The following is a slide taken from NCETM Checkpoints. I was happy with the fraction pair on the right but the left stumped me! Then I had that 'aha' moment!
What I used to do
I never used to teach equivalent fractions like the one on the left to my classes. I would just use arrows to multiply both numerator and denominator to find an equivalent fraction, very similar to the fractions on the right.
The issue with this though is, like me, students don't necessarily see all of the multiplicative relationships between the fractions as well as within the fraction. They are missing that key knowledge to support them answering the first pair of fractions.
What I do now
Ratio tables allow students to see those multiplicative links. By doing this it makes questions like the checkpoints task much easier for students to do.
Disclaimer: this isn't the only way I teach equivalent fractions. I also show students how prime factors can also help us. There will be a future blog post showing this.
Using a ratio table links the multiplicative relationship of equivalent fractions to similar relationships with converting units, exchange rates and even speed. If students have a strong understanding of the multiplicative relationship in equivalent fractions they are able to simplify fractions easily. This also supports students understanding when simplifying and calculating with algebraic fractions at a higher level.
So the next time you are teaching students to find equivalent fractions use ratio tables... As well as prime factors.