how to teach fractions

Teaching Fractions: How To Introduce Fraction Concepts

I find it to be very interesting that many people, adults and kids alike, are scared of fractions.


Each year of teaching, I encounter students who are in one of two camps: they are overwhelmed by how abstract fractions are, or they enjoy fractions because of how concrete they are!


Wow! What a huge divide (pun intended)!


I love investigating this type of difference.


What I have found is that students’  attitudes towards fractions can often be traced back to their introduction to fractions.


When parents or teachers introduce fractions in a way that pushes new symbols and vocabulary too soon, kids are turned off. Think about it, most kids are exposed to fractions even before division.  If their first fraction experiences are with written fractions, all at once they are…

  • dividing numbers into equal pieces for the first time,
  • thinking about values between zero and 1 (talk about abstract!),
  • learning words they never hear in everyday conversation (e.g. numerator and denominator),
  • seeing numbers written in a new way (one on top of the other), and
  • seeing a new symbol that looks like a subtraction sign but isn’t (it’s called a vinculum, by the way. I had to look that up!).


YIKES!  That’s introducing wayyyy too much at once! 


On the other hand…

When students begin their fraction journey with hands-on activities, they seem to feel that fractions are a natural part of life.


Fractions are all around us. Kids have heard about sharing for years by the time they learn about fractions in school. They have felt cheated when given less than exactly one half of a cookie. Many of them know there are 4 quarters in a dollar. Most of the time, they have played with plenty of blocks, which has built their proportional reasoning.


We see many cutesy activities with pizzas and candy bars representing fractions, and while that’s a good start, it doesn’t guarantee the authentic experience students need.  If you know me well, you know I’m often skeptical of cutesy educational products! I appreciate the real-life connection, but it’s what students are doing with the pieces of pizza and candy I pay close attention to.


We want students getting their hands on fraction pieces, exploring proportions, and sharing aloud the patterns and connections they find.fraction-tiles


Before any other fraction work, students need many activities that simply require them to observe what happens as they work with physical, concrete fraction tiles or pieces.


This is why I created the game Fraction Swap.




Playing Fraction Swap is super fun, and it gives students the hands-on experiences they need to understand fractions in a concrete way.


As they play, students physically compare fraction pieces to see if they can make equivalent fractions.


4th grade 5th grade fractions math game


Fraction Swap works for everyone because it’s a game of strategy. It lets kids who are new to equivalent fractions learn by using the size and shapes of the blocks. It’s also engaging for kids who are ready for operations with fractions. They play strategically and have rich discussion afterward about how to represent their moves with equations.


The goal of the game is to completely cover 2 whole rectangles with the fewest number of fraction pieces. Players strategically swap groups of small fraction pieces for larger, equivalent fraction pieces.


fraction math for elementary teachers


These hands-on actions are essential for building a strong foundational understanding of fractions.


Kids build and deconstruct fractions over and over during this game. Teachers can take this activity as far as they like with the discussion questions included in the provided lesson plan:

  • Share a strategy you used in this game.
  • How did you know when fractions were equivalent? Show and explain, please.
  • What patterns or connections do you see between equivalent fractions? (On the board, write some equivalent fractions. Ask class to call out patterns they notice.)
  • What factors helped you win or lose a round?
  • Which cards were best or worst to pick and why? (This gets kids talking about larger and smaller fractions. Larger fractions help you cover the board, smaller fractions (1/12 for example) are useful in making “swaps” that help you get larger fractions eventually.)
  • When did you multiply a fraction by a whole number? (“Swapping” two 1/4 pieces for a 1/2 piece is 1/4 x 2 = 1/2)
  • When did you divide a fraction by a whole number? (“Swapping” 1/2 piece for two 1/4 pieces. 1/2 ÷ 2 = 1/4)
  • How could I represent this game board (put some fractions on a board) as an equation? (This can be an addition or multiplication equation.)

fraction game for teaching elementary math


Fractions don’t have to be scary. Elementary students learn so much from hands-on play. It is fun for kids, easy on the teacher, and highly effective. Win-win-win!


fraction game for elementary math students

improve math education at elementary schools

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