Comparing Fractions with Unlike Denominators Using Journaling
Grade Levels: 3 - 5
This is an introduction to comparing fractions with unlike denominators. Students will compare fractions represented by drawings or models with unlike denominators.
Fraction: A number used to name a part of a group or a whole. The number below the bar is the denominator, and the number above the bar is the numerator.
Numerator: The number above the line in a fraction. The numerator represents how many pieces of the whole that are discussed.
Denominator: The bottom part of a fraction. The denominator represents the total number of equal parts in the whole or the set.
Unlike Denominator: Fractions that have different numbers as the denominator.
Journaling. Have students write a short definition of a denominator in their journals. This is meant to access their prior knowledge of fractions, specifically denominators. Example of journal entry: A denominator is the bigger number in a fraction.
Review parts of a fraction using models. Draw a square divided into 4 equal parts with 3 parts shaded. Write the fraction 3/4 and review how it represents three of four equal parts shaded. The 3, or numerator, tells how many parts are shaded, while the 4, or denominator, shows how many equal parts the whole is divided into. Ask students to volunteer their definitions and discuss the correct definition, which could be something like: The number below the line in a fraction. The number that represents the whole, or total number of equal parts in a fraction. Draw a model of the fraction 1/3 and compare the two fractions. Ask, "Which fraction is greater?" Discuss the idea that the amount of space that is shaded shows which fraction is greater.
Journaling. Have students answer: How do you know if a fraction is greater than another fraction? This is meant to help students access their thinking and problem solving in comparing fractions. Example of journal entry: The fraction with larger numbers is the bigger fraction. Compare the numbers and the larger numbers will show the greater fraction.
Provide students with this handout with rectangles divided into 2 parts, 3 parts, 4 parts, 5 parts, 6 parts, etc. Demonstrate the first example. Cover one equal part of the first model. Cut a piece of construction paper to the size that fits one equal part and cover it on the handout. Write the numerical fraction for the covered area, 1/2. Then have students cut pieces of construction paper to place over one part of each model on the handout, and write the numerical fractions for the covered area of each model. Be sure that the numerators are all the same as students are doing this activity.
Journaling. Have students write what happens when the denominator of a fraction increases. Pair up students, have them exchange notebooks, and discuss what they found. This is meant have students think about what they found, and record their observations and conclusions. Example of journal entries: I noticed that as the denominator got larger, the fraction pieces got smaller. The number of parts covered is the same, but the number of equal parts changes. The fraction gets smaller when the denominator increases, and only one part is covered. A smaller denominator should give a larger fraction. It didn't make sense to me at first, but when I worked with fractions like 1/2, the pieces were big, and when I worked with fractions like 1/8, the pieces were smaller. So, as the denominator gets greater, the pieces get smaller.
As a class, have students share what they wrote, and discuss their findings.
Journaling. List fractions with a numerator of one, and have students order them from least to greatest. For example, list 1/5, 1/25, 1/50. Have students use their journals to explain how they figured out how to order the fractions. Example journal entry: If the numerators are the same, the fraction with a smaller denominator will be the greater fraction. A larger denominator should give a smaller fraction.
Compare fractions. Introduce or review the inequality symbols of greater than, > and less than, <. Have students use the fraction pieces to show the fraction 1/5, and then to show the fraction 1/8. Explain how to write an inequality, from left to right, and read it as a sentence. For example, 1/5 > 1/8 is read as "One-fifth is greater than one-eighth." If students need help in remembering which symbol to use, you might want to have them think of an animal, such as an alligator, who wants to eat the greatest fraction. The "mouth" of the animal should be opened to the greatest fraction.
To provide guided practice comparing fractions with unlike denominators, have each student in a pair choose one rectangle on the handout, cover one part of any rectangle, then compare the two fractions that are made. Have pairs determine which is greater, by stating the fractions aloud. For example: 1/5 is less than 1/3; 1/2 is greater than 1/8.
Have students reflect on the lesson and journaling. Have them write about what they liked about journaling and if they learned more about the topic of comparing fractions. Share their ideas during a class discussion.
Have students draw several examples of fractions with unlike denominators, and write the fractions with an inequality symbol, comparing the fractions.