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This lesson provided by:
Author: Scott McKinnon
System: Florence City
School: Harlan Elementary School
General Lesson Information
Lesson Plan ID:
26348
Title:
Fractions on a Number Line
Overview/Annotation:
As students master the concept of the number line, they may be curious about where fractions would fit on a standard number line. Students will work cooperatively to explore the possibilities where fractions lie on number lines. Students will also work independently to extend and enrich their new knowledge of fractions on number lines.
This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.
Associated Standards and Objectives
Content Standard(s):
MA2015 (3) 15. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. [3NF3]
a. Understand two fractions as equivalent (equal) if they are the same size or the same point on a number line. [3NF3a]
b. Recognize and generate simple equivalent fractions, e.g., ^{1} /_{2} = ^{2} /_{4} , ^{4} /_{6} = ^{2} /_{3} . Explain why the fractions are equivalent, e.g., by using a visual fraction model. [3NF3b]
c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. [3NF3c]
Examples: Express 3 in the form 3 = ^{3} /_{1} ; recognize that ^{6} /_{1} = 6; locate ^{4} /_{4} and 1 at the same point of a number line diagram.
d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. [3NF3d]
MA2015 (4) 12. Explain why a fraction ^{a} /_{b} is equivalent to a fraction ^{nxa} /_{nxb} by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. [4NF1]
Local/National Standards:
NCTM Grade 3
* develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers;
Primary Learning Objective(s):
The students will identify fractions on a number line.
Additional Learning Objective(s):
The students will create posters with fractions shown on number lines.
Preparation Information
Total Duration:
61 to 90 Minutes
Materials and Resources:
Technology Resources Needed:
1. Document camera
2. LCD Projector
3. Computers with Internet access
4. Plugins via Help section of ALEX
Background/Preparation:
Teacher preparation  The teacher needs to be familiar with Internet activities #13, listed in the Extension section of this lesson plan. The teacher needs to print 2 KWL charts (one for number lines, one for fractions). Each student will need one copy of each KWL chart. The teacher needs to generate four number lines (010 by 1's, 020 by 2's, 050 by 5's, and 0100 by 10's) on the number line generator listed in the materials section. These are for display purposes (via LCD projector). The teacher needs to print one copy of blank fraction number lines per student (see attachments). The teacher needs to print one copy of black line fraction strips per pair. The teacher should have previously grouped students in pairs (shoulder partners , A/B partners, etc).
Student preparation  The students should have background knowledge on number lines, skip counting, and fractions (numerator, denominator, parts of the whole, etc). The students will need general computer skills for extension activities located on the Internet. The students should have background knowledge of measurement and rulers.
Procedures/Activities:
Engage 
The teacher will engage the students in a discussion of the number line. The teacher will remind the students that they have already studied many number lines, including number lines counting by 1's, 2's, 5's, and 10's. The teacher will display the number line KWL chart and the students will receive their own number line KWL chart to fill in together. The teacher will ask students what they know about number lines and what they want to know about number lines. The group will fill in the first two sections of the number line KWL chart. Then, the teacher will lead students in a choral count by 1's to 10, 2's to 20, 5's to 50, and 10's to 100, to encourage participation and instill confidence in these skills they have already mastered (the teacher will use the number line generator found in the materials section to generate the number lines the students are chorally counting by and will display these for all to see on the document camera, while the students are chorally counting). The teacher will then "shift gears" and lead the students in a discussion of fractions, by examining a ruler and completing the first two sections of the fractions KWL chart. The teacher will ask the students measure their pencils with rulers, using inches. The teacher will demonstrate that not all pencils will have a whole number measurement. Some pencils will lie in between the whole numbers. The teacher will point out the "tick marks" that lie between the whole numbers. These are fractional portions of inches! Next, the teacher and students will complete the fractions KWL chart. Then, the teacher will then ask the key question of this lesson, "Where do fractions go on the number line?" This question is important because it is the main focus of this lesson and it will show how the two KWL charts are related.
*Evaluate  Teacher will assess students understanding of fractions and number lines via KWL charts, confirming and correcting as needed.
Explore 
The teacher will encourage students to make predictions, about where fractions should be placed on a number line labeled to "1". The students are then given a blank fraction number line sheet and are partnered with their shoulder partner. The teacher will write "1/2" on the board and will ask the students to place 1/2 on the first number line (the students will place fractions on the number line much like normal digits; a small line (tick mark) crossing the number line, with the fraction written underneath the tick mark). The students at this point may or may not know where some of the fractions will lie on the number line. The teacher will write the following fractions one at a time and will ask the partnered students to place the fractions on the corresponding number lines (second line  1/3...2/3, third number line  1/4...2/4...3/4, fourth number line  1/6...2/6...3/6...4/6...5/6, fifth number line  1/8...2/8...3/8...4/8...5/8...6/8...7/8)
*Evaluate  The teacher will observe the students' work, listening to conversations about where the fractions will lie on the number lines. The teacher will neither confirm nor deny student work at this point.
Explain 
The Teacher will now distribute one copy of Black Line Fraction Strips per pair. The teacher will ask the students how they did with their blank number lines. The teacher will listen to students as they describe fractions they labeled correctly and incorrectly. The teacher will state that as fractions are labeled, it's important to remember that these fractions are equal parts of the whole. The teacher will demonstrate (using the document camera) how the fraction pieces are equal (1/2 = two equal pieces, 1/3 = three equal pieces, 1/4 = four equal pieces, etc). The teacher will state that the denominator represents how many equal pieces are on the number line, while the numerator represents a certain piece on the line.
*Evaluate  The teacher will listen to student comments about the placement of fractions and will lead a discussion about fractions that were easy or hard to place.
Extend 
The teacher will now explain that the students will be working in centers. In the first center (majority of the students), shoulderpartnered students will use chart paper to create a poster of fractions on number lines. A number line will need to be created for each of the fraction sets (denominators 210). See Fractions on the Number Line Poster Rubric (in attachments) for poster grading guidelines. The second center will be computer stations in which shoulderpartnered pairs will complete Internet activities listed in the Extensions section. Students will be given a 45 minute block of time to complete the poster. Students will spend 15 minutes on the computer activities. The rotating strategy and timeline for the two centers will depend on how many students are involved and how many computers are available.
*Evaluate  Students are evaluated on posters created based on the Fractions on the Number Line Poster Rubric.
Attachments: **Some files will display in a new window. Others will prompt you to download.
Assessment
Assessment Strategies
*Evaluate  Teacher will assess students understanding of fractions and number lines via KWL charts and direct observation, confirming and correcting as needed.
*Evaluate  The teacher will observe the students' work, listening to conversations about where the fractions will lie on the number lines.
*Evaluate  The teacher will listen to student comments about the placement of fractions and will lead a discussion about fractions that were easy or hard to place.
*Evaluate  Students are evaluated on posters created based on the Fractions on the Number Line Poster Rubric (see attachments).
Acceleration:
Intervention:
The students will work with partners, so peer remediation will be an option during the course of the lesson. Also, some students may need extra help with placing whole numbers on a number line. The teacher can use sheets from blank number lines for remediation (listed in the materials section) to reinforce this skill.