After I wrote the last entry on fractions and number lines, I realized that due to Covid, my 7th grade students missed out on learning to differentiate between fractions that represent parts of a whole (like 1 part of 4) and fractions that represent a distance or volume. It can be quite challenging to teach students to differentiate but it can be easier when using with the correct strategies.
Begin by using a variety of visual representations, some of which are better to portray parts of a whole while others work better to show distance. Fraction bars, circles,, or rectangular models are the better choice to show parts of a whole since they show how fractions represent a part of a whole. On the other hand, number lines are a better way to represent distance or rectangular models to represent volume.
Next, one should provide real-world examples to illustrate the difference. For parts of a whole, use examples like dividing a pizza into equal slices or sharing a candy bar. For fractions representing distance or volume, use examples like measuring cups or rulers to show how fractions can represent lengths or volumes.
In addition, present word problems that require students to interpret the meaning of the fraction in context. For example, "Sara drank 1/3 of her juice. If she had 12 ounces of juice to start with, how many ounces did she drink?" This helps students see how fractions can represent parts of a whole or a quantity.
Take this a step further by comparing fractions representing parts of a whole with fractions representing distance of volume. This comparison can help them learn to differentiate how fractions are used and what each type represents.
Include hands-on activities to help students visualize fractions. For example, have students use fraction circles to compare and manipulate fractions, or use measuring cups to measure and compare volumes represented by fractions.
Finally, encourage students to verbally describe the fractions they are working with, including the context of the fractions. Ask them to explain the difference between half of a pizza versus half an inch on the ruler, or half way to the next town in their own words.
By using these strategies, you can help students develop a deeper understanding of the difference between fractions that represent parts of a whole and fractions that represent distances or volumes. Let me know what you think, I'd love to hear.
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