Note: Blank templates for fraction strips and fraction circles are available if needed (M-4-3-1_Fraction Circle Template.doc and M-4-3-1_Fraction Strip Template.doc).
Say to the class, “Let’s review some of the things we know about fractions. A fraction represents part of a whole unit or part of a group of objects. Fractional parts of a whole unit must be equal in size.”
Draw the following pictures on the board.
Write the following on the board:
Have a student name the fraction for the shaded part of each circle:
Ask “Which is more?” questions, starting with the samples on the board. Point out that figures A and C show two representations of one-half and are equal, although both the numerator and denominator in figure C are larger than those in figure A. Also have students explain in their own words how they know that figure B represents a fraction that is less than the others and what it would take to make it equal or greater than one-half. Encourage students to demonstrate their thinking using fraction circles, chips, 1-inch color tiles, pictures, or number lines.
- “Which is more, of a dozen eggs?”
- “Which is more, of a pie?”
- “Which is more, of an energy bar?”
- “Which is more, of a pizza?”
Students’ responses will provide a quick check of their skills in comparing and ordering fractions. Introduce the term benchmark fractions to students. Explain that benchmark fractions are commonly used fractions. Tell them, “We will be comparing fractions to 0, , and 1.”
Have students fold a sheet of paper to create a three-column benchmark chart and record their answers in the chart.
Fractions Nearest to 0
Fractions Nearest to
Fractions Nearest to 1
On the board or overhead transparency, write the following fractions:
Have students analyze each fraction in relation to 0, , and 1. Provide parallel number lines (M-4-3-1_Parallel Number Line Sheet.doc) or fraction circles for students to use. Ask,
- “Which fractions are closest to 0?
- Which fractions are closest to ?
- Which fractions are closest to 1?
- Do you see any patterns among the fractions in each column?”
Help students discover and describe the following patterns between the fractions in each column:
- Fractions closest to 0 have numerators that are very small in comparison to their denominators.
- Fractions closest to have denominators that are about twice as great as their numerators, or the numerators are half as great as their denominators.
- Fractions closest to 1 have numerators and denominators that are about equal.
Write the following groups of fractions on the board:
Have students discuss how to order each group of fractions from least to greatest. Have students use the Parallel Number Line worksheet.
When ordering unit fractions from least to greatest, the fraction with the largest denominator has the smallest value.
Note: Be sure students understand the above pattern only applies when the numerators are all 1.
Say to the class, “Now that you can order fractions, we are going to compare fractions using the symbols <, >, or =.” Write and draw the following on the board:
Be sure to point out that the fraction strips are equal in length.
Ask for a student volunteer to circle and on the fraction strips.
Ask, “Which fraction is greater?” Have another student place the appropriate symbol in the box.
For additional practice, write the following problems on the board (without the symbols filled in).
Give students a few minutes to do the practice problems. Call on students to supply the answers and discuss any misunderstandings.
“Now that we know more about comparing fractions we will look at this problem.” Present a “fair-share” problem. Students should work with a partner.
Jenny, Marcus, and Renee bought two 1-foot-long submarine sandwiches. They want to share the sandwiches equally. How much should each of the three friends get? Draw a picture of the context of the problem on chart paper.
Ask students to talk to their partners for a few minutes about how to divide the two sandwiches equally among three people.
- “How much does each friend get?” ( of each sandwich or of the total sandwiches)
- “How is it possible for three people to share two sandwiches?” (They divided each sandwich by thirds to make 6 parts and took 2 parts each.)
Encourage students to use any materials they find useful to compare the fractions (paper strips to fold, linking cubes) and to make drawings to help them. It is important that students construct a way to show the problem. Do not provide materials with the fractions already labeled. Making and drawing the fractional pieces encourages students to think about the meaning of the fractions.
For additional practice, have students complete the Fair Share Problems worksheet (M-4-3-1_Fair Share Problems and KEY.doc).
When students have completed all activities, discuss the results and clear up any confusion. Then have each of them complete the Lesson 1 Assessment (M-4-3-1_Lesson 1 Assessment and KEY.doc).
- Routine: Create a set of fraction cards and randomly select two cards. Have students select the greater or lesser fraction of the pair. Repeat the activity for daily review or to remind students how to compare fractions throughout the school year.
- Small Group: Separate the class into groups of two (pairs). Give each student a number cube. Have students write a fraction with a denominator of 7 and a blank numerator. Have students roll the number cube and use the number rolled as the numerator of their fraction. Encourage students to compare and record each pair of fractions. Repeat this activity using other denominators greater than 6.
- Have students determine which benchmark fractions, 0, , or 1, the given fractions are nearer. Include fractions that are equally between the two benchmarks for students to discuss (for example, and are equidistant from ). A resource worksheet is available to help students organize work (M-4-3-1_Expansion Resource Sheet.doc).
- To extend the idea, list several improper fractions and have students determine the wholes or halves each is nearer to. For example, is between 1 and 2 but nearer to 2, or . (For additional examples, use ).