Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 49794
The Human Number Line
This lesson uses a human number line to help students estimate a fraction's approximate position on the number line between zero and one. It also
helps students visualize and understand the relative size of fractions, preparing them to be able to make comparisons.
Subject(s): Mathematics
Grade Level(s): 3
Intended Audience: Educators
Suggested Technology: Document Camera
Instructional Time: 1 Hour(s)
Freely Available: Yes
Keywords: fraction, comparing, ordering, number line, equivalent, numerator, denominator
Resource Collection: CPALMS Lesson Plan Development Initiative
LESSON CONTENT
Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
Students will:
use a number line to represent fractions
be able to compare two fractions using a number line
Prior Knowledge: What prior knowledge should students have for this lesson?
Prior to this lesson students should have learned Mathematics Standard 3.NF.1.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is
partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b:
Students should
know that fractions represent equal parts of the same whole.
know that the denominator represents the number of equal parts.
know that the numerator represents the number of equal parts that are shaded or somehow different from the other parts.
Guiding Questions: What are the guiding questions for this lesson?
Can you correctly place a given fraction less than one on a number line?
How did you decide where to place your fraction on the number line? What information does the denominator give you? What information does the numerator give
you?
Can you use the number line to compare two fractions and tell which one is greater?
Teaching Phase: How will the teacher present the concept or skill to students?
At the beginning of the lesson, the teacher will review students' previous knowledge of fractions, including Mathematics Standard 3.NF.1.1 Understand a fraction 1/b
as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b and review
that fractions must have equal parts.
that a fraction can show parts of a whole and parts of a set.
that when a whole is cut into equal parts, the denominator names the number of equal parts
that the numerator of a fraction is the count of the number of equal parts that are shaded or somehow different from the other parts.
page 1 of 4 Many students will not be familiar with the idea that a number line can include numbers between the whole numbers.
For this lesson, we are focusing on the number line between zero and one. To initially activate students' prior knowledge, I show them a ruler.
Do you ever have to precisely measure items that are not exactly one inch, two inches, or three inches long? What do you do? Have you ever
had to measure a very small object that is even smaller than one inch long? How can you do it?
Most of the students will have an idea that things can measure one-half inch; some will even understand the idea of a quarter inch.
We then discuss other wholes that we commonly break into fractional parts:
a quarter or a half of an hour
a quarter of a dollar
first quarter, half time, third quarter, whole game completed in a football game
measurements in recipes
How can we plot these fractions (numbers smaller than one) on a number line?
Guided Practice: What activities or exercises will the students complete with teacher guidance?
1. Prior to the math lesson, draw a large number line with chalk or create a number line with masking tape in a spacious area outside your classroom. Mark 0 and 1
on your number line.
2. Explain we are going to be forming a human number line outside the classroom. Students are to follow the same rules they would normally follow doing a math
activity in the classroom. They will need to listen carefully to directions and then speak in whispers as they try to create a correct number line together as a group.
3. Hand each student a fraction card as they line up to exit the classroom.
4. As the students come near the large number line you have marked, explain that their task is to arrange themselves correctly on the number line. They can help
each other, but each person gets to make his/her own final decision as to where he thinks he belongs.
5. Let the students move around and find their place on the number line. Do not help them! Encourage them to help one another and discuss the mathematics. If one
student is in the wrong place, let another student explain where he should move and why.
6. At this point, the students are usually in the correct order, but they probably have not thought about spacing themselves correctly. Should one-eighth be closer to
zero or to one-fourth? How close should eleven-twelfths be to one whole? Why?
7. Ask students: Which fraction on the number line is the largest? How can you tell? Which is the smallest? How can you tell? Guide them to the realization that the
largest fraction is closest to one, while the smallest is closest to zero on the number line.
8. Collect the cards, shuffle them, and pass them out to different students. Repeat the activity, encouraging the students to do it faster the second time. You can even
use a timer or challenge the students to find their places on the number line without talking at all.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
1. Bring the students back inside and hand out baggies containing 5 of the fraction cards along with a long, thin strip of construction paper to create their number line.
(I cut up copies of the fraction cards prior to beginning the lesson and place them in baggies, so that each student has a fraction equal to or near one-half, equal to
or near one whole, and equal to or near zero, along with 2 other fractions. Not all of the baggies contain the same fractions, leading to better discussions during the
Closure portion of the lesson)
2. Ask students to label zero, one half, and one on their number line. Have the students place the fraction cards in the correct place on the number line.
3. The teacher should circulate and check to make sure the fractions are in the correct place.If students have made mistakes, ask guiding questions to help.
This fraction has the same denominator as this one, but a larger numerator. What does that tell you?
