on Prime numbers. Then, I'll attach a 1 page version of the same information.

You can take a look and decide which of those might be useful to you. (Hopefully, there's be something there you can use!;))

Here's a smaller version of the Fraction/Prime/Composite Vocabulary on 1 page. Students can cut it up to use as flashcards, or they can keep the entire page in their notebooks.

(I had to re-copy the table and put it all on a new document so that it would upload.) Hope someone can use it! ;)

I love your idea of walking around the school to look for fractions, lismac. If your crunched for time, though, you can also have the students stand in different-sized groups and take pictures of them. The students have really liked this in the past. They can write things like, "2/5 of the students are wearing glasses" or "1/4 of the students have red hair." My students have liked this in the past, because it is about themselves.

I had paper plates that I marked for cutting. (halves, thirds, fourths, sixes and eights)
I had the children label the fractions on each section of the plate. 1/2 etc.

Then I had them work in groups to make as many equivilent fractions as they could out of those plates and then glue them to construction paper and write "Equivilent Fractions", then for example 1/2 = 4/8" I also made them write it in words: one half equals four eighths. Another teacher copied my idea, but her kids colored the plates to look like pizza slices, which was much cuter in the hallway than my plain old plates.

It would be easier to run off circles (and more accurate). I'd make them about 2-3 inches in diameter. Also, be sure to tell them only match one fraction type to another. Some kids tried to match one third and one sixth = one half (which is true, but...) Also, because of inaccuracies, some kids tried to do stuff like 5/8 = 2/3. So you have to watch them.

I have put M&Ms (you can use more than one kind: peanut, plain, etc.) in plastic bags. I put random amounts, you may want to count. Generally I try to have 20-30. Even numbers reduce easier. It helps also if you do not allow them to take them out of the bag. Easy to count and doesn't make a mess.

In class, I give each student pieces of paper cut into 4ths. The students count the number of M&Ms, this becomes the denominator of the fractions. (This is a good review for denominator and numerator.) I call out for them to show the fraction that represents the number of blue M&Ms or the larger M&Ms they have in their bag on one sheet of paper. They must also write the simplified/reduced answer beside the orginal. They compare with their classmates and if they have the same answer they go to the front of the room.

Sometimes you will get students that just get the same orginal fraction. Ex: 3/16 & 3/16. That's not what you really look for. You can eliminate them from going to the front. It's really neat when there is two different orginal answers but then the reduced answer shows that they are equivalent. Ex: 4/20 = 1/5 & 7/35 = 1/5. If this isn't happening frequently then have the kids eat some of the M&Ms to make their denominators divisible my more numbers. The kids really enjoy that part.

I just realized you wanted an extra credit idea. Maybe you can use this one in the class. :)

I teach 5th grade as well. I think you need to allow your students to explore a variety of approaches, starting with a conceptual approach. Have you tried drawing/using visual models of different fraction amounts when comparing? In my opinion, students should not solely be taught a procedure and expected to memorize steps and/or any "short cuts", like cross multiplying, without first having a good understanding of the actual concept or skill. There will be those students who prefer a procedural approach and will do well with it, but we shouldn't expect all students to use one method. We need to show kids a variety of "tools" or methods they can use when approaching a problem. Then we can guide towards evaluating different methods and reasoning why one method may be a "better" method (more time-efficient, etc) for solving a problem.

We walked around the school in small groups armed with cameras and looked for fractions occuring in our school. Each child had to find one scene to capture with the camera. Another group stayed in the classroom and created their fractions with classroom materials. Example- 10 pencils. 9 were yellow and one was red. Then the small groups would come to our computer and insert their picture. Each child then inserted text boxes to type in the fractions. Example- 9/10 of the pencils are yellow. 1/10 of the pencils are red. 9/10 + 1/10= 10/10 They could choose the fonts and colors and such... they used word art to add their names. They loved it! We also do one using multiplication.

One activity that went over pretty well with my class was putting fractions in order. After completing a lesson on comparing fractions, each student was given a fraction on a 3x5 card and asked to tape it to their chest. Then they were instructed to line up in order from greatest to least. After they had completed the task, after much deliberation, I informed them of the correct order. They did pretty well considering there were fifteen students.

I created an interactive fraction number line from 0 to 2 on my wall. I have about 40 fraction cards with different fractions and I have students take turns putting the cards on the number line. They get the chance to see that some of the fractions are equivelent to others.

You can use a multiplication chart to find equivalent fractions and also to reduce fractions.
Example:
Find 1 and 3 in the first column follow your fingers over to the next number in the row- 2 and 6, then to the next numbers 3 and 9 etc.
This might help with the multiplication problem as well!!! I hope I explained this ok and I hope this helps.

Hi, im student teaching right now and the fourth grade teacher I am with taught them to find equivalent fractions by multiplying the original fraction by a number over itself ... or a whole basically...

for example the fraction is 1/2 then you multiply that by 2/2, 3/3, 4/4, 5/5 and so on... and it will give you equivalents.

Well, you are not alone. Fractions lessons sometimes need repeating over and over until they understand the CONCEPTS. Try giving them a mnemonic device to help them remember what to do. My kids decided to use GCF as Greatest Calories n Fat so that's why you REDUCE!! This just helped them to know when to use the GCF but it still needs lots of practice. Also, do a lot of hands-on activities that show equivalency in fractions. Make fraction strips using construction paper, and the kids can show all the equivalent fractions by matching up the strips. Or try the pizza fraction pieces that you can buy. I believe that it just takes lots of fun practice as well as drills on the procedures. Take your time and don't rush through it or you'll be sorry to see that they won't remember any of it by Christmas!!

My 7th graders prefer this method, too. If they can't see an obvious relationship between the 2 denominators (x/5 and y/20) where they can just multiply the numerator, then they cross multiply. The important thing is remembering that you go from bottom and cross up. So if it were 4/7 and 5/6, you'd multiply the 7 up to the 5, then that product stays on the right. You multiply the 6 up to the 4, and it stays on the left side. With 24 on the left, and 35 on the right, you can compare the fractions.

As mathtch said, it's essentially just finding a common denominator by multiplying the numbers times each other. But it's faster for comparing 2 individual fractions than going through the steps for an LCD.

The cross mult. method


3 5
4 6 works every time. In this example 6x3=18 &
4x5=20. The 18 (ends up on left side) is less than the 20 on the right, so 3/4<5/6. This method gives kids a fighting chance when comparing fractions.

I used 10 x 10 grids with my students. They were allowed to "design a tile" they would like to see in their homes. You may want to start with only allowing them the use of one crayon and add more colors later. After the design process was finished, they identified shaded and/or unshaded parts of their tile as equivalent fractions, decimals, and percents. Depending on how far you want to go with this activity, you could also used other sized grids (5 x 5, etc.) and have students identify equivalent fractions, decimals, and percents with calculators and/or long division.

Yep, agree that it is meant to be simplified and then converted. We also did a lot of work on converting some of the more common fractions in decimals, like 1/3, 1/4, 1/5, 1/6, 1/8 and 1/10. Most of the kids did not remember that 1/8 = 12.5%, but there were a few that remembered 1/8 was 1/2 of 1/4, and 1/4 was 25%, so 1/8 must be half of that.... I was impressed they figured that out!

But, agree with other poster. I teach the kids (who all get calculators on state tests) that the line in a fraction actually signifies "divided by" so 6/8 is actually the same as 6 divided by 8, and the decimal can be found that way as well. I try to teach them many ways to find the decimals so they have options. Some kids understand one way better than another.

--I don't think kids have to know their multiplication facts to understand equivalent fractions. They just have to know how to "count by." If the fraction is 1/4, they have to be able to count by one in the numerator and four in the denominator.

--Another thing I did was draw fractions number lines (about seven inches long) on a piece of paper, one under another with enough space between lines so my students could label the points. The first line was not divided. The points were labeled 0 and 1.

The second line was divided into halves. The students labeled the points on the line 0/2, 1/2, and 2/2.

The third line was divided into thirds. The students labeled the points 0/3, 1/3, 2/3, 3/3.

You probably get the idea. The remaining lines were divided into fourths, fifths, sixths, eighths, tenths, and twelfths, and the points were labeled. (It is very important to be sure that 1/2, 2/4, 3/6 etc. line up vertically.)

Then my students took a piece of string and laid it vertically. It touched the equivalent fractions. You have not only taught equivalent fractions, you have also taught labeling a number line with fractions between zero and one.

I'm not sure about multiplying the denominators but cross multiplication works but they will have to simplify if needed. Cross multplying is like using the product of both denominators as the LCM.
18 20
3 5
4 6 Since 18 < 20 then 3/4 < 5/6.

It would be the same as saying that the lowest common denominator is 24 because you would be multiplying 3x6 and 5x4. It's hard to explain in written form.

Hope this helps.

Make up index cards before hand. Group them in 3's (.25 on one card, 1/4 on another, 25% on the third) make up however many sets of three you need to give a card to each of the students in your class. Once the cards have been shuffled, pass one to each student. Have them find their 'family' WITHOUT MAKING A SOUND. When .20, 1/5 and 20% find each other they have to put their cards on a large number line in the front of the class. It's a great way to get them all involved, and gets them up and around the classroom.

Here's the blackline version of the same table

This is not easy for kids that are just really learning how fractions, decimals and percentages relate. There was a question like this on our state test last year (I only know because they ALL raised their hands and asked how to do it...poor kids.) Anyway, here's what was expected.

6/8 is not in simplest form. If you reduce (by dividing by 2/2) you'll get 3/4. Three fourths is one of those benchmark fractions (like 1/4, & 1/2) that our kids are supposed to be able to easily convert to a percentage (1/4=25%, 1/2=50%, 3/4=75% because of money). To actually do the math to convert it, you'd turn 3/4 into an equivalent fraction, using 100 as your new denominator. 4 must be mult. by 25 to = 100, so you need to mult. the numerator 3 by 25 as well (to be sure you are multiplying by a fraction name for 1). 3x25 =75. 75/100 is = to 75 percent (since percent means out of 100).

For some reason, the 9 & 10 year olds I teach think this is a bit complicated. Wonder why?;)

This is one of the first things I teach my 5th grade class because they need to find their own percentages on tests and quizzes all year.

We start off using a calculator. Simply tell them that you divide from top to bottom. 6/8 = 6 divided by 8 = They will get a decimal that we convert to a percent.

Later in the year we look at the ratio and figure out how to divide by hand. I tell them to push the top of ratio (numerator) off to create the division problem. 6/8 = 8)6 For some fun, we yell, "Timber!" when we push over the fraction. After all of the practice with the calculator, they understand how to convert the decimal easier and the whole concept is not such a big deal to them.

I strongly recommend having them do this for their own grades. The repeated practice is what solidifies the skill.

I teach 5th but this is what I show them. Let's say the mixed number is 3 1/4. I tell them that changing it into an improper fraction is really putting the whole thing into fraction form. I remind them that the denominator tells me how big the pieces are and the numerator tells me how many of those pieces I have. Then I draw four circles on the board. (We also use individual white boards a lot, so sometimes I have them draw the circles and do this process.) Then I tell them to think of these as pizzas (or pies - whatever). I tell them I have 3 whole pizzas, so I shade in three of the circles - and I also have 1/4th of a pizza, so I divide the 4th circle into 4ths and color in one of the pieces. I show them how this represents 3 1/4. Then I ask, how many pieces would we have altogether if I "cut" the other pizzas up into the same size pieces? (I remind them that I'm not taking any of the pizza away or adding any more to it.) So then I draw lines on the other (whole) circles showing them divided into 4ths and mention that "all of these pieces are 4ths, right?" (even though they are are still together as a "whole" pizza). So then I ask "now how many pieces (4ths) do we have all together?" and we count up all the pieces. We see that we have 13 pieces and those pieces are 4ths, which makes 13/4. Then I do a quick "review" of how multiplication is like counting sets of things - and don't we have 3 sets of 4 pieces here? So 3 times 4 is twelve, but we also have to count the one other piece, so that makes 13 pieces altogether. I then use another mixed number and show them that now I can multiply the whole number by the denominator and then add the numerator to find out how many pieces there would be if I were to cut up the wholes into the same size pieces as the fractional part and that gives me the equivalent improper fraction. (I'm assuming they already know what "improper fraction" means.) Then to change from improper fraction to mixed numbers, just do the whole process backwards (explaining how division is putting things into groups).

I suppose if you wanted to, you could even use paper circles (or paper bars - call them candy bars) and have them actually cut them into pieces. You may need to have them do this a few times to see the connection between "cutting up the pieces" and just multiplying the whole number by the denominator and adding the numerator. Hope it helps. Have fun!

Have boxes drawn onto paper. Have one box for 1/4, 1/2, 1/8 etc. Then, they roll the dice and fill in the box they have rolled. The first person to get a black out wins (whole paper filled in.)

If you have little fraction pieces already cut out or made of plastic (pizza slices?) they can roll and draw the corresponding piece. The kids have to make 1 whole with the pieces they drew.

I also have my student play Fraction Tic Tac Toe, on a 4 x 4 grid filled with halves, fourths, and eighths. They have to make a whole with 3 fractions in a row. They love it!!! I'm not sure where the gamesheet come from, but I am sure you can make your own.

A few weeks ago I made a quickie table for my fourth grade students when we were studying the relationships between fractions, decimals, percents and money. Now that I've had more time, I took another look, made some changes and reprinted it.

Knowing that others may be able to use such a table with their students I'm posting two versions.
(1) Color version
(2) Blackline version

If you find any errors, please feel free to let me know. I've come to realize that when we look at something for a long time, we THINK we caught all the mistakes or typos, but inevitably there always seems to be one more little thing that got past us! :confused: (I hate when that happens!;)) Sheesh! Even just a minute ago, as I was reviewing it just to make sure, I found a typo! Arggh!