File Folder Games for Middle Grade Students

Maybe it's because my initial teacher training focused on the primary grades, but when I decided it was time to start making supplies for my future classroom, file folder games quickly came to mind.

Doing a quick Google search showed me that few, if any, teachers are using this concept with older students. I'm not sure why this might be, but I have decided I will not let it stop me in my quest for useful and independent activities students can work with once their classroom work is complete.

Why would I use these with older students?

1. Portability It is likely that I will work as an occasional teacher for a while, so portability is mandatory. Even within a single school, there is a chance I would need to move from classroom to classroom depending on the school's schedule, so portability is always a desired feature.
2. Enrichment Opportunities No student wants to be faced with "more of the same" or be forced to help other students when their work is complete. Providing recreational math games in one way to help students extend concepts without extra drill and encourages them to think strategically.
3. Thriftiness The cost of purchasing plastic commercial versions of some of these games would be prohibitive. The bulk of the games would also make them cumbersome to carry and difficult to store. I can make similar versions of these that cost less, take up less space, and are laminated to improve durability. A missing piece can be easily reprinted.
4. Versatility Laminated surfaces lend themselves well to dry-erase markers (or even crayons that can be wiped off in a pinch). This means games can be adapted to suit current needs, and it also means that popular paper-and-pencil games can be played with less paper waste involved.
5. Novelty If I can't find them online, chances are good that most middle grade kids aren't used to seeing file folder games as part of their math instruction.
6. Play Value Introducing new concepts through play can help students develop a deeper understanding of the underlying concepts. Playing a code-breaking game can help introduce the concept of combinations and permutations, for example. Probability, geometry, co-ordinates etc. can also be introduced through game play. While the folders lend themselves well to after-work activities, they can also be used to introduce concepts to the entire group. When the focus moves away from computation and "right answers only" into the underlying concepts and strategies, many students feel less threatened with the introduction of new concepts. As we would not forbid a toddler to use a word he or she could not yet write or spell, we can encourage students to develop meaning and concept through games and exploration before demanding computational accuracy.

The games I will be making include many from my math pages here: http://llemonade.com/math and here: http://llemonade.com/math2 These include classics such as Dots, Hex, Black, Birdcage and several others. What is wonderful about these kinds of games is that most of them are traditional and quite old, and as such, remain in the public domain.
If you wish to use any of the boards I have drawn specifically for my site, you may, with the caveat that these are for personal use, which includes homeschooling for a single family, use for a single classroom, or recreational use at home. Many hours of work go into the development of the resources I share. If you wish to make these and sell them or otherwise distribute them, you will need to contact me with the details so we can come to an arrangement.
Once I have completed the math games, I will likely print out some Madlibs from my print page as well, primarily for ESL students, but also available to all students upon completion of the main classroom activities.

As I have completed the basic games and ensured that the layout works, I will share those printable boards and rules on the print page as well.

This is the process I use:

1. Determine the game to be used and divide it into three main sections: the rules, the board, and any playing pieces.
2. Create separate files for each section and print these out. Since the games are aimed older, they are less clip-art oriented and quite minimalist, but clip art and other graphic features can be added as desired.
3. Create a cover piece that included the title of the game and the number of players required.
4. Print all of these out on regular printer paper.
   
5. Trim the printouts as needed.
6. Paste the board to the inside of the folder. Larger boards must not bridge the folded area as they may make the folder too bulky to fold. Paste the cover on the front and the rules either on the inside left of the folder, or on the back for larger boards.Laminate the folder and playing pieces separately.
7. To make a pocket that is both laminated but which you can open up, see this excellent blog post I found that has clear instructions complete with pictures http://lifeasaconvert.blogspot.ca/2011/09/how-to-attach-pockets-to-file-folder.html
8. You can also paste the pocket right onto the folder before laminating if you do not need to be able to close a flap. This eliminates the need to use velcro to attach it later. If you want the best of both worlds--a pocket that has a flap you can close and is sealed onto the board with the lamination rather than velcro, try lining up the pocket at the edge of the folder so the flap extends beyond the edge. It can then be folded at the edge of the folder. It may be a little bulky, but the pocket will not be easily lost.

Enjoy!

Frugal Fractions

Ice cube trays, floor tiles, egg cartons, Lego bricks, wall tiles, chocolate bars, pizzas, notes in an octave, an analogue clock face, flower petals, graph paper, oranges, a flat of canning jars, a football field; what do all of these things have in common?

Perhaps my title gave it away, but each of these things (and many more) are common examples of fractions in everyday life. Each of these involves a whole divided into parts--a whole dozen eggs, a whole tray of ice cubes, a whole orange, etc.

If you have already visited my math page, you may sensed where I am going with this post.

It is my belief that the purchase of expensive, specialized math manipulatives is unnecessary and does little to accomplish one of the goals some profess to have by using them, that of relating mathematical concepts with the "real world".

There are exceptions, of course. I have loved using pattern blocks with my students and kids for many years, and would not hesitate to recommend them. Their uses are many, both in terms of math and art. And were I to be in a hurry, I might consider purchasing or borrowing a class set of base-ten manipulatives, although the students would miss out on some learning involved in measuring and cutting their own sets.

