Fractions & Geometry

I love when math strands overlap and students can see the connections between them.  Fractions and Geometry overlap quite a bit.  There are three ways to think about fractions:

1. The Set Model
This model works with fractions of groups, like ¼ of 24, so ¼ would be a number, like 6.
Example: One third of the students in the class are wearing blue.

2. The Linear Model
This model works with fractions of lengths, so ¼ would be a specific point on a line.
Example: Measure to the nearest quarter inch.

3. The Area Model
This model works with fractions of space, so ¼ would be an amount of space, or an area.
Example: Cut this cookie in half.

It's this last one, the area model, where fractions and geometry meet.  This is where students learn to partition rectangles, circles, and other shapes into halves, thirds, fourths, etc.






A strong understanding of the area fraction model is also super important for being able to find the area of more complex shapes in later grades.  (And that’s the Measurement & Data strand, so really, now we are working on concepts that support THREE different Common Core math strands- what a great way to get the most out of class time!)

Here are a few tips for teaching this area model of fractions and incorporating geometry into your lessons:

1. Use geoboards and rubber bands.  Kids tend to naturally be good at making patterns on the geoboards.  Encourage them to divide the whole board in half, thirds, etc.  This is also a great way to include a lesson or review on symmetry.

2. Cut and fold paper.  Folding something in half and then half again is a simple way to make equal fourths.  Fold it a third time for eighths.  Students may fold their papers in different ways to make pieces that are different shapes, but they will be equal areas.

3. Divide up your classroom (or hallway or bulletin board or gym or playground).  Use painter’s tape or chalk and lots of measuring tools.  The bigger the space and the more fractional pieces, the harder it is.  Good teamwork is needed for this one!

4. Make spinners.  Have the kids trace any circular object (bowl, cup, any other container- be creative!) onto a paper and then try to divide it into 2, 3, 4, 6, 8, 10…  equal spaces.  They can use them for math games or they can make up their own fun spinners (like MASH when we were kids…).

5. Cut up playdough (or real!) cakes, brownies, and cookies (or sandwiches, pizzas, bagels… food is great for this!!) 
PRO TIP: This is also a great way for families to get involved.  Have a fraction of the week and encourage them to have the kids cut all their food into that fraction.  Start with halves, then move on to thirds and fourths… maybe even fifths or sixths for more of a challenge!


6. Make fraction art.  Ed Emberley's book Picture Pie is perfect for this.  Students can cut out fractions of a circle and make a collage.  (For a FREE printable fractions of a circle template, 
click here.)  This works particularly well for fractions of a circle, and is a great way for students to become more familiar and comfortable working with those fractions.  This also builds important understandings for when students go on to learn about angles, later in geometry.






Happy (fraction & geometry) teaching!!

Christine Cadalzo


pssst... for a ready-made math unit for teaching geometric shares, click here.