Comparing Fractions

Est. Class Sessions: 2

Developing the Lesson

Part 2. Comparing Fractions

Use One-Half as a Benchmark.

Use the following discussion prompts to facilitate a class discussion in which students compare fractions to 1/2.

Show 1/2 of the red circle using your circle pieces. [Students show one pink piece.] Leave the pink and red pieces out on your desks.

Use your circle pieces to show 1/3 of the red circle. [Students show an orange piece.]
Is 1/3 more or less than 1/2? How do you know? (Possible response: 1/3 is less than 1/2 because the orange piece is smaller than the pink piece.)
Who would get more pizza, two girls who divided the pizza fairly or three boys who divided the same size pizza fairly? (the two girls)
What part of the pizza would each girl get? Each boy? (1/2 and 1/3)
Which fraction is larger, 1/2 or 1/3? (1/2)

Direct students' attention to the Comparing Fractions to One-Half chart that you prepared before the lesson. See Figure 1. Tell students that they are going to sort fractions into three groups: fractions less than 1/2, fractions equal to 1/2, and fractions greater than 1/2. Ask a student to write 1/3 in the correct column of the chart. Then ask students if they agree or disagree.

Continue the discussion by asking students to work with a partner to decide where 2/3 goes on the chart. Tell them that they must be able to defend their choice to the class. Ask volunteers to place 2/3 on the chart and explain their thinking to the class. Students can either use circle pieces, their Fraction Chart from Lesson 4, the Fraction Chart from the Reference section of the Student Guide, or reasoning to explain their choice.

Repeat the discussion with the fraction 2/4 . Use the following sample prompts:

Is 2/4 less than, greater than or equal to 1/2? How do you know? (Possible response: 2/4 of the circle is 2 yellows. Two yellows fit on one pink piece exactly, so I know that 2/4 is the same as 1/2. Two-fourths goes in the middle column.)
Did anyone think of it another way? Can you use another tool? (I used the fraction chart we made with the fraction strips. Two fourths ends at the same line as one-half, so they are equal.)

Ask student pairs to think of a fraction they would like to see added to the chart. Each pair should be ready to represent the fraction using fraction pieces or the Fraction Chart. Then, add fractions to the Comparing Fractions to One-Half chart.

Ask pairs to come to the front of the class, show their fraction, and decide where the fraction belongs on the chart. Ask students to explain how they know whether the fraction is less than, equal to, or greater than one. Encourage the students to use either fraction pieces or the fraction chart to compare the fraction to 1/2. The students then asks the class whether they agree or disagree. If a student disagrees, he or she explains where the fraction should go and explains his or her reasoning.

Compare Fractions Using Strategies. If students do not select the following fractions, suggest them and ask a student to add them to the chart: 3/3, 1/4, 3/4, 1/6, 3/6, 5/6, 1/8, 3/8, 4/8 and 7/8.

After the fractions have been added to the chart, ask students what they notice about the fractions in each column of the chart. Give them a chance to discuss the question with a partner. Then, ask what they see.

If necessary, use prompts similar to the following:

What do you notice about the fractions that are equal to 1/2? Look at the numerators and the denominators in each one. (Possible response: all of the numbers on the bottom are doubles of the numbers on the top. Or, all of the numbers on the top are half of the numbers on the bottom.)
What happens when you double the numerator, the number on the top? (You get the number on the bottom, the denominator.)
Why do you think that is? If I divide a circle into four pieces, how many cover one-half? (Two because two is half of four.)
If I divide a circle into six equal pieces, how many cover one-half of the circle? (Three because three is half of six.)

Choose a fraction from the first column and a fraction from the third column such as 1/3 and 3/4 and ask which is larger. Students can use any of the tools that they have used so far to answer the question. Some students will need to use physical models to compare the fractions others will be able to visualize those models to compare two fractions.

Assign Check-In: Questions 5–7 in the Student Activity Book. Students sort fractions using 1/2 as a benchmark in Question 5. To complete Question 6, students need to recognize that when you divide the same unit whole into more pieces, the size of the pieces gets smaller. In Question 7, students use strategies to compare fractions to solve a problem.

Before students begin to work on these questions direct them to the Math Practices page in the Reference section of the Student Guide. Ask students to read Math Practices Expectations 1, 2, and 5 carefully and to think about how these math practices can help them think about the work they are going to do.

Ask:

Why is it important to read each question carefully before you try to solve it? (You need to read each problem carefully so you know what is being asked and what numbers you need to use.)
What tools or strategies do you think you can use as you solve these questions? (You can use fraction circles or the fraction chart.)
In Questions 6–7 you are going to explain how you found your answer. What do you need to include in your answer so someone else will know what you are thinking? (You need to use words and labels to show how you solved each question. You can also use drawings to help show your thinking.)

Use Check-In: Questions 5–7 to assess students' abilities to compare fractions using area models and one-half as a benchmark [E10] and find equivalent fraction using models [E9].

Check-In: Questions 6–7 can also be used to assess students on the following Math Practice Expectations:

MPE1.: Know the problem. I read the problem carefully. I know the questions to answer and what information is important.
MPE2.: Find a strategy. I choose good tools and an efficient strategy for solving the problem.
MPE5.: Show my work. I show or tell how I arrived at my answer so someone else can understand my thinking.