Students sometimes have a difficult time understanding how fractions and decimals are related and how they can be compared. As always, providing a visual is essential for student understanding. Once students have a strong understanding on how to compare fractions, you can add decimals to the mix.
Begin by having students put together their fraction tiles. Give students 2 fractions to compare using one of the 5 strategies for Comparing Fractions. For example, 2/5 and 2/8. Have a discussion on how 2/5 is larger because both fractions have 2 pieces and fifths are larger than eighths.
Ask, how would the decimal 0.3 compare to those two fractions? Students should realize that 0.3 is 3/10 and therefore would fall between the two fractions.
Finally, ask students “where would the decimal 0.35 fall?” Discuss with students who this decimal is half way between 0.3 and 0.4.
This is a common misconception for students and providing that visual is a great way to strengthen student understanding of fractions and decimals. Have students try several similar problems to strengthen their understanding of how decimals and fractions compare.
What strategies do you have for comparing fractions and decimals?