What does the denominator in your fraction tell you about the size of the piece?
If your numerator is small, what does that tell you?
How can you tell if your fraction is close to one-half? one whole? zero?
4. Have the students glue their fractions onto the number line.Have each student choose three fractions and justify how he/she decided where it belonged by writing
notes below the fraction.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
1. The teacher will gather the students back together at the end of the practice activity (on the rug or other gathering area, if possible).
2. Have students share their strategies for placing the fractions on the number line.
Which fractions did you place first? Why?
How did you decide how to space your fractions?
If I gave you the fraction
where would you place it? Why?
How does using the number line help you to visualize which fraction is greater?
3. Have students go back to their desk and write a 3-2-1 response in their math journals.
Three things I learned during the lesson
Two questions I still have, or things I am wondering
One thing I enjoyed about the math lesson today
Summative Assessment
The students will work independently to sort a set of five fraction cards and place them correctly on the number line between zero and one. They will then choose
three of the fractions and justify (using words and/or pictures) how they decided where to place that fraction on the number line.
Students will also write in their math journals to reflect upon their learning and log any questions they may have at the end of the lesson.
Formative Assessment
The teacher will
List some common unit fractions for the students:
,
,
,
,
and ask them to put them in order from least to greatest on an individual
whiteboard or in their math journals.
Then ask students to share their answers with a partner and explain the way they ordered their fractions. Meanwhile, the teacher should circulate and check for
understanding.
Choose a student to share his or her thinking with the group. What strategy did you use to put the fractions in order? What did you notice? Allow other students to
agree, disagree, or share different methods of ordering the fractions.
The teacher will use the students' responses to adjust instructions, as needed, to meet the needs of the students.
page 2 of 4 Feedback to Students
The above activity allows the teacher to assess students' understanding of the idea of fractions as parts of whole numbers. Third grade students strongly identify with
the idea that larger digits = larger number value, but with fractions that is often not the case. It is important that students have many hands-on experiences with
fractions in different contexts, so they can develop a true number sense about fraction size. Early misconceptions can be corrected by using fraction tiles or having
students draw their own pictures to see the size relationships.
Student feedback through guided questions will be included and misconceptions corrected throughout the Teaching Phase, Guided Practice, and Independent Practice.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
This human number line portion of this lesson usually works for students at all ability levels because it allows for movement, and the class is working as a team to
create the number line correctly.
If students struggle while trying to glue the fraction cards on the number line independently, allow them to use their fraction tile manipulatives. You can also give
struggling students fewer cards to work with.
English Language Learners may need extra support with vocabulary. The teacher should note, if the students need extra instruction with visuals or definitions to
understand the vocabulary they are expected to know and use.
Extensions:
To extend this lesson and make it more challenging, repeat the number line activity, but this time include equivalent fractions. Wait and see if the students make this
discovery on their own!
Use the fraction cards to play "Fraction War." Student pairs shuffle the cards and then deal them all out. Each student turns over a fraction card at the same time. The
player with the larger fraction wins both cards.
Suggested Technology: Document Camera
Special Materials Needed:
For the teacher:
one set of fraction cards
large number line (created using chalk or masking tape)
For the students:
one envelope or baggie of 5 fraction cards for each student
long strip of construction paper to serve as the student number line
scissors
glue stick
Further Recommendations:
You can change this lesson by using fewer fraction cards or by altering the fractions you include to make them easier or more challenging. For example, I change the
fractions to include equivalent fractions as we learn that skill or include several fractions equal to or close to one-half to explore "friendly fractions."
Additional Information/Instructions
By Author/Submitter
This resource is likely to support student engagement in the following Mathematical Practices:
MAFS.K12.MP.2.1 - Reason abstractly and quantitatively
MAFS.K12.MP.4.1 - Model with mathematics
SOURCE AND ACCESS INFORMATION
Contributed by: Karyn Cole
Name of Author/Source: Karyn Cole
District/Organization of Contributor(s): Brevard
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
page 3 of 4 Name
Description
Understand a fraction as a number on the number line; represent fractions on a number line diagram.
a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning
it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the
number 1/b on the number line.
b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the
resulting interval has size a/b and that its endpoint locates the number a/b on the number line.
Remarks/Examples:
Example of Opportunities for In-Depth Focus
MAFS.3.NF.1.2:
Developing an understanding of fractions as numbers is essential for future work with the number system. It is
critical that students at this grade are able to place fractions on a number line diagram and understand them as a
related component of their ever- expanding number system.
Fluency Expectations or Examples of Culminating Standards
Students fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of
operations, and/or the relationship between addition and subtraction. 3.NBT.1.2 a relatively small and incremental
expectation.
page 4 of 4