You may have noticed that kids have a few issues with fractions… but it can be tricky to understand what is going on, particularly when the difficulties only tend to show up on NAPLAN. Here is a great video to show what kids really think, along with four principles to master.
Check for these misconceptions with your class:
Often in lower primary, circles and squares are the main models used to teach fractions. You can find lots of misconceptions simply by using rectangles instead of circles. Here are a few simple examples:
Principles to master
Principle 1: Fractions need to be fair
Fractions need to be fair. Try folding an A4 piece of paper like this. Often kids think through the problem in the following order. Here are their assumptions:
- The pieces are quarters, just because there are four .
- They are “uneven” quarters: there are four of them but they are different sizes.
- They aren’t quarters because the pieces aren’t “even” (Note: students use “even” as meaning “symmetrical”)
- They are the same size!! They are quarters because of their size even though they look different.


Principle 2: Fractions are named for size, not the number of pieces
Try showing this image to students. Five of the shapes show halves. Watch out for the following issues:
- The thirds must be “three halves” or “three quarters”
- Diagonal halves are triangles, so can’t be “half” as they are not symmetrical
- The star shows halves
- Two quarters is not half
- Halves can’t be 3D

This image shows another check for the same issue of fractions being named for size rather than shape. Watch out for the following:
- The pieces are thirds, because there are three of them
- They are “uneven” thirds (or “improper”, or “irregular”)
- The image shows “three quarters”
Principle 3: The whole needs to be the same size when comparing
I tend to recommend blank paper rather than grid books to avoid this issue!


Principle 4: The whole need should not get bigger
Arrays are a great way of representing fractions as they show the multiplicative relationship.
Remember too… fractions are numbers more often than shapes
Think of a number line between 0 and 2… try these questions.
- Where would 1/2 go? Most kids put it in the middle of the line, but it can’t be the middle, because that would be one! 1/2 is a number, not just about folding or finding the mid point. And 1/2 doesn’t go in the middle of every line.
- Where would 2/3 go? How about 3/2?
- How about 0.23?
- And what would you add to 2/3 to find an answer of 3/2?
Here are different students’ answers… from different schools… being wrong in the exact same way due to misconceptions.
Next steps:
Fractions: If you want to find out what your kids really understand, download this free diagnostic test from our book, Fixing Misconceptions in Fractions. Follow the advice for interpreting the results, then use the first 8 lessons suggested and redo the test to check your effect size.
Decimals and percent: If your kids are ok with fractions, you might want to try our free diagnostic test for decimals and percent, or order Fixing Misconceptions in Decimals and Percent.
Want more?
And finally…
Check out this 13 minute video on teaching fractions operations. More videos are available for members 0n the Professional Learning Videos page as well as embedded into the work program.
Operating with fractions