Fraction Fill-In

Players: 2 or more
Ages: 8 and up
Cost: Free!
Math Ideas: Equivalence, fractions, addition, decomposition
Questions to Ask: 
    What fraction did you get? What other fractions could you fill in that would be equivalent?
    How many ways can you fill in 1/2 on the paper? How many ways can you fill in 2/2?
    What do you think 3/2 means?

One reason that games make such great teaching tools is that they give kids a reason to care about the math they are using.

Hand a kid a worksheet full of multiplication problems, and they might balk. But play a game where multiplication is used to calculate the score, and suddenly they have a desperate need to find out what 6*8 is.

Similarly, football fans in 3rd grade are lucky: the 7s times table, notoriously the most difficult to memorize, is a breeze if you've spent the past few years counting touchdowns. Whats 5*7? That's just five touchdowns: 35 points.

Anyway, ever since I launched this newsletter I've been looking for a game that would be fun and strategic, yet help kids grapple directly with the most challenging topic in elementary math: fractions.

I think I found that game. I've seen it by a couple names, but I'll just call it Fraction Fill-In.

How to Play

To play Fraction Fill-In, you will need to print a game sheet for each player. The game sheet contains a blank fraction wall, which is a very common representation of fractions. Each row is a different set of fractions that equal a whole. You have two halves, three thirds, four fourths, and so on.

You'll also need a pair of dice labeled as follows:

Dice One:  1, 2, 2, 3, 3, 4

Dice Two: */2,  */3,  */4,  */6,  */8,  */12

Dice One tells you the numerator of your fraction, while Dice Two tells you the denominator. So if you roll 2 and */6, your fraction is 2/6.

(If you don't have blank dice and sharpies lying around, you can print and shuffle up these cards, which provide the same fractions)

Each player rolls the dice and then has to color in a portion of their fraction wall that is equivalent to that fraction. 

So if you roll 1/2, you can color in 1/2, or you can color in 2/4 or 3/6 or 4/8 or anything else that is the same length as 1/2. You can even combine fractions of different sizes: If you want to color in 1/3 and then 1/6, you can! Those fractions combine to 1/2. You can see several ways to color in 1/2 in the image at right.

So let's say you roll 1/2 and decide to shade in 1/4 and 2/8. With a colored pencil or marker, you color in your fractions. Then, under the fraction wall, you write "1/2" as what you rolled and "1/4 + 2/8" as what you colored. 

This step, which is extremely important, gets kids thinking about the ways that fractions can be combined using addition to make larger fractions. We'll come back to that later...

Anyway, your opponent then takes a turn rolling the dice and shading in their own fractions. If you cannot shade in your fraction or an equivalent fraction for some reason, you must pass. The first person to fill in their entire board is the winner. 

Where's the Math?

I love this game because there is plenty to talk about, whether you're a third grader or an eighth grader.

One of the core ideas in the game is equivalent fractions. Kids spend years finding and simplifying equivalent fractions, but rarely is the connection between 2/3 and 4/6 made visually clear in later years. 

But in Fraction Fill-In, you can clearly see that 4/6 has exactly the same length as 2/3, and therefore it is another way of describing the same amount of space. 

Additionally, kids will occasionally roll fractions that are greater than 1, such as 3/2 or 4/3. This may even be the first time they've seen a fraction with a numerator that is greater than the denominator. Is that even allowed? How can you shade in four thirds if you only have three thirds on the fraction wall?

The beauty of the game is that the fraction wall creates a visual scaffold for these conversations. Kids can compare lengths to find equivalence. So they might realize that 3/3 is simply a whole, which means they can shade in an entire row to represent that amount. And since every row is the same length, they can shade in 12/12 or 8/8 just as easily as 3/3. 

This semester, I had a girl who simply refused to do anything related to fractions. When we analyzed probability, she said she didn't understand the meaning of 2/3 as a fraction. 

But a mont h or two later, when I pulled this game out, she dove straight in. Every roll, she asked me to confirm that her choice of fraction was, indeed, equivalent. And every roll, she was right! 

As a middle school math teacher, I know that many of my students hate fractions. It's my hope that games such as these make fractions feel more fun, more approachable, and more comprehensible for students.

Questions to Ask

The first question to ask is the core of the game: "I see you rolled 2/3. What other ways can you color in that length of fraction?"  

Fraction Fill-In is a game that benefits from repeated plays, so don't be upset if your child tends toward the easier solutions at first. The structure of the game, with its dwindling set of available fractions, will encourage them to think creatively over time.

You can also reverse the question: Ask them to confirm your own decisions:  "I rolled 1/2, so I'm going to color in 1/4 and 1/6. Is that alright?" 

If they correctly identify the error, get them to explain why! The more time they spend justifying their reasoning and describing fractions out loud, the more deeply they are internalizing the main lessons that the game has to offer.

If you're a teacher using this in a classroom setting, you could turn each person's table of fractions into a set of problems to prove. "Ok, Tara filled in 1/3 and 1/6 and says that equals 1/2. Can everyone use what we've learned about fraction addition to prove that she's correct?"

Once your kids get more comfortable with the game, you can turn it into a puzzle! Ask them "How many unique ways can we shade in 1/2?" This, by the way, is a really fun activity to try on your own. Combine your own methods with your child's ideas to see how many you can create together! Then get them to suggest the next fraction and find all the ways to fill in that amount.

Fraction Fill-In is a great game that can be returned to over and over as kids learn more about equivalent fractions, comparing fractions, and adding fractions. If you're starting to see your child get frustrated by the abstract rules of fractions, this game is a great chance to say "let's step back from this problem and just play a game for a few minutes."