But for fractions, I believe we can do much better using everyday and homemade items.

Chances are, if you were to read the above list, you would see you have at least one of the concrete examples available to you in your home right now. What makes a good example of an everyday fraction set? These are my criteria:

1. It must have equal parts that form a whole that can be somehow identified (floor tiles of a whole room, or ones in the area marked off with masking tape, for example).

2. It must be present, measurable and real in order to be considered concrete (time is not so concrete, but a calendar or analogue clock face can be).

Some examples will be easier to use than others. If you choose to use an egg carton, hard-boiled eggs, marbles or other place holders might be well advised, or you can cut up the carton into egg sections and use a second one to hold the cut up pieces.

Using food containers alone you could probably find examples of halves, thirds, quarters, fifths, sixths, eighths (hotdog buns), tenths, twelfths (hotdogs), 20ths, 24ths, etc. Some quantities seem to be more common than others, which is another cause for classroom discussion.

There will likely become a time not far into the discussion of fractions where some smaller and more manageable examples will become more practical.

I often have my students use construction paper or coloured copy paper (which has the bonus of being recyclable), to create their own fraction sets.

Along with providing an inexpensive solution, the actual making of the manipulatives helps to reinforce the concepts. The language alone contributes to making mathematical connections as you must divide the paper into equal sections. Other related skills include measurement, reviewing the concept of equivalency, fine motor skills of marking and cutting, division, area, perimeter, and can spin off in other directions as well--even into Pythagoras' famous theorem if you start working on right-angled triangles as your base shape.

So, how do you start?

First, you need to start with a base shape. For this example, I'll use a rectangle.

Next, you need to decide on the shape's dimensions. I'll start with a 10 cm by 24 cm shape, mainly because these dimensions are convenient for easy division.

To reduce the amount of work involved, have students cut four of these in one go. Give each student four sheets of different coloured paper (using a sheet of 1 cm graph paper as one of these sheets can help provide a stronger visual representation). Show them how to use paper clips to hold the pieces together in place as they cut. Once they have measured and cut their pieces, they should have four rectangles of the same size but of different colours.

Now they choose one colour (usually centimeter graph paper, but you can vary this if desired) to keep whole as a base, and the other three to divide into equal parts. Remind students to stop after dividing each colour to label the fraction on each piece; for example, if you divided the yellow sheet into halves, label each half as 1/2 before moving to the next sheet in order to avoid confusion.* Using a paper clip to hold all of the same sized pieces together also helps keep things organized. Provide a large envelope for each student or pair to store their set.

If you used a 10 cm by 24 cm guide, you might suggest they divide one into halves, another into thirds and another into quarters. Or you can use higher denominators as you wish. If all the students are working with the same dimensions, you could have them work with a partner and provide each pair with 8 different colours so that they can work with additional fractions, such as fifths (a bit challenging to figure out, but definitely possible!), sixths, sevenths (very challenging as these dimensions do not divide evenly by 7) eighths, etc.

For halves and quarters, you can have students fold the paper to divide it, then cut or use the "lick and tear" method to separate sections. You can then challenge them to find ways to fold the paper equally into thirds, fifths and other fractions not divisible by 2, or simply ask them to measure and cut, depending on your time and intended focus.

Students can now use their labeled fraction kits to compare different fractions, add and subtract fractions, etc. Which is larger, 3/5 or 2/3? You will know they understand the concept when they can explain it both visually and by making the operational connection to division, ie. 3/4 = three divided by four = 0.75 = 75%. Showing the relationship between halves, quarters and eighths and/or thirds and sixths is a good way to start a discussion on finding the lowest common denominator, or as I like to introduce it, the simplest way to show that amount (but it is important that they also learn the proper terminology!). In fact, it is a good idea to review the terminology often. Remembering that multiplication can also mean "groups of" or just "of" can help make the concepts more accessible. Likewise, a reminder that the "denominator" is "down" and shows how many parts you need to make a whole, and that the "numerator" is the "number of parts of the denominator that are actually there" can go a long way for many students. Others will find it easier to directly treat all fractions as division questions, so providing parallel terminology will help those students make that connection. For example, in 1/2, the 2 is the divisor and the 1 is the dividend; the quotient would be 0.5, and the remainder would be 0.

You can repeat this exercise with circles (have students draw a circle using a compass), a square, or even a right-angled triangle. When you use a circle, some of the students may wish to start exploring circular geometry, which can be a good way to double-check answers.

A related discussion to explore might be how to represent a fraction with the denominator of 0. What might dividing by 0 really mean, and how mathematicians work with / around such problems.

For classroom use, it may be useful to make a teacher copy of each type of set from coloured transparencies.

For homeschooling, try ordering a pizza and ask for it to remain uncut (or make your own pizza). Use this to reinforce size comparisons in fractions, ie., assuming you like pizza, would you rather have 2/5 or 1/3 of one?

Or try making some lasagne or magic bars (shown in the photo at the top).
Beware though, you may be in for some very detailed measuring!

*You can also show students how 1/2 is the same as "1 of 2"; etc. to show the relationship in terms of language already encountered in arithmetic, since "of" is a multiplication word. This helps show that fractions are actually little division problems too, and also helps reinforce the connection between multiplication and